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Methodology

Research Methods | Definitions, Types, Examples

Research methods are specific procedures for collecting and analyzing data. Developing your research methods is an integral part of your research design . When planning your methods, there are two key decisions you will make.

First, decide how you will collect data . Your methods depend on what type of data you need to answer your research question :

Qualitative vs. quantitative : Will your data take the form of words or numbers?
Primary vs. secondary : Will you collect original data yourself, or will you use data that has already been collected by someone else?
Descriptive vs. experimental : Will you take measurements of something as it is, or will you perform an experiment?

Second, decide how you will analyze the data .

For quantitative data, you can use statistical analysis methods to test relationships between variables.
For qualitative data, you can use methods such as thematic analysis to interpret patterns and meanings in the data.

Methods for collecting data, examples of data collection methods, methods for analyzing data, examples of data analysis methods, other interesting articles, frequently asked questions about research methods.

Data is the information that you collect for the purposes of answering your research question . The type of data you need depends on the aims of your research.

Qualitative vs. quantitative data

Your choice of qualitative or quantitative data collection depends on the type of knowledge you want to develop.

For questions about ideas, experiences and meanings, or to study something that can’t be described numerically, collect qualitative data .

If you want to develop a more mechanistic understanding of a topic, or your research involves hypothesis testing , collect quantitative data .


Qualitative		to broader populations. .
Quantitative		.

You can also take a mixed methods approach , where you use both qualitative and quantitative research methods.

Primary vs. secondary research

Primary research is any original data that you collect yourself for the purposes of answering your research question (e.g. through surveys , observations and experiments ). Secondary research is data that has already been collected by other researchers (e.g. in a government census or previous scientific studies).

If you are exploring a novel research question, you’ll probably need to collect primary data . But if you want to synthesize existing knowledge, analyze historical trends, or identify patterns on a large scale, secondary data might be a better choice.


Primary	.	methods.
Secondary

Descriptive vs. experimental data

In descriptive research , you collect data about your study subject without intervening. The validity of your research will depend on your sampling method .

In experimental research , you systematically intervene in a process and measure the outcome. The validity of your research will depend on your experimental design .

To conduct an experiment, you need to be able to vary your independent variable , precisely measure your dependent variable, and control for confounding variables . If it’s practically and ethically possible, this method is the best choice for answering questions about cause and effect.


Descriptive		. .
Experimental

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Research methods for collecting data
Research method	Primary or secondary?	Qualitative or quantitative?	When to use
	Primary	Quantitative	To test cause-and-effect relationships.
	Primary	Quantitative	To understand general characteristics of a population.
Interview/focus group	Primary	Qualitative	To gain more in-depth understanding of a topic.
Observation	Primary	Either	To understand how something occurs in its natural setting.
	Secondary	Either	To situate your research in an existing body of work, or to evaluate trends within a research topic.
	Either	Either	To gain an in-depth understanding of a specific group or context, or when you don’t have the resources for a large study.

Your data analysis methods will depend on the type of data you collect and how you prepare it for analysis.

Data can often be analyzed both quantitatively and qualitatively. For example, survey responses could be analyzed qualitatively by studying the meanings of responses or quantitatively by studying the frequencies of responses.

Qualitative analysis methods

Qualitative analysis is used to understand words, ideas, and experiences. You can use it to interpret data that was collected:

From open-ended surveys and interviews , literature reviews , case studies , ethnographies , and other sources that use text rather than numbers.
Using non-probability sampling methods .

Qualitative analysis tends to be quite flexible and relies on the researcher’s judgement, so you have to reflect carefully on your choices and assumptions and be careful to avoid research bias .

Quantitative analysis methods

Quantitative analysis uses numbers and statistics to understand frequencies, averages and correlations (in descriptive studies) or cause-and-effect relationships (in experiments).

You can use quantitative analysis to interpret data that was collected either:

During an experiment .
Using probability sampling methods .

Because the data is collected and analyzed in a statistically valid way, the results of quantitative analysis can be easily standardized and shared among researchers.

Research methods for analyzing data
Research method	Qualitative or quantitative?	When to use
	Quantitative	To analyze data collected in a statistically valid manner (e.g. from experiments, surveys, and observations).
Meta-analysis	Quantitative	To statistically analyze the results of a large collection of studies. Can only be applied to studies that collected data in a statistically valid manner.
	Qualitative	To analyze data collected from interviews, , or textual sources. To understand general themes in the data and how they are communicated.
	Either	To analyze large volumes of textual or visual data collected from surveys, literature reviews, or other sources. Can be quantitative (i.e. frequencies of words) or qualitative (i.e. meanings of words).

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If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

Chi square test of independence
Statistical power
Descriptive statistics
Degrees of freedom
Pearson correlation
Null hypothesis
Double-blind study
Case-control study
Research ethics
Data collection
Hypothesis testing
Structured interviews

Research bias

Hawthorne effect
Unconscious bias
Recall bias
Halo effect
Self-serving bias
Information bias

Quantitative research deals with numbers and statistics, while qualitative research deals with words and meanings.

Quantitative methods allow you to systematically measure variables and test hypotheses . Qualitative methods allow you to explore concepts and experiences in more detail.

In mixed methods research , you use both qualitative and quantitative data collection and analysis methods to answer your research question .

A sample is a subset of individuals from a larger population . Sampling means selecting the group that you will actually collect data from in your research. For example, if you are researching the opinions of students in your university, you could survey a sample of 100 students.

In statistics, sampling allows you to test a hypothesis about the characteristics of a population.

The research methods you use depend on the type of data you need to answer your research question .

If you want to measure something or test a hypothesis , use quantitative methods . If you want to explore ideas, thoughts and meanings, use qualitative methods .
If you want to analyze a large amount of readily-available data, use secondary data. If you want data specific to your purposes with control over how it is generated, collect primary data.
If you want to establish cause-and-effect relationships between variables , use experimental methods. If you want to understand the characteristics of a research subject, use descriptive methods.

Methodology refers to the overarching strategy and rationale of your research project . It involves studying the methods used in your field and the theories or principles behind them, in order to develop an approach that matches your objectives.

Methods are the specific tools and procedures you use to collect and analyze data (for example, experiments, surveys , and statistical tests ).

In shorter scientific papers, where the aim is to report the findings of a specific study, you might simply describe what you did in a methods section .

In a longer or more complex research project, such as a thesis or dissertation , you will probably include a methodology section , where you explain your approach to answering the research questions and cite relevant sources to support your choice of methods.

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Indian J Anaesth
v.60(9); 2016 Sep

Basic statistical tools in research and data analysis

Zulfiqar ali.

Department of Anaesthesiology, Division of Neuroanaesthesiology, Sheri Kashmir Institute of Medical Sciences, Soura, Srinagar, Jammu and Kashmir, India

S Bala Bhaskar

1 Department of Anaesthesiology and Critical Care, Vijayanagar Institute of Medical Sciences, Bellary, Karnataka, India

Statistical methods involved in carrying out a study include planning, designing, collecting data, analysing, drawing meaningful interpretation and reporting of the research findings. The statistical analysis gives meaning to the meaningless numbers, thereby breathing life into a lifeless data. The results and inferences are precise only if proper statistical tests are used. This article will try to acquaint the reader with the basic research tools that are utilised while conducting various studies. The article covers a brief outline of the variables, an understanding of quantitative and qualitative variables and the measures of central tendency. An idea of the sample size estimation, power analysis and the statistical errors is given. Finally, there is a summary of parametric and non-parametric tests used for data analysis.

INTRODUCTION

Statistics is a branch of science that deals with the collection, organisation, analysis of data and drawing of inferences from the samples to the whole population.[ 1 ] This requires a proper design of the study, an appropriate selection of the study sample and choice of a suitable statistical test. An adequate knowledge of statistics is necessary for proper designing of an epidemiological study or a clinical trial. Improper statistical methods may result in erroneous conclusions which may lead to unethical practice.[ 2 ]

Variable is a characteristic that varies from one individual member of population to another individual.[ 3 ] Variables such as height and weight are measured by some type of scale, convey quantitative information and are called as quantitative variables. Sex and eye colour give qualitative information and are called as qualitative variables[ 3 ] [ Figure 1 ].

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Classification of variables

Quantitative variables

Quantitative or numerical data are subdivided into discrete and continuous measurements. Discrete numerical data are recorded as a whole number such as 0, 1, 2, 3,… (integer), whereas continuous data can assume any value. Observations that can be counted constitute the discrete data and observations that can be measured constitute the continuous data. Examples of discrete data are number of episodes of respiratory arrests or the number of re-intubations in an intensive care unit. Similarly, examples of continuous data are the serial serum glucose levels, partial pressure of oxygen in arterial blood and the oesophageal temperature.

A hierarchical scale of increasing precision can be used for observing and recording the data which is based on categorical, ordinal, interval and ratio scales [ Figure 1 ].

Categorical or nominal variables are unordered. The data are merely classified into categories and cannot be arranged in any particular order. If only two categories exist (as in gender male and female), it is called as a dichotomous (or binary) data. The various causes of re-intubation in an intensive care unit due to upper airway obstruction, impaired clearance of secretions, hypoxemia, hypercapnia, pulmonary oedema and neurological impairment are examples of categorical variables.

Ordinal variables have a clear ordering between the variables. However, the ordered data may not have equal intervals. Examples are the American Society of Anesthesiologists status or Richmond agitation-sedation scale.

Interval variables are similar to an ordinal variable, except that the intervals between the values of the interval variable are equally spaced. A good example of an interval scale is the Fahrenheit degree scale used to measure temperature. With the Fahrenheit scale, the difference between 70° and 75° is equal to the difference between 80° and 85°: The units of measurement are equal throughout the full range of the scale.

Ratio scales are similar to interval scales, in that equal differences between scale values have equal quantitative meaning. However, ratio scales also have a true zero point, which gives them an additional property. For example, the system of centimetres is an example of a ratio scale. There is a true zero point and the value of 0 cm means a complete absence of length. The thyromental distance of 6 cm in an adult may be twice that of a child in whom it may be 3 cm.

STATISTICS: DESCRIPTIVE AND INFERENTIAL STATISTICS

Descriptive statistics[ 4 ] try to describe the relationship between variables in a sample or population. Descriptive statistics provide a summary of data in the form of mean, median and mode. Inferential statistics[ 4 ] use a random sample of data taken from a population to describe and make inferences about the whole population. It is valuable when it is not possible to examine each member of an entire population. The examples if descriptive and inferential statistics are illustrated in Table 1 .

Example of descriptive and inferential statistics

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Descriptive statistics

The extent to which the observations cluster around a central location is described by the central tendency and the spread towards the extremes is described by the degree of dispersion.

Measures of central tendency

The measures of central tendency are mean, median and mode.[ 6 ] Mean (or the arithmetic average) is the sum of all the scores divided by the number of scores. Mean may be influenced profoundly by the extreme variables. For example, the average stay of organophosphorus poisoning patients in ICU may be influenced by a single patient who stays in ICU for around 5 months because of septicaemia. The extreme values are called outliers. The formula for the mean is

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where x = each observation and n = number of observations. Median[ 6 ] is defined as the middle of a distribution in a ranked data (with half of the variables in the sample above and half below the median value) while mode is the most frequently occurring variable in a distribution. Range defines the spread, or variability, of a sample.[ 7 ] It is described by the minimum and maximum values of the variables. If we rank the data and after ranking, group the observations into percentiles, we can get better information of the pattern of spread of the variables. In percentiles, we rank the observations into 100 equal parts. We can then describe 25%, 50%, 75% or any other percentile amount. The median is the 50 th percentile. The interquartile range will be the observations in the middle 50% of the observations about the median (25 th -75 th percentile). Variance[ 7 ] is a measure of how spread out is the distribution. It gives an indication of how close an individual observation clusters about the mean value. The variance of a population is defined by the following formula:

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where σ 2 is the population variance, X is the population mean, X i is the i th element from the population and N is the number of elements in the population. The variance of a sample is defined by slightly different formula:

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where s 2 is the sample variance, x is the sample mean, x i is the i th element from the sample and n is the number of elements in the sample. The formula for the variance of a population has the value ‘ n ’ as the denominator. The expression ‘ n −1’ is known as the degrees of freedom and is one less than the number of parameters. Each observation is free to vary, except the last one which must be a defined value. The variance is measured in squared units. To make the interpretation of the data simple and to retain the basic unit of observation, the square root of variance is used. The square root of the variance is the standard deviation (SD).[ 8 ] The SD of a population is defined by the following formula:

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where σ is the population SD, X is the population mean, X i is the i th element from the population and N is the number of elements in the population. The SD of a sample is defined by slightly different formula:

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where s is the sample SD, x is the sample mean, x i is the i th element from the sample and n is the number of elements in the sample. An example for calculation of variation and SD is illustrated in Table 2 .

Example of mean, variance, standard deviation

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Normal distribution or Gaussian distribution

Most of the biological variables usually cluster around a central value, with symmetrical positive and negative deviations about this point.[ 1 ] The standard normal distribution curve is a symmetrical bell-shaped. In a normal distribution curve, about 68% of the scores are within 1 SD of the mean. Around 95% of the scores are within 2 SDs of the mean and 99% within 3 SDs of the mean [ Figure 2 ].

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Normal distribution curve

Skewed distribution

It is a distribution with an asymmetry of the variables about its mean. In a negatively skewed distribution [ Figure 3 ], the mass of the distribution is concentrated on the right of Figure 1 . In a positively skewed distribution [ Figure 3 ], the mass of the distribution is concentrated on the left of the figure leading to a longer right tail.

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Curves showing negatively skewed and positively skewed distribution

Inferential statistics

In inferential statistics, data are analysed from a sample to make inferences in the larger collection of the population. The purpose is to answer or test the hypotheses. A hypothesis (plural hypotheses) is a proposed explanation for a phenomenon. Hypothesis tests are thus procedures for making rational decisions about the reality of observed effects.

Probability is the measure of the likelihood that an event will occur. Probability is quantified as a number between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty).

In inferential statistics, the term ‘null hypothesis’ ( H 0 ‘ H-naught ,’ ‘ H-null ’) denotes that there is no relationship (difference) between the population variables in question.[ 9 ]

Alternative hypothesis ( H 1 and H a ) denotes that a statement between the variables is expected to be true.[ 9 ]

The P value (or the calculated probability) is the probability of the event occurring by chance if the null hypothesis is true. The P value is a numerical between 0 and 1 and is interpreted by researchers in deciding whether to reject or retain the null hypothesis [ Table 3 ].

P values with interpretation

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If P value is less than the arbitrarily chosen value (known as α or the significance level), the null hypothesis (H0) is rejected [ Table 4 ]. However, if null hypotheses (H0) is incorrectly rejected, this is known as a Type I error.[ 11 ] Further details regarding alpha error, beta error and sample size calculation and factors influencing them are dealt with in another section of this issue by Das S et al .[ 12 ]

Illustration for null hypothesis

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PARAMETRIC AND NON-PARAMETRIC TESTS

Numerical data (quantitative variables) that are normally distributed are analysed with parametric tests.[ 13 ]

Two most basic prerequisites for parametric statistical analysis are:

The assumption of normality which specifies that the means of the sample group are normally distributed
The assumption of equal variance which specifies that the variances of the samples and of their corresponding population are equal.

However, if the distribution of the sample is skewed towards one side or the distribution is unknown due to the small sample size, non-parametric[ 14 ] statistical techniques are used. Non-parametric tests are used to analyse ordinal and categorical data.

Parametric tests

The parametric tests assume that the data are on a quantitative (numerical) scale, with a normal distribution of the underlying population. The samples have the same variance (homogeneity of variances). The samples are randomly drawn from the population, and the observations within a group are independent of each other. The commonly used parametric tests are the Student's t -test, analysis of variance (ANOVA) and repeated measures ANOVA.

Student's t -test

Student's t -test is used to test the null hypothesis that there is no difference between the means of the two groups. It is used in three circumstances:

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where X = sample mean, u = population mean and SE = standard error of mean

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where X 1 − X 2 is the difference between the means of the two groups and SE denotes the standard error of the difference.

To test if the population means estimated by two dependent samples differ significantly (the paired t -test). A usual setting for paired t -test is when measurements are made on the same subjects before and after a treatment.

The formula for paired t -test is:

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where d is the mean difference and SE denotes the standard error of this difference.

The group variances can be compared using the F -test. The F -test is the ratio of variances (var l/var 2). If F differs significantly from 1.0, then it is concluded that the group variances differ significantly.

Analysis of variance

The Student's t -test cannot be used for comparison of three or more groups. The purpose of ANOVA is to test if there is any significant difference between the means of two or more groups.

In ANOVA, we study two variances – (a) between-group variability and (b) within-group variability. The within-group variability (error variance) is the variation that cannot be accounted for in the study design. It is based on random differences present in our samples.

However, the between-group (or effect variance) is the result of our treatment. These two estimates of variances are compared using the F-test.

A simplified formula for the F statistic is:

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where MS b is the mean squares between the groups and MS w is the mean squares within groups.

Repeated measures analysis of variance

As with ANOVA, repeated measures ANOVA analyses the equality of means of three or more groups. However, a repeated measure ANOVA is used when all variables of a sample are measured under different conditions or at different points in time.

As the variables are measured from a sample at different points of time, the measurement of the dependent variable is repeated. Using a standard ANOVA in this case is not appropriate because it fails to model the correlation between the repeated measures: The data violate the ANOVA assumption of independence. Hence, in the measurement of repeated dependent variables, repeated measures ANOVA should be used.

Non-parametric tests

When the assumptions of normality are not met, and the sample means are not normally, distributed parametric tests can lead to erroneous results. Non-parametric tests (distribution-free test) are used in such situation as they do not require the normality assumption.[ 15 ] Non-parametric tests may fail to detect a significant difference when compared with a parametric test. That is, they usually have less power.

As is done for the parametric tests, the test statistic is compared with known values for the sampling distribution of that statistic and the null hypothesis is accepted or rejected. The types of non-parametric analysis techniques and the corresponding parametric analysis techniques are delineated in Table 5 .

Analogue of parametric and non-parametric tests

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Median test for one sample: The sign test and Wilcoxon's signed rank test

The sign test and Wilcoxon's signed rank test are used for median tests of one sample. These tests examine whether one instance of sample data is greater or smaller than the median reference value.

This test examines the hypothesis about the median θ0 of a population. It tests the null hypothesis H0 = θ0. When the observed value (Xi) is greater than the reference value (θ0), it is marked as+. If the observed value is smaller than the reference value, it is marked as − sign. If the observed value is equal to the reference value (θ0), it is eliminated from the sample.

If the null hypothesis is true, there will be an equal number of + signs and − signs.

The sign test ignores the actual values of the data and only uses + or − signs. Therefore, it is useful when it is difficult to measure the values.

Wilcoxon's signed rank test

There is a major limitation of sign test as we lose the quantitative information of the given data and merely use the + or – signs. Wilcoxon's signed rank test not only examines the observed values in comparison with θ0 but also takes into consideration the relative sizes, adding more statistical power to the test. As in the sign test, if there is an observed value that is equal to the reference value θ0, this observed value is eliminated from the sample.

Wilcoxon's rank sum test ranks all data points in order, calculates the rank sum of each sample and compares the difference in the rank sums.

Mann-Whitney test

It is used to test the null hypothesis that two samples have the same median or, alternatively, whether observations in one sample tend to be larger than observations in the other.

Mann–Whitney test compares all data (xi) belonging to the X group and all data (yi) belonging to the Y group and calculates the probability of xi being greater than yi: P (xi > yi). The null hypothesis states that P (xi > yi) = P (xi < yi) =1/2 while the alternative hypothesis states that P (xi > yi) ≠1/2.

Kolmogorov-Smirnov test

The two-sample Kolmogorov-Smirnov (KS) test was designed as a generic method to test whether two random samples are drawn from the same distribution. The null hypothesis of the KS test is that both distributions are identical. The statistic of the KS test is a distance between the two empirical distributions, computed as the maximum absolute difference between their cumulative curves.

Kruskal-Wallis test

The Kruskal–Wallis test is a non-parametric test to analyse the variance.[ 14 ] It analyses if there is any difference in the median values of three or more independent samples. The data values are ranked in an increasing order, and the rank sums calculated followed by calculation of the test statistic.

Jonckheere test

In contrast to Kruskal–Wallis test, in Jonckheere test, there is an a priori ordering that gives it a more statistical power than the Kruskal–Wallis test.[ 14 ]

Friedman test

The Friedman test is a non-parametric test for testing the difference between several related samples. The Friedman test is an alternative for repeated measures ANOVAs which is used when the same parameter has been measured under different conditions on the same subjects.[ 13 ]

Tests to analyse the categorical data

Chi-square test, Fischer's exact test and McNemar's test are used to analyse the categorical or nominal variables. The Chi-square test compares the frequencies and tests whether the observed data differ significantly from that of the expected data if there were no differences between groups (i.e., the null hypothesis). It is calculated by the sum of the squared difference between observed ( O ) and the expected ( E ) data (or the deviation, d ) divided by the expected data by the following formula:

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A Yates correction factor is used when the sample size is small. Fischer's exact test is used to determine if there are non-random associations between two categorical variables. It does not assume random sampling, and instead of referring a calculated statistic to a sampling distribution, it calculates an exact probability. McNemar's test is used for paired nominal data. It is applied to 2 × 2 table with paired-dependent samples. It is used to determine whether the row and column frequencies are equal (that is, whether there is ‘marginal homogeneity’). The null hypothesis is that the paired proportions are equal. The Mantel-Haenszel Chi-square test is a multivariate test as it analyses multiple grouping variables. It stratifies according to the nominated confounding variables and identifies any that affects the primary outcome variable. If the outcome variable is dichotomous, then logistic regression is used.

SOFTWARES AVAILABLE FOR STATISTICS, SAMPLE SIZE CALCULATION AND POWER ANALYSIS

Numerous statistical software systems are available currently. The commonly used software systems are Statistical Package for the Social Sciences (SPSS – manufactured by IBM corporation), Statistical Analysis System ((SAS – developed by SAS Institute North Carolina, United States of America), R (designed by Ross Ihaka and Robert Gentleman from R core team), Minitab (developed by Minitab Inc), Stata (developed by StataCorp) and the MS Excel (developed by Microsoft).

There are a number of web resources which are related to statistical power analyses. A few are:

StatPages.net – provides links to a number of online power calculators
G-Power – provides a downloadable power analysis program that runs under DOS
Power analysis for ANOVA designs an interactive site that calculates power or sample size needed to attain a given power for one effect in a factorial ANOVA design
SPSS makes a program called SamplePower. It gives an output of a complete report on the computer screen which can be cut and paste into another document.

It is important that a researcher knows the concepts of the basic statistical methods used for conduct of a research study. This will help to conduct an appropriately well-designed study leading to valid and reliable results. Inappropriate use of statistical techniques may lead to faulty conclusions, inducing errors and undermining the significance of the article. Bad statistics may lead to bad research, and bad research may lead to unethical practice. Hence, an adequate knowledge of statistics and the appropriate use of statistical tests are important. An appropriate knowledge about the basic statistical methods will go a long way in improving the research designs and producing quality medical research which can be utilised for formulating the evidence-based guidelines.

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Statistical Methods for Data Analysis: a Comprehensive Guide

In today’s data-driven world, understanding statistical methods for data analysis is like having a superpower.

Whether you’re a student, a professional, or just a curious mind, diving into the realm of data can unlock insights and decisions that propel success.

Statistical methods for data analysis are the tools and techniques used to collect, analyze, interpret, and present data in a meaningful way.

From businesses optimizing operations to researchers uncovering new discoveries, these methods are foundational to making informed decisions based on data.

In this blog post, we’ll embark on a journey through the fascinating world of statistical analysis, exploring its key concepts, methodologies, and applications.

Introduction to Statistical Methods

At its core, statistical methods are the backbone of data analysis, helping us make sense of numbers and patterns in the world around us.

Whether you’re looking at sales figures, medical research, or even your fitness tracker’s data, statistical methods are what turn raw data into useful insights.

But before we dive into complex formulas and tests, let’s start with the basics.

Data comes in two main types: qualitative and quantitative data .

Qualitative vs Quantitative Data - a simple infographic

Quantitative data is all about numbers and quantities (like your height or the number of steps you walked today), while qualitative data deals with categories and qualities (like your favorite color or the breed of your dog).

And when we talk about measuring these data points, we use different scales like nominal, ordinal , interval , and ratio.

These scales help us understand the nature of our data—whether we’re ranking it (ordinal), simply categorizing it (nominal), or measuring it with a true zero point (ratio).

Scales of Data Measurement - an infographic

In a nutshell, statistical methods start with understanding the type and scale of your data.

This foundational knowledge sets the stage for everything from summarizing your data to making complex predictions.

Descriptive Statistics: Simplifying Data

What is Descriptive Statistics - an infographic

Imagine you’re at a party and you meet a bunch of new people.

When you go home, your roommate asks, “So, what were they like?” You could describe each person in detail, but instead, you give a summary: “Most were college students, around 20-25 years old, pretty fun crowd!”

That’s essentially what descriptive statistics does for data.

It summarizes and describes the main features of a collection of data in an easy-to-understand way. Let’s break this down further.

The Basics: Mean, Median, and Mode

Mean is just a fancy term for the average. If you add up everyone’s age at the party and divide by the number of people, you’ve got your mean age.
Median is the middle number in a sorted list. If you line up everyone from the youngest to the oldest and pick the person in the middle, their age is your median. This is super handy when someone’s age is way off the chart (like if your grandma crashed the party), as it doesn’t skew the data.
Mode is the most common age at the party. If you notice a lot of people are 22, then 22 is your mode. It’s like the age that wins the popularity contest.

Spreading the News: Range, Variance, and Standard Deviation

Range gives you an idea of how spread out the ages are. It’s the difference between the oldest and the youngest. A small range means everyone’s around the same age, while a big range means a wider variety.
Variance is a bit more complex. It measures how much the ages differ from the average age. A higher variance means ages are more spread out.
Standard Deviation is the square root of variance. It’s like variance but back on a scale that makes sense. It tells you, on average, how far each person’s age is from the mean age.

Picture Perfect: Graphical Representations

Histograms are like bar charts showing how many people fall into different age groups. They give you a quick glance at how ages are distributed.
Bar Charts are great for comparing different categories, like how many men vs. women were at the party.
Box Plots (or box-and-whisker plots) show you the median, the range, and if there are any outliers (like grandma).
Scatter Plots are used when you want to see if there’s a relationship between two things, like if bringing more snacks means people stay longer at the party.

Why Descriptive Statistics Matter?

Descriptive statistics are your first step in data analysis.

They help you understand your data at a glance and prepare you for deeper analysis.

Without them, you’re like someone trying to guess what a party was like without any context.

Whether you’re looking at survey responses, test scores, or party attendees, descriptive statistics give you the tools to summarize and describe your data in a way that’s easy to grasp.

This approach is crucial in educational settings, particularly for enhancing math learning outcomes. For those looking to deepen their understanding of math or seeking additional support, check out this link: https://www.mathnasium.com/ math-tutors-near-me .

Remember, the goal of descriptive statistics is to simplify the complex.

Inferential Statistics: Beyond the Basics

Let’s keep the party analogy rolling, but this time, imagine you couldn’t attend the party yourself.

You’re curious if the party was as fun as everyone said it would be.

Instead of asking every single attendee, you decide to ask a few friends who went.

Based on their experiences, you try to infer what the entire party was like.

This is essentially what inferential statistics does with data.

It allows you to make predictions or draw conclusions about a larger group (the population) based on a smaller group (a sample). Let’s dive into how this works.

Probability

Inferential statistics is all about playing the odds.

When you make an inference, you’re saying, “Based on my sample, there’s a certain probability that my conclusion about the whole population is correct.”

It’s like betting on whether the party was fun, based on a few friends’ opinions.

The Central Limit Theorem (CLT)

The Central Limit Theorem is the superhero of statistics.

It tells us that if you take enough samples from a population, the sample means (averages) will form a normal distribution (a bell curve), no matter what the population distribution looks like.

This is crucial because it allows us to use sample data to make inferences about the population mean with a known level of uncertainty.

Confidence Intervals

Imagine you’re pretty sure the party was fun, but you want to know how fun.

A confidence interval gives you a range of values within which you believe the true mean fun level of the party lies.

It’s like saying, “I’m 95% confident the party’s fun rating was between 7 and 9 out of 10.”

Hypothesis Testing

This is where you get to be a bit of a detective. You start with a hypothesis (a guess) about the population.

For example, your null hypothesis might be “the party was average fun.” Then you use your sample data to test this hypothesis.

If the data strongly suggests otherwise, you might reject the null hypothesis and accept the alternative hypothesis, which could be “the party was super fun.”

The p-value tells you how likely it is that your data would have occurred by random chance if the null hypothesis were true.

A low p-value (typically less than 0.05) indicates that your findings are significant—that is, unlikely to have happened by chance.

It’s like saying, “The chance that all my friends are exaggerating about the party being fun is really low, so the party probably was fun.”

Why Inferential Statistics Matter?

Inferential statistics let us go beyond just describing our data.

They allow us to make educated guesses about a larger population based on a sample.

This is incredibly useful in almost every field—science, business, public health, and yes, even planning your next party.

By using probability, the Central Limit Theorem, confidence intervals, hypothesis testing, and p-values, we can make informed decisions without needing to ask every single person in the population.

It saves time, resources, and helps us understand the world more scientifically.

Remember, while inferential statistics gives us powerful tools for making predictions, those predictions come with a level of uncertainty.

Being a good data scientist means understanding and communicating that uncertainty clearly.

So next time you hear about a party you missed, use inferential statistics to figure out just how much FOMO (fear of missing out) you should really feel!

Common Statistical Tests: Choosing Your Data’s Best Friend

Data Analysis Research and Statistics Concept

Alright, now that we’ve covered the basics of descriptive and inferential statistics, it’s time to talk about how we actually apply these concepts to make sense of data.

It’s like deciding on the best way to find out who was the life of the party.

You have several tools (tests) at your disposal, and choosing the right one depends on what you’re trying to find out and the type of data you have.

Let’s explore some of the most common statistical tests and when to use them.

T-Tests: Comparing Averages

Imagine you want to know if the average fun level was higher at this year’s party compared to last year’s.

A t-test helps you compare the means (averages) of two groups to see if they’re statistically different.

There are a couple of flavors:

Independent t-test : Use this when comparing two different groups, like this year’s party vs. last year’s party.
Paired t-test : Use this when comparing the same group at two different times or under two different conditions, like if you measured everyone’s fun level before and after the party.

ANOVA : When Three’s Not a Crowd.

But what if you had three or more parties to compare? That’s where ANOVA (Analysis of Variance) comes in handy.

It lets you compare the means across multiple groups at once to see if at least one of them is significantly different.

It’s like comparing the fun levels across several years’ parties to see if one year stood out.

Chi-Square Test: Categorically Speaking

Now, let’s say you’re interested in whether the type of music (pop, rock, electronic) affects party attendance.

Since you’re dealing with categories (types of music) and counts (number of attendees), you’ll use the Chi-Square test.

It’s great for seeing if there’s a relationship between two categorical variables.

Correlation and Regression: Finding Relationships

What if you suspect that the amount of snacks available at the party affects how long guests stay? To explore this, you’d use:

Correlation analysis to see if there’s a relationship between two continuous variables (like snacks and party duration). It tells you how closely related two things are.
Regression analysis goes a step further by not only showing if there’s a relationship but also how one variable predicts the other. It’s like saying, “For every extra bag of chips, guests stay an average of 10 minutes longer.”

Non-parametric Tests: When Assumptions Don’t Hold

All the tests mentioned above assume your data follows a normal distribution and meets other criteria.

But what if your data doesn’t play by these rules?

Enter non-parametric tests, like the Mann-Whitney U test (for comparing two groups when you can’t use a t-test) or the Kruskal-Wallis test (like ANOVA but for non-normal distributions).

Picking the Right Test

Choosing the right statistical test is crucial and depends on:

The type of data you have (categorical vs. continuous).
Whether you’re comparing groups or looking for relationships.
The distribution of your data (normal vs. non-normal).

Why These Tests Matter?

Just like you’d pick the right tool for a job, selecting the appropriate statistical test helps you make valid and reliable conclusions about your data.

Whether you’re trying to prove a point, make a decision, or just understand the world a bit better, these tests are your gateway to insights.

By mastering these tests, you become a detective in the world of data, ready to uncover the truth behind the numbers!

Regression Analysis: Predicting the Future

Ever wondered if you could predict how much fun you’re going to have at a party based on the number of friends going, or how the amount of snacks available might affect the overall party vibe?

That’s where regression analysis comes into play, acting like a crystal ball for your data.

What is Regression Analysis?

Regression analysis is a powerful statistical method that allows you to examine the relationship between two or more variables of interest.

Think of it as detective work, where you’re trying to figure out if, how, and to what extent certain factors (like snacks and music volume) predict an outcome (like the fun level at a party).

The Two Main Characters: Independent and Dependent Variables

Independent Variable(s): These are the predictors or factors that you suspect might influence the outcome. For example, the quantity of snacks.
Dependent Variable: This is the outcome you’re interested in predicting. In our case, it could be the fun level of the party.

Linear Regression: The Straight Line Relationship

The most basic form of regression analysis is linear regression .

It predicts the outcome based on a linear relationship between the independent and dependent variables.

If you plot this on a graph, you’d ideally see a straight line where, as the amount of snacks increases, so does the fun level (hopefully!).

Simple Linear Regression involves just one independent variable. It’s like saying, “Let’s see if just the number of snacks can predict the fun level.”
Multiple Linear Regression takes it up a notch by including more than one independent variable. Now, you’re looking at whether the quantity of snacks, type of music, and number of guests together can predict the fun level.

Logistic Regression: When Outcomes are Either/Or

Not all predictions are about numbers.

Sometimes, you just want to know if something will happen or not—will the party be a hit or a flop?

Logistic regression is used for these binary outcomes.

Instead of predicting a precise fun level, it predicts the probability of the party being a hit based on the same predictors (snacks, music, guests).

Making Sense of the Results

Coefficients: In regression analysis, each predictor has a coefficient, telling you how much the dependent variable is expected to change when that predictor changes by one unit, all else being equal.
R-squared : This value tells you how much of the variation in your dependent variable can be explained by the independent variables. A higher R-squared means a better fit between your model and the data.

Why Regression Analysis Rocks?

Regression analysis is like having a superpower. It helps you understand which factors matter most, which can be ignored, and how different factors come together to influence the outcome.

This insight is invaluable whether you’re planning a party, running a business, or conducting scientific research.

Bringing It All Together

Imagine you’ve gathered data on several parties, including the number of guests, type of music, and amount of snacks, along with a fun level rating for each.

By running a regression analysis, you can start to predict future parties’ success, tailoring your planning to maximize fun.

It’s a practical tool for making informed decisions based on past data, helping you throw legendary parties, optimize business strategies, or understand complex relationships in your research.

In essence, regression analysis helps turn your data into actionable insights, guiding you towards smarter decisions and better predictions.

So next time you’re knee-deep in data, remember: regression analysis might just be the key to unlocking its secrets.

Non-parametric Methods: Playing By Different Rules

So far, we’ve talked a lot about statistical methods that rely on certain assumptions about your data, like it being normally distributed (forming that classic bell curve) or having a specific scale of measurement.

But what happens when your data doesn’t fit these molds?

Maybe the scores from your last party’s karaoke contest are all over the place, or you’re trying to compare the popularity of various party games but only have rankings, not scores.

This is where non-parametric methods come to the rescue.

Breaking Free from Assumptions

Non-parametric methods are the rebels of the statistical world.

They don’t assume your data follows a normal distribution or that it meets strict requirements regarding measurement scales.

These methods are perfect for dealing with ordinal data (like rankings), nominal data (like categories), or when your data is skewed or has outliers that would throw off other tests.

When to Use Non-parametric Methods?

Your data is not normally distributed, and transformations don’t help.
You have ordinal data (like survey responses that range from “Strongly Disagree” to “Strongly Agree”).
You’re dealing with ranks or categories rather than precise measurements.
Your sample size is small, making it hard to meet the assumptions required for parametric tests.

Some Popular Non-parametric Tests

Mann-Whitney U Test: Think of it as the non-parametric counterpart to the independent samples t-test. Use this when you want to compare the differences between two independent groups on a ranking or ordinal scale.
Kruskal-Wallis Test: This is your go-to when you have three or more groups to compare, and it’s similar to an ANOVA but for ranked/ordinal data or when your data doesn’t meet ANOVA’s assumptions.
Spearman’s Rank Correlation: When you want to see if there’s a relationship between two sets of rankings, Spearman’s got your back. It’s like Pearson’s correlation for continuous data but designed for ranks.
Wilcoxon Signed-Rank Test: Use this for comparing two related samples when you can’t use the paired t-test, typically because the differences between pairs are not normally distributed.

The Beauty of Flexibility

The real charm of non-parametric methods is their flexibility.

They let you work with data that’s not textbook perfect, which is often the case in the real world.

Whether you’re analyzing customer satisfaction surveys, comparing the effectiveness of different marketing strategies, or just trying to figure out if people prefer pizza or tacos at parties, non-parametric tests provide a robust way to get meaningful insights.

Keeping It Real

It’s important to remember that while non-parametric methods are incredibly useful, they also come with their own limitations.

They might be more conservative, meaning you might need a larger effect to detect a significant result compared to parametric tests.

Plus, because they often work with ranks rather than actual values, some information about your data might get lost in translation.

Non-parametric methods are your statistical toolbox’s Swiss Army knife, ready to tackle data that doesn’t fit into the neat categories required by more traditional tests.

They remind us that in the world of data analysis, there’s more than one way to uncover insights and make informed decisions.

So, the next time you’re faced with skewed distributions or rankings instead of scores, remember that non-parametric methods have got you covered, offering a way to navigate the complexities of real-world data.

Data Cleaning and Preparation: The Unsung Heroes of Data Analysis

Before any party can start, there’s always a bit of housecleaning to do—sweeping the floors, arranging the furniture, and maybe even hiding those laundry piles you’ve been ignoring all week.

Similarly, in the world of data analysis, before we can dive into the fun stuff like statistical tests and predictive modeling, we need to roll up our sleeves and get our data nice and tidy.

This process of data cleaning and preparation might not be the most glamorous part of data science, but it’s absolutely critical.

Let’s break down what this involves and why it’s so important.

Why Clean and Prepare Data?

Imagine trying to analyze party RSVPs when half the responses are “yes,” a quarter are “Y,” and the rest are a creative mix of “yup,” “sure,” and “why not?”

Without standardization, it’s hard to get a clear picture of how many guests to expect.

The same goes for any data set. Cleaning ensures that your data is consistent, accurate, and ready for analysis.

Preparation involves transforming this clean data into a format that’s useful for your specific analysis needs.

The Steps to Sparkling Clean Data

Dealing with Missing Values: Sometimes, data is incomplete. Maybe a survey respondent skipped a question, or a sensor failed to record a reading. You’ll need to decide whether to fill in these gaps (imputation), ignore them, or drop the observations altogether.
Identifying and Handling Outliers: Outliers are data points that are significantly different from the rest. They might be errors, or they might be valuable insights. The challenge is determining which is which and deciding how to handle them—remove, adjust, or analyze separately.
Correcting Inconsistencies: This is like making sure all your RSVPs are in the same format. It could involve standardizing text entries, correcting typos, or converting all measurements to the same units.
Formatting Data: Your analysis might require data in a specific format. This could mean transforming data types (e.g., converting dates into a uniform format) or restructuring data tables to make them easier to work with.
Reducing Dimensionality: Sometimes, your data set might have more information than you actually need. Reducing dimensionality (through methods like Principal Component Analysis) can help simplify your data without losing valuable information.
Creating New Variables: You might need to derive new variables from your existing ones to better capture the relationships in your data. For example, turning raw survey responses into a numerical satisfaction score.

The Tools of the Trade

There are many tools available to help with data cleaning and preparation, ranging from spreadsheet software like Excel to programming languages like Python and R.

These tools offer functions and libraries specifically designed to make data cleaning as painless as possible.

Why It Matters

Skipping the data cleaning and preparation stage is like trying to cook without prepping your ingredients first.

Sure, you might end up with something edible, but it’s not going to be as good as it could have been.

Clean and well-prepared data leads to more accurate, reliable, and meaningful analysis results.

It’s the foundation upon which all good data analysis is built.

Data cleaning and preparation might not be the flashiest part of data science, but it’s where all successful data analysis projects begin.

By taking the time to thoroughly clean and prepare your data, you’re setting yourself up for clearer insights, better decisions, and, ultimately, more impactful outcomes.

Software Tools for Statistical Analysis: Your Digital Assistants

Diving into the world of data without the right tools can feel like trying to cook a gourmet meal without a kitchen.

Just as you need pots, pans, and a stove to create a culinary masterpiece, you need the right software tools to analyze data and uncover the insights hidden within.

These digital assistants range from user-friendly applications for beginners to powerful suites for the pros.

Let’s take a closer look at some of the most popular software tools for statistical analysis.

R and RStudio: The Dynamic Duo

R is like the Swiss Army knife of statistical analysis. It’s a programming language designed specifically for data analysis, graphics, and statistical modeling. Think of R as the kitchen where you’ll be cooking up your data analysis.
RStudio is an integrated development environment (IDE) for R. It’s like having the best kitchen setup with organized countertops (your coding space) and all your tools and ingredients within reach (packages and datasets).

Why They Rock:

R is incredibly powerful and can handle almost any data analysis task you throw at it, from the basics to the most advanced statistical models.

Plus, there’s a vast community of users, which means a wealth of tutorials, forums, and free packages to add on.

Python with pandas and scipy: The Versatile Virtuoso

Python is not just for programming; with the right libraries, it becomes an excellent tool for data analysis. It’s like a kitchen that’s not only great for baking but also equipped for gourmet cooking.
pandas is a library that provides easy-to-use data structures and data analysis tools for Python. Imagine it as your sous-chef, helping you to slice and dice data with ease.
scipy is another library used for scientific and technical computing. It’s like having a set of precision knives for the more intricate tasks.

Why They Rock: Python is known for its readability and simplicity, making it accessible for beginners. When combined with pandas and scipy, it becomes a powerhouse for data manipulation, analysis, and visualization.

SPSS: The Point-and-Click Professional

SPSS (Statistical Package for the Social Sciences) is a software package used for interactive, or batched, statistical analysis. Long produced by SPSS Inc., it was acquired by IBM in 2009.

Why It Rocks: SPSS is particularly user-friendly with its point-and-click interface, making it a favorite among non-programmers and researchers in the social sciences. It’s like having a kitchen gadget that does the job with the push of a button—no manual setup required.

SAS: The Corporate Chef

SAS (Statistical Analysis System) is a software suite developed for advanced analytics, multivariate analysis, business intelligence, data management, and predictive analytics.

Why It Rocks: SAS is a powerhouse in the corporate world, known for its stability, deep analytical capabilities, and support for large data sets. It’s like the industrial kitchen used by professional chefs to serve hundreds of guests.

Excel: The Accessible Apprentice

Excel might not be a specialized statistical software, but it’s widely accessible and capable of handling basic statistical analyses. Think of Excel as the microwave in your kitchen—it might not be fancy, but it gets the job done for quick and simple tasks.

Why It Rocks: Almost everyone has access to Excel and knows the basics, making it a great starting point for those new to data analysis. Plus, with add-ons like the Analysis ToolPak, Excel’s capabilities can be extended further into statistical territory.

Choosing Your Tool

Selecting the right software tool for statistical analysis is like choosing the right kitchen for your cooking style—it depends on your needs, expertise, and the complexity of your recipes (data).

Whether you’re a coding chef ready to tackle R or Python, or someone who prefers the straightforwardness of SPSS or Excel, there’s a tool out there that’s perfect for your data analysis kitchen.

Ethical Considerations

Digital Ethics and Privacy Abstract Concept

Embarking on a data analysis journey is like setting sail on the vast ocean of information.

Just as a captain needs a compass to navigate the seas safely and responsibly, a data analyst requires a strong sense of ethics to guide their exploration of data.

Ethical considerations in data analysis are the moral compass that ensures we respect privacy, consent, and integrity while uncovering the truths hidden within data. Let’s delve into why ethics are so crucial and what principles you should keep in mind.

Respect for Privacy

Imagine you’ve found a diary filled with personal secrets.

Reading it without permission would be a breach of privacy.

Similarly, when you’re handling data, especially personal or sensitive information, it’s essential to ensure that privacy is protected.

This means not only securing data against unauthorized access but also anonymizing data to prevent individuals from being identified.

Informed Consent

Before you can set sail, you need the ship owner’s permission.

In the world of data, this translates to informed consent. Participants should be fully aware of what their data will be used for and voluntarily agree to participate.

This is particularly important in research or when collecting data directly from individuals. It’s like asking for permission before you start the journey.

Data Integrity

Maintaining data integrity is like keeping the ship’s log accurate and unaltered during your voyage.

It involves ensuring the data is not corrupted or modified inappropriately and that any data analysis is conducted accurately and reliably.

Tampering with data or cherry-picking results to fit a narrative is not just unethical—it’s like falsifying the ship’s log, leading to mistrust and potentially dangerous outcomes.

Avoiding Bias

The sea is vast, and your compass must be calibrated correctly to avoid going off course. Similarly, avoiding bias in data analysis ensures your findings are valid and unbiased.

This means being aware of and actively addressing any personal, cultural, or statistical biases that might skew your analysis.

It’s about striving for objectivity and ensuring your journey is guided by truth, not preconceived notions.

Transparency and Accountability

A trustworthy captain is open about their navigational choices and ready to take responsibility for them.

In data analysis, this translates to transparency about your methods and accountability for your conclusions.

Sharing your methodologies, data sources, and any limitations of your analysis helps build trust and allows others to verify or challenge your findings.

Ethical Use of Findings

Finally, just as a captain must consider the impact of their journey on the wider world, you must consider how your data analysis will be used.

This means thinking about the potential consequences of your findings and striving to ensure they are used to benefit, not harm, society.

It’s about being mindful of the broader implications of your work and using data for good.

Navigating with a Moral Compass

In the realm of data analysis, ethical considerations form the moral compass that guides us through complex moral waters.

They ensure that our work respects individuals’ rights, contributes positively to society, and upholds the highest standards of integrity and professionalism.

Just as a captain navigates the seas with respect for the ocean and its dangers, a data analyst must navigate the world of data with a deep commitment to ethical principles.

This commitment ensures that the insights gained from data analysis serve to enlighten and improve, rather than exploit or harm.

Conclusion and Key Takeaways

And there you have it—a whirlwind tour through the fascinating landscape of statistical methods for data analysis.

From the grounding principles of descriptive and inferential statistics to the nuanced details of regression analysis and beyond, we’ve explored the tools and ethical considerations that guide us in turning raw data into meaningful insights.

The Takeaway

Think of data analysis as embarking on a grand adventure, one where numbers and facts are your map and compass.

Just as every explorer needs to understand the terrain, every aspiring data analyst must grasp these foundational concepts.

Whether it’s summarizing data sets with descriptive statistics, making predictions with inferential statistics, choosing the right statistical test, or navigating the ethical considerations that ensure our analyses benefit society, each aspect is a crucial step on your journey.

The Importance of Preparation

Remember, the key to a successful voyage is preparation.

Cleaning and preparing your data sets the stage for a smooth journey, while choosing the right software tools ensures you have the best equipment at your disposal.

And just as every responsible navigator respects the sea, every data analyst must navigate the ethical dimensions of their work with care and integrity.

Charting Your Course

As you embark on your own data analysis adventures, remember that the path you chart is unique to you.

Your questions will guide your journey, your curiosity will fuel your exploration, and the insights you gain will be your treasure.

The world of data is vast and full of mysteries waiting to be uncovered. With the tools and principles we’ve discussed, you’re well-equipped to start uncovering those mysteries, one data set at a time.

The Journey Ahead

The journey of statistical methods for data analysis is ongoing, and the landscape is ever-evolving.

As new methods emerge and our understanding deepens, there will always be new horizons to explore and new insights to discover.

But the fundamentals we’ve covered will remain your steadfast guide, helping you navigate the challenges and opportunities that lie ahead.

So set your sights on the questions that spark your curiosity, arm yourself with the tools of the trade, and embark on your data analysis journey with confidence.

About The Author

Silvia Valcheva

Silvia Valcheva is a digital marketer with over a decade of experience creating content for the tech industry. She has a strong passion for writing about emerging software and technologies such as big data, AI (Artificial Intelligence), IoT (Internet of Things), process automation, etc.

Statistics for Research Students

(2 reviews)

Erich C Fein, Toowoomba, Australia

John Gilmour, Toowoomba, Australia

Tayna Machin, Toowoomba, Australia

Liam Hendry, Toowoomba, Australia

ISBN 13: 9780645326109

Publisher: University of Southern Queensland

Language: English

Formats Available

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Reviewed by Sojib Bin Zaman, Assistant Professor, James Madison University on 3/18/24

From exploring data in Chapter One to learning advanced methodologies such as moderation and mediation in Chapter Seven, the reader is guided through the entire process of statistical methodology. With each chapter covering a different statistical... read more

Comprehensiveness rating: 5 see less

Content Accuracy rating: 5

During my review of the textbook, I did not find any notable errors or omissions. In my opinion, the material was comprehensive, resulting in an enjoyable learning experience.

Relevance/Longevity rating: 5

A majority of the textbook's content is aligned with current trends, advancements, and enduring principles in the field of statistics. Several emerging methodologies and technologies are incorporated into this textbook to enhance students' statistical knowledge. It will be a valuable resource in the long run if students and researchers can properly utilize this textbook.

Clarity rating: 5

A clear explanation of complex statistical concepts such as moderation and mediation is provided in the writing style. Examples and problem sets are provided in the textbook in a comprehensive and well-explained manner.

Consistency rating: 5

Each chapter maintains consistent formatting and language, with resources organized consistently. Headings and subheadings worked well.

Modularity rating: 5

The textbook is well-structured, featuring cohesive chapters that flow smoothly from one to another. It is carefully crafted with a focus on defining terms clearly, facilitating understanding, and ensuring logical flow.

Organization/Structure/Flow rating: 5

From basic to advanced concepts, this book provides clarity of progression, logical arranging of sections and chapters, and effective headings and subheadings that guide readers. Further, the organization provides students with a lot of information on complex statistical methodologies.

Interface rating: 5

The available formats included PDFs, online access, and e-books. The e-book interface was particularly appealing to me, as it provided seamless navigation and viewing of content without compromising usability.

Grammatical Errors rating: 5

I found no significant errors in this document, and the overall quality of the writing was commendable. There was a high level of clarity and coherence in the text, which contributed to a positive reading experience.

Cultural Relevance rating: 5

The content of the book, as well as its accompanying examples, demonstrates a dedication to inclusivity by taking into account cultural diversity and a variety of perspectives. Furthermore, the material actively promotes cultural diversity, which enables readers to develop a deeper understanding of various cultural contexts and experiences.

In summary, this textbook provides a comprehensive resource tailored for advanced statistics courses, characterized by meticulous organization and practical supplementary materials. This book also provides valuable insights into the interpretation of computer output that enhance a greater understanding of each concept presented.

Reviewed by Zhuanzhuan Ma, Assistant Professor, University of Texas Rio Grande Valley on 3/7/24

The textbook covers all necessary areas and topics for students who want to conduct research in statistics. It includes foundational concepts, application methods, and advanced statistical techniques relevant to research methodologies. read more

The textbook presents statistical methods and data accurately, with up-to-date statistical practices and examples.

Relevance/Longevity rating: 4

The textbook's content is relevant to current research practices. The book includes contemporary examples and case studies that are currently prevalent in research communities. One small drawback is that the textbook did not include the example code for conduct data analysis.

The textbook break down complex statistical methods into understandable segments. All the concepts are clearly explained. Authors used diagrams, examples, and all kinds of explanations to facilitate learning for students with varying levels of background knowledge.

The terminology, framework, and presentation style (e.g. concepts, methodologies, and examples) seem consistent throughout the book.

The textbook is well organized that each chapter and section can be used independently without losing the context necessary for understanding. Also, the modular structure allows instructors and students to adapt the materials for different study plans.

The textbook is well-organized and progresses from basic concepts to more complex methods, making it easier for students to follow along. There is a logical flow of the content.

The digital format of the textbook has an interface that includes the design, layout, and navigational features. It is easier to use for readers.

The quality of writing is very high. The well-written texts help both instructors and students to follow the ideas clearly.

The textbook does not perpetuate stereotypes or biases and are inclusive in their examples, language, and perspectives.

Acknowledgement of Country
Accessibility Information
About the Authors
Introduction
I. Chapter One - Exploring Your Data
II. Chapter Two - Test Statistics, p Values, Confidence Intervals and Effect Sizes
III. Chapter Three- Comparing Two Group Means
IV. Chapter Four - Comparing Associations Between Two Variables
V. Chapter Five- Comparing Associations Between Multiple Variables
VI. Chapter Six- Comparing Three or More Group Means
VII. Chapter Seven- Moderation and Mediation Analyses
VIII. Chapter Eight- Factor Analysis and Scale Reliability
IX. Chapter Nine- Nonparametric Statistics

Ancillary Material

About the book.

This book aims to help you understand and navigate statistical concepts and the main types of statistical analyses essential for research students.

About the Contributors

Dr Erich C. Fein is an Associate Professor at the University of Southern Queensland. He received substantial training in research methods and statistics during his PhD program at Ohio State University. He currently teaches four courses in research methods and statistics. His research involves leadership, occupational health, and motivation, as well as issues related to research methods such as the following article: “ Safeguarding Access and Safeguarding Meaning as Strategies for Achieving Confidentiality .” Click here to link to his Google Scholar profile.

Dr John Gilmour is a Lecturer at the University of Southern Queensland and a Postdoctoral Research Fellow at the University of Queensland, His research focuses on the locational and temporal analyses of crime, and the evaluation of police training and procedures. John has worked across many different sectors including PTSD, social media, criminology, and medicine.

Dr Tanya Machin is a Senior Lecturer and Associate Dean at the University of Southern Queensland. Her research focuses on social media and technology across the lifespan. Tanya has co-taught Honours research methods with Erich, and is also interested in ethics and qualitative research methods. Tanya has worked across many different sectors including primary schools, financial services, and mental health.

Dr Liam Hendry is a Lecturer at the University of Southern Queensland. His research interests focus on long-term and short-term memory, measurement of human memory, attention, learning & diverse aspects of cognitive psychology.

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What Is Statistical Analysis?

Statistical analysis helps you pull meaningful insights from data. The process involves working with data and deducing numbers to tell quantitative stories.

Statistical analysis is a technique we use to find patterns in data and make inferences about those patterns to describe variability in the results of a data set or an experiment.

In its simplest form, statistical analysis answers questions about:

Quantification — how big/small/tall/wide is it?
Variability — growth, increase, decline
The confidence level of these variabilities

What Are the 2 Types of Statistical Analysis?

Descriptive Statistics: Descriptive statistical analysis describes the quality of the data by summarizing large data sets into single measures.
Inferential Statistics: Inferential statistical analysis allows you to draw conclusions from your sample data set and make predictions about a population using statistical tests.

What’s the Purpose of Statistical Analysis?

Using statistical analysis, you can determine trends in the data by calculating your data set’s mean or median. You can also analyze the variation between different data points from the mean to get the standard deviation . Furthermore, to test the validity of your statistical analysis conclusions, you can use hypothesis testing techniques, like P-value, to determine the likelihood that the observed variability could have occurred by chance.

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Statistical Analysis Methods

There are two major types of statistical data analysis: descriptive and inferential.

Descriptive Statistical Analysis

Descriptive statistical analysis describes the quality of the data by summarizing large data sets into single measures.

Within the descriptive analysis branch, there are two main types: measures of central tendency (i.e. mean, median and mode) and measures of dispersion or variation (i.e. variance , standard deviation and range).

For example, you can calculate the average exam results in a class using central tendency or, in particular, the mean. In that case, you’d sum all student results and divide by the number of tests. You can also calculate the data set’s spread by calculating the variance. To calculate the variance, subtract each exam result in the data set from the mean, square the answer, add everything together and divide by the number of tests.

Inferential Statistics

On the other hand, inferential statistical analysis allows you to draw conclusions from your sample data set and make predictions about a population using statistical tests.

There are two main types of inferential statistical analysis: hypothesis testing and regression analysis. We use hypothesis testing to test and validate assumptions in order to draw conclusions about a population from the sample data. Popular tests include Z-test, F-Test, ANOVA test and confidence intervals . On the other hand, regression analysis primarily estimates the relationship between a dependent variable and one or more independent variables. There are numerous types of regression analysis but the most popular ones include linear and logistic regression .

Statistical Analysis Steps

In the era of big data and data science, there is a rising demand for a more problem-driven approach. As a result, we must approach statistical analysis holistically. We may divide the entire process into five different and significant stages by using the well-known PPDAC model of statistics: Problem, Plan, Data, Analysis and Conclusion.

In the first stage, you define the problem you want to tackle and explore questions about the problem.

2. Plan

Next is the planning phase. You can check whether data is available or if you need to collect data for your problem. You also determine what to measure and how to measure it.

The third stage involves data collection, understanding the data and checking its quality.

4. Analysis

Statistical data analysis is the fourth stage. Here you process and explore the data with the help of tables, graphs and other data visualizations. You also develop and scrutinize your hypothesis in this stage of analysis.

5. Conclusion

The final step involves interpretations and conclusions from your analysis. It also covers generating new ideas for the next iteration. Thus, statistical analysis is not a one-time event but an iterative process.

Statistical Analysis Uses

Statistical analysis is useful for research and decision making because it allows us to understand the world around us and draw conclusions by testing our assumptions. Statistical analysis is important for various applications, including:

Statistical quality control and analysis in product development
Clinical trials
Customer satisfaction surveys and customer experience research
Marketing operations management
Process improvement and optimization
Training needs

More on Statistical Analysis From Built In Experts Intro to Descriptive Statistics for Machine Learning

Benefits of Statistical Analysis

Here are some of the reasons why statistical analysis is widespread in many applications and why it’s necessary:

Understand Data

Statistical analysis gives you a better understanding of the data and what they mean. These types of analyses provide information that would otherwise be difficult to obtain by merely looking at the numbers without considering their relationship.

Find Causal Relationships

Statistical analysis can help you investigate causation or establish the precise meaning of an experiment, like when you’re looking for a relationship between two variables.

Make Data-Informed Decisions

Businesses are constantly looking to find ways to improve their services and products . Statistical analysis allows you to make data-informed decisions about your business or future actions by helping you identify trends in your data, whether positive or negative.

Determine Probability

Statistical analysis is an approach to understanding how the probability of certain events affects the outcome of an experiment. It helps scientists and engineers decide how much confidence they can have in the results of their research, how to interpret their data and what questions they can feasibly answer.

You’ve Got Questions. Our Experts Have Answers. Confidence Intervals, Explained!

What Are the Risks of Statistical Analysis?

Statistical analysis can be valuable and effective, but it’s an imperfect approach. Even if the analyst or researcher performs a thorough statistical analysis, there may still be known or unknown problems that can affect the results. Therefore, statistical analysis is not a one-size-fits-all process. If you want to get good results, you need to know what you’re doing. It can take a lot of time to figure out which type of statistical analysis will work best for your situation .

Thus, you should remember that our conclusions drawn from statistical analysis don’t always guarantee correct results. This can be dangerous when making business decisions. In marketing , for example, we may come to the wrong conclusion about a product . Therefore, the conclusions we draw from statistical data analysis are often approximated; testing for all factors affecting an observation is impossible.

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Statistical Analysis in Research: Meaning, Methods and Types

Home » Videos » Statistical Analysis in Research: Meaning, Methods and Types

The scientific method is an empirical approach to acquiring new knowledge by making skeptical observations and analyses to develop a meaningful interpretation. It is the basis of research and the primary pillar of modern science. Researchers seek to understand the relationships between factors associated with the phenomena of interest. In some cases, research works with vast chunks of data, making it difficult to observe or manipulate each data point. As a result, statistical analysis in research becomes a means of evaluating relationships and interconnections between variables with tools and analytical techniques for working with large data. Since researchers use statistical power analysis to assess the probability of finding an effect in such an investigation, the method is relatively accurate. Hence, statistical analysis in research eases analytical methods by focusing on the quantifiable aspects of phenomena.

What is Statistical Analysis in Research? A Simplified Definition

Statistical analysis uses quantitative data to investigate patterns, relationships, and patterns to understand real-life and simulated phenomena. The approach is a key analytical tool in various fields, including academia, business, government, and science in general. This statistical analysis in research definition implies that the primary focus of the scientific method is quantitative research. Notably, the investigator targets the constructs developed from general concepts as the researchers can quantify their hypotheses and present their findings in simple statistics.

When a business needs to learn how to improve its product, they collect statistical data about the production line and customer satisfaction. Qualitative data is valuable and often identifies the most common themes in the stakeholders’ responses. On the other hand, the quantitative data creates a level of importance, comparing the themes based on their criticality to the affected persons. For instance, descriptive statistics highlight tendency, frequency, variation, and position information. While the mean shows the average number of respondents who value a certain aspect, the variance indicates the accuracy of the data. In any case, statistical analysis creates simplified concepts used to understand the phenomenon under investigation. It is also a key component in academia as the primary approach to data representation, especially in research projects, term papers and dissertations.

Most Useful Statistical Analysis Methods in Research

Using statistical analysis methods in research is inevitable, especially in academic assignments, projects, and term papers. It’s always advisable to seek assistance from your professor or you can try research paper writing by CustomWritings before you start your academic project or write statistical analysis in research paper. Consulting an expert when developing a topic for your thesis or short mid-term assignment increases your chances of getting a better grade. Most importantly, it improves your understanding of research methods with insights on how to enhance the originality and quality of personalized essays. Professional writers can also help select the most suitable statistical analysis method for your thesis, influencing the choice of data and type of study.

Descriptive Statistics

Descriptive statistics is a statistical method summarizing quantitative figures to understand critical details about the sample and population. A description statistic is a figure that quantifies a specific aspect of the data. For instance, instead of analyzing the behavior of a thousand students, research can identify the most common actions among them. By doing this, the person utilizes statistical analysis in research, particularly descriptive statistics.

Measures of central tendency . Central tendency measures are the mean, mode, and media or the averages denoting specific data points. They assess the centrality of the probability distribution, hence the name. These measures describe the data in relation to the center.
Measures of frequency . These statistics document the number of times an event happens. They include frequency, count, ratios, rates, and proportions. Measures of frequency can also show how often a score occurs.
Measures of dispersion/variation . These descriptive statistics assess the intervals between the data points. The objective is to view the spread or disparity between the specific inputs. Measures of variation include the standard deviation, variance, and range. They indicate how the spread may affect other statistics, such as the mean.
Measures of position . Sometimes researchers can investigate relationships between scores. Measures of position, such as percentiles, quartiles, and ranks, demonstrate this association. They are often useful when comparing the data to normalized information.

Inferential Statistics

Inferential statistics is critical in statistical analysis in quantitative research. This approach uses statistical tests to draw conclusions about the population. Examples of inferential statistics include t-tests, F-tests, ANOVA, p-value, Mann-Whitney U test, and Wilcoxon W test. This

Common Statistical Analysis in Research Types

Although inferential and descriptive statistics can be classified as types of statistical analysis in research, they are mostly considered analytical methods. Types of research are distinguishable by the differences in the methodology employed in analyzing, assembling, classifying, manipulating, and interpreting data. The categories may also depend on the type of data used.

Predictive Analysis

Predictive research analyzes past and present data to assess trends and predict future events. An excellent example of predictive analysis is a market survey that seeks to understand customers’ spending habits to weigh the possibility of a repeat or future purchase. Such studies assess the likelihood of an action based on trends.

Prescriptive Analysis

On the other hand, a prescriptive analysis targets likely courses of action. It’s decision-making research designed to identify optimal solutions to a problem. Its primary objective is to test or assess alternative measures.

Causal Analysis

Causal research investigates the explanation behind the events. It explores the relationship between factors for causation. Thus, researchers use causal analyses to analyze root causes, possible problems, and unknown outcomes.

Mechanistic Analysis

This type of research investigates the mechanism of action. Instead of focusing only on the causes or possible outcomes, researchers may seek an understanding of the processes involved. In such cases, they use mechanistic analyses to document, observe, or learn the mechanisms involved.

Exploratory Data Analysis

Similarly, an exploratory study is extensive with a wider scope and minimal limitations. This type of research seeks insight into the topic of interest. An exploratory researcher does not try to generalize or predict relationships. Instead, they look for information about the subject before conducting an in-depth analysis.

The Importance of Statistical Analysis in Research

As a matter of fact, statistical analysis provides critical information for decision-making. Decision-makers require past trends and predictive assumptions to inform their actions. In most cases, the data is too complex or lacks meaningful inferences. Statistical tools for analyzing such details help save time and money, deriving only valuable information for assessment. An excellent statistical analysis in research example is a randomized control trial (RCT) for the Covid-19 vaccine. You can download a sample of such a document online to understand the significance such analyses have to the stakeholders. A vaccine RCT assesses the effectiveness, side effects, duration of protection, and other benefits. Hence, statistical analysis in research is a helpful tool for understanding data.

Sources and links For the articles and videos I use different databases, such as Eurostat, OECD World Bank Open Data, Data Gov and others. You are free to use the video I have made on your site using the link or the embed code. If you have any questions, don’t hesitate to write to me!

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Effective Use of Statistics in Research – Methods and Tools for Data Analysis

Remember that impending feeling you get when you are asked to analyze your data! Now that you have all the required raw data, you need to statistically prove your hypothesis. Representing your numerical data as part of statistics in research will also help in breaking the stereotype of being a biology student who can’t do math.

Statistical methods are essential for scientific research. In fact, statistical methods dominate the scientific research as they include planning, designing, collecting data, analyzing, drawing meaningful interpretation and reporting of research findings. Furthermore, the results acquired from research project are meaningless raw data unless analyzed with statistical tools. Therefore, determining statistics in research is of utmost necessity to justify research findings. In this article, we will discuss how using statistical methods for biology could help draw meaningful conclusion to analyze biological studies.

Table of Contents

Role of Statistics in Biological Research

Statistics is a branch of science that deals with collection, organization and analysis of data from the sample to the whole population. Moreover, it aids in designing a study more meticulously and also give a logical reasoning in concluding the hypothesis. Furthermore, biology study focuses on study of living organisms and their complex living pathways, which are very dynamic and cannot be explained with logical reasoning. However, statistics is more complex a field of study that defines and explains study patterns based on the sample sizes used. To be precise, statistics provides a trend in the conducted study.

Biological researchers often disregard the use of statistics in their research planning, and mainly use statistical tools at the end of their experiment. Therefore, giving rise to a complicated set of results which are not easily analyzed from statistical tools in research. Statistics in research can help a researcher approach the study in a stepwise manner, wherein the statistical analysis in research follows –

1. Establishing a Sample Size

Usually, a biological experiment starts with choosing samples and selecting the right number of repetitive experiments. Statistics in research deals with basics in statistics that provides statistical randomness and law of using large samples. Statistics teaches how choosing a sample size from a random large pool of sample helps extrapolate statistical findings and reduce experimental bias and errors.

2. Testing of Hypothesis

When conducting a statistical study with large sample pool, biological researchers must make sure that a conclusion is statistically significant. To achieve this, a researcher must create a hypothesis before examining the distribution of data. Furthermore, statistics in research helps interpret the data clustered near the mean of distributed data or spread across the distribution. These trends help analyze the sample and signify the hypothesis.

3. Data Interpretation Through Analysis

When dealing with large data, statistics in research assist in data analysis. This helps researchers to draw an effective conclusion from their experiment and observations. Concluding the study manually or from visual observation may give erroneous results; therefore, thorough statistical analysis will take into consideration all the other statistical measures and variance in the sample to provide a detailed interpretation of the data. Therefore, researchers produce a detailed and important data to support the conclusion.

Types of Statistical Research Methods That Aid in Data Analysis

Statistical analysis is the process of analyzing samples of data into patterns or trends that help researchers anticipate situations and make appropriate research conclusions. Based on the type of data, statistical analyses are of the following type:

1. Descriptive Analysis

The descriptive statistical analysis allows organizing and summarizing the large data into graphs and tables . Descriptive analysis involves various processes such as tabulation, measure of central tendency, measure of dispersion or variance, skewness measurements etc.

2. Inferential Analysis

The inferential statistical analysis allows to extrapolate the data acquired from a small sample size to the complete population. This analysis helps draw conclusions and make decisions about the whole population on the basis of sample data. It is a highly recommended statistical method for research projects that work with smaller sample size and meaning to extrapolate conclusion for large population.

3. Predictive Analysis

Predictive analysis is used to make a prediction of future events. This analysis is approached by marketing companies, insurance organizations, online service providers, data-driven marketing, and financial corporations.

4. Prescriptive Analysis

Prescriptive analysis examines data to find out what can be done next. It is widely used in business analysis for finding out the best possible outcome for a situation. It is nearly related to descriptive and predictive analysis. However, prescriptive analysis deals with giving appropriate suggestions among the available preferences.

5. Exploratory Data Analysis

EDA is generally the first step of the data analysis process that is conducted before performing any other statistical analysis technique. It completely focuses on analyzing patterns in the data to recognize potential relationships. EDA is used to discover unknown associations within data, inspect missing data from collected data and obtain maximum insights.

6. Causal Analysis

Causal analysis assists in understanding and determining the reasons behind “why” things happen in a certain way, as they appear. This analysis helps identify root cause of failures or simply find the basic reason why something could happen. For example, causal analysis is used to understand what will happen to the provided variable if another variable changes.

7. Mechanistic Analysis

This is a least common type of statistical analysis. The mechanistic analysis is used in the process of big data analytics and biological science. It uses the concept of understanding individual changes in variables that cause changes in other variables correspondingly while excluding external influences.

Important Statistical Tools In Research

Researchers in the biological field find statistical analysis in research as the scariest aspect of completing research. However, statistical tools in research can help researchers understand what to do with data and how to interpret the results, making this process as easy as possible.

1. Statistical Package for Social Science (SPSS)

It is a widely used software package for human behavior research. SPSS can compile descriptive statistics, as well as graphical depictions of result. Moreover, it includes the option to create scripts that automate analysis or carry out more advanced statistical processing.

2. R Foundation for Statistical Computing

This software package is used among human behavior research and other fields. R is a powerful tool and has a steep learning curve. However, it requires a certain level of coding. Furthermore, it comes with an active community that is engaged in building and enhancing the software and the associated plugins.

3. MATLAB (The Mathworks)

It is an analytical platform and a programming language. Researchers and engineers use this software and create their own code and help answer their research question. While MatLab can be a difficult tool to use for novices, it offers flexibility in terms of what the researcher needs.

4. Microsoft Excel

Not the best solution for statistical analysis in research, but MS Excel offers wide variety of tools for data visualization and simple statistics. It is easy to generate summary and customizable graphs and figures. MS Excel is the most accessible option for those wanting to start with statistics.

5. Statistical Analysis Software (SAS)

It is a statistical platform used in business, healthcare, and human behavior research alike. It can carry out advanced analyzes and produce publication-worthy figures, tables and charts .

6. GraphPad Prism

It is a premium software that is primarily used among biology researchers. But, it offers a range of variety to be used in various other fields. Similar to SPSS, GraphPad gives scripting option to automate analyses to carry out complex statistical calculations.

This software offers basic as well as advanced statistical tools for data analysis. However, similar to GraphPad and SPSS, minitab needs command over coding and can offer automated analyses.

Use of Statistical Tools In Research and Data Analysis

Statistical tools manage the large data. Many biological studies use large data to analyze the trends and patterns in studies. Therefore, using statistical tools becomes essential, as they manage the large data sets, making data processing more convenient.

Following these steps will help biological researchers to showcase the statistics in research in detail, and develop accurate hypothesis and use correct tools for it.

There are a range of statistical tools in research which can help researchers manage their research data and improve the outcome of their research by better interpretation of data. You could use statistics in research by understanding the research question, knowledge of statistics and your personal experience in coding.

Have you faced challenges while using statistics in research? How did you manage it? Did you use any of the statistical tools to help you with your research data? Do write to us or comment below!

Frequently Asked Questions

Statistics in research can help a researcher approach the study in a stepwise manner: 1. Establishing a sample size 2. Testing of hypothesis 3. Data interpretation through analysis

Statistical tools in research can help researchers understand what to do with data and how to interpret the results, making this process as easy as possible. They can manage large data sets, making data processing more convenient. A great number of tools are available to carry out statistical analysis of data like SPSS, SAS (Statistical Analysis Software), and Minitab.

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Understanding and Using Statistical Methods

Statistics is a set of tools used to organize and analyze data. Data must either be numeric in origin or transformed by researchers into numbers. For instance, statistics could be used to analyze percentage scores English students receive on a grammar test: the percentage scores ranging from 0 to 100 are already in numeric form. Statistics could also be used to analyze grades on an essay by assigning numeric values to the letter grades, e.g., A=4, B=3, C=2, D=1, and F=0.

Employing statistics serves two purposes, (1) description and (2) prediction. Statistics are used to describe the characteristics of groups. These characteristics are referred to as variables . Data is gathered and recorded for each variable. Descriptive statistics can then be used to reveal the distribution of the data in each variable.

Statistics is also frequently used for purposes of prediction. Prediction is based on the concept of generalizability : if enough data is compiled about a particular context (e.g., students studying writing in a specific set of classrooms), the patterns revealed through analysis of the data collected about that context can be generalized (or predicted to occur in) similar contexts. The prediction of what will happen in a similar context is probabilistic . That is, the researcher is not certain that the same things will happen in other contexts; instead, the researcher can only reasonably expect that the same things will happen.

Prediction is a method employed by individuals throughout daily life. For instance, if writing students begin class every day for the first half of the semester with a five-minute freewriting exercise, then they will likely come to class the first day of the second half of the semester prepared to again freewrite for the first five minutes of class. The students will have made a prediction about the class content based on their previous experiences in the class: Because they began all previous class sessions with freewriting, it would be probable that their next class session will begin the same way. Statistics is used to perform the same function; the difference is that precise probabilities are determined in terms of the percentage chance that an outcome will occur, complete with a range of error. Prediction is a primary goal of inferential statistics.

Revealing Patterns Using Descriptive Statistics

Descriptive statistics, not surprisingly, "describe" data that have been collected. Commonly used descriptive statistics include frequency counts, ranges (high and low scores or values), means, modes, median scores, and standard deviations. Two concepts are essential to understanding descriptive statistics: variables and distributions .

Statistics are used to explore numerical data (Levin, 1991). Numerical data are observations which are recorded in the form of numbers (Runyon, 1976). Numbers are variable in nature, which means that quantities vary according to certain factors. For examples, when analyzing the grades on student essays, scores will vary for reasons such as the writing ability of the student, the students' knowledge of the subject, and so on. In statistics, these reasons are called variables. Variables are divided into three basic categories:

Nominal Variables

Nominal variables classify data into categories. This process involves labeling categories and then counting frequencies of occurrence (Runyon, 1991). A researcher might wish to compare essay grades between male and female students. Tabulations would be compiled using the categories "male" and "female." Sex would be a nominal variable. Note that the categories themselves are not quantified. Maleness or femaleness are not numerical in nature, rather the frequencies of each category results in data that is quantified -- 11 males and 9 females.

Ordinal Variables

Ordinal variables order (or rank) data in terms of degree. Ordinal variables do not establish the numeric difference between data points. They indicate only that one data point is ranked higher or lower than another (Runyon, 1991). For instance, a researcher might want to analyze the letter grades given on student essays. An A would be ranked higher than a B, and a B higher than a C. However, the difference between these data points, the precise distance between an A and a B, is not defined. Letter grades are an example of an ordinal variable.

Interval Variables

Interval variables score data. Thus the order of data is known as well as the precise numeric distance between data points (Runyon, 1991). A researcher might analyze the actual percentage scores of the essays, assuming that percentage scores are given by the instructor. A score of 98 (A) ranks higher than a score of 87 (B), which ranks higher than a score of 72 (C). Not only is the order of these three data points known, but so is the exact distance between them -- 11 percentage points between the first two, 15 percentage points between the second two and 26 percentage points between the first and last data points.

Distributions

A distribution is a graphic representation of data. The line formed by connecting data points is called a frequency distribution. This line may take many shapes. The single most important shape is that of the bell-shaped curve, which characterizes the distribution as "normal." A perfectly normal distribution is only a theoretical ideal. This ideal, however, is an essential ingredient in statistical decision-making (Levin, 1991). A perfectly normal distribution is a mathematical construct which carries with it certain mathematical properties helpful in describing the attributes of the distribution. Although frequency distribution based on actual data points seldom, if ever, completely matches a perfectly normal distribution, a frequency distribution often can approach such a normal curve.

The closer a frequency distribution resembles a normal curve, the more probable that the distribution maintains those same mathematical properties as the normal curve. This is an important factor in describing the characteristics of a frequency distribution. As a frequency distribution approaches a normal curve, generalizations about the data set from which the distribution was derived can be made with greater certainty. And it is this notion of generalizability upon which statistics is founded. It is important to remember that not all frequency distributions approach a normal curve. Some are skewed. When a frequency distribution is skewed, the characteristics inherent to a normal curve no longer apply.

Making Predictions Using Inferential Statistics

Inferential statistics are used to draw conclusions and make predictions based on the descriptions of data. In this section, we explore inferential statistics by using an extended example of experimental studies. Key concepts used in our discussion are probability, populations, and sampling.

Experiments

A typical experimental study involves collecting data on the behaviors, attitudes, or actions of two or more groups and attempting to answer a research question (often called a hypothesis). Based on the analysis of the data, a researcher might then attempt to develop a causal model that can be generalized to populations.

A question that might be addressed through experimental research might be "Does grammar-based writing instruction produce better writers than process-based writing instruction?" Because it would be impossible and impractical to observe, interview, survey, etc. all first-year writing students and instructors in classes using one or the other of these instructional approaches, a researcher would study a sample – or a subset – of a population. Sampling – or the creation of this subset of a population – is used by many researchers who desire to make sense of some phenomenon.

To analyze differences in the ability of student writers who are taught in each type of classroom, the researcher would compare the writing performance of the two groups of students.

Dependent Variables

In an experimental study, a variable whose score depends on (or is determined or caused by) another variable is called a dependent variable. For instance, an experiment might explore the extent to which the writing quality of final drafts of student papers is affected by the kind of instruction they received. In this case, the dependent variable would be writing quality of final drafts.

Independent Variables

In an experimental study, a variable that determines (or causes) the score of a dependent variable is called an independent variable. For instance, an experiment might explore the extent to which the writing quality of final drafts of student papers is affected by the kind of instruction they received. In this case, the independent variable would be the kind of instruction students received.

Probability

Beginning researchers most often use the word probability to express a subjective judgment about the likelihood, or degree of certainty, that a particular event will occur. People say such things as: "It will probably rain tomorrow." "It is unlikely that we will win the ball game." It is possible to assign a number to the event being predicted, a number between 0 and 1, which represents degree of confidence that the event will occur. For example, a student might say that the likelihood an instructor will give an exam next week is about 90 percent, or .9. Where 100 percent, or 1.00, represents certainty, .9 would mean the student is almost certain the instructor will give an exam. If the student assigned the number .6, the likelihood of an exam would be just slightly greater than the likelihood of no exam. A rating of 0 would indicate complete certainty that no exam would be given(Shoeninger, 1971).

The probability of a particular outcome or set of outcomes is called a p-value . In our discussion, a p-value will be symbolized by a p followed by parentheses enclosing a symbol of the outcome or set of outcomes. For example, p(X) should be read, "the probability of a given X score" (Shoeninger). Thus p(exam) should be read, "the probability an instructor will give an exam next week."

A population is a group which is studied. In educational research, the population is usually a group of people. Researchers seldom are able to study every member of a population. Usually, they instead study a representative sample – or subset – of a population. Researchers then generalize their findings about the sample to the population as a whole.

Sampling is performed so that a population under study can be reduced to a manageable size. This can be accomplished via random sampling, discussed below, or via matching.

Random sampling is a procedure used by researchers in which all samples of a particular size have an equal chance to be chosen for an observation, experiment, etc (Runyon and Haber, 1976). There is no predetermination as to which members are chosen for the sample. This type of sampling is done in order to minimize scientific biases and offers the greatest likelihood that a sample will indeed be representative of the larger population. The aim here is to make the sample as representative of the population as possible. Note that the closer a sample distribution approximates the population distribution, the more generalizable the results of the sample study are to the population. Notions of probability apply here. Random sampling provides the greatest probability that the distribution of scores in a sample will closely approximate the distribution of scores in the overall population.

Matching is a method used by researchers to gain accurate and precise results of a study so that they may be applicable to a larger population. After a population has been examined and a sample has been chosen, a researcher must then consider variables, or extrinsic factors, that might affect the study. Matching methods apply when researchers are aware of extrinsic variables before conducting a study. Two methods used to match groups are:

Precision Matching

In precision matching , there is an experimental group that is matched with a control group. Both groups, in essence, have the same characteristics. Thus, the proposed causal relationship/model being examined allows for the probabilistic assumption that the result is generalizable.

Frequency Distribution

Frequency distribution is more manageable and efficient than precision matching. Instead of one-to-one matching that must be administered in precision matching, frequency distribution allows the comparison of an experimental and control group through relevant variables. If three Communications majors and four English majors are chosen for the control group, then an equal proportion of three Communications major and four English majors should be allotted to the experiment group. Of course, beyond their majors, the characteristics of the matched sets of participants may in fact be vastly different.

Although, in theory, matching tends to produce valid conclusions, a rather obvious difficulty arises in finding subjects which are compatible. Researchers may even believe that experimental and control groups are identical when, in fact, a number of variables have been overlooked. For these reasons, researchers tend to reject matching methods in favor of random sampling.

Statistics can be used to analyze individual variables, relationships among variables, and differences between groups. In this section, we explore a range of statistical methods for conducting these analyses.

Statistics can be used to analyze individual variables, relationships among variables, and differences between groups.

Analyzing Individual Variables

The statistical procedures used to analyze a single variable describing a group (such as a population or representative sample) involve measures of central tendency and measures of variation . To explore these measures, a researcher first needs to consider the distribution , or range of values of a particular variable in a population or sample. Normal distribution occurs if the distribution of a population is completely normal. When graphed, this type of distribution will look like a bell curve; it is symmetrical and most of the scores cluster toward the middle. Skewed Distribution simply means the distribution of a population is not normal. The scores might cluster toward the right or the left side of the curve, for instance. Or there might be two or more clusters of scores, so that the distribution looks like a series of hills.

Once frequency distributions have been determined, researchers can calculate measures of central tendency and measures of variation. Measures of central tendency indicate averages of the distribution, and measures of variation indicate the spread, or range, of the distribution (Hinkle, Wiersma and Jurs 1988).

Measures of Central Tendency

Central tendency is measured in three ways: mean , median and mode . The mean is simply the average score of a distribution. The median is the center, or middle score within a distribution. The mode is the most frequent score within a distribution. In a normal distribution, the mean, median and mode are identical.

Student	# of Crayons
A	8
B	16
C	16
D	32
E	32
F	32
G	48
H	48
J	56

Measures of Variation

Measures of variation determine the range of the distribution, relative to the measures of central tendency. Where the measures of central tendency are specific data points, measures of variation are lengths between various points within the distribution. Variation is measured in terms of range, mean deviation, variance, and standard deviation (Hinkle, Wiersma and Jurs 1988).

The range is the distance between the lowest data point and the highest data point. Deviation scores are the distances between each data point and the mean.

Mean deviation is the average of the absolute values of the deviation scores; that is, mean deviation is the average distance between the mean and the data points. Closely related to the measure of mean deviation is the measure of variance .

Variance also indicates a relationship between the mean of a distribution and the data points; it is determined by averaging the sum of the squared deviations. Squaring the differences instead of taking the absolute values allows for greater flexibility in calculating further algebraic manipulations of the data. Another measure of variation is the standard deviation .

Standard deviation is the square root of the variance. This calculation is useful because it allows for the same flexibility as variance regarding further calculations and yet also expresses variation in the same units as the original measurements (Hinkle, Wiersma and Jurs 1988).

Analyzing Differences Between Groups

Statistical tests can be used to analyze differences in the scores of two or more groups. The following statistical tests are commonly used to analyze differences between groups:

A t-test is used to determine if the scores of two groups differ on a single variable. A t-test is designed to test for the differences in mean scores. For instance, you could use a t-test to determine whether writing ability differs among students in two classrooms.

Note: A t-test is appropriate only when looking at paired data. It is useful in analyzing scores of two groups of participants on a particular variable or in analyzing scores of a single group of participants on two variables.

Matched Pairs T-Test

This type of t-test could be used to determine if the scores of the same participants in a study differ under different conditions. For instance, this sort of t-test could be used to determine if people write better essays after taking a writing class than they did before taking the writing class.

Analysis of Variance (ANOVA)

The ANOVA (analysis of variance) is a statistical test which makes a single, overall decision as to whether a significant difference is present among three or more sample means (Levin 484). An ANOVA is similar to a t-test. However, the ANOVA can also test multiple groups to see if they differ on one or more variables. The ANOVA can be used to test between-groups and within-groups differences. There are two types of ANOVAs:

One-Way ANOVA: This tests a group or groups to determine if there are differences on a single set of scores. For instance, a one-way ANOVA could determine whether freshmen, sophomores, juniors, and seniors differed in their reading ability.

Multiple ANOVA (MANOVA): This tests a group or groups to determine if there are differences on two or more variables. For instance, a MANOVA could determine whether freshmen, sophomores, juniors, and seniors differed in reading ability and whether those differences were reflected by gender. In this case, a researcher could determine (1) whether reading ability differed across class levels, (2) whether reading ability differed across gender, and (3) whether there was an interaction between class level and gender.

Analyzing Relationships Among Variables

Statistical relationships between variables rely on notions of correlation and regression. These two concepts aim to describe the ways in which variables relate to one another:

Correlation

Correlation tests are used to determine how strongly the scores of two variables are associated or correlated with each other. A researcher might want to know, for instance, whether a correlation exists between students' writing placement examination scores and their scores on a standardized test such as the ACT or SAT. Correlation is measured using values between +1.0 and -1.0. Correlations close to 0 indicate little or no relationship between two variables, while correlations close to +1.0 (or -1.0) indicate strong positive (or negative) relationships (Hayes et al. 554).

Correlation denotes positive or negative association between variables in a study. Two variables are positively associated when larger values of one tend to be accompanied by larger values of the other. The variables are negatively associated when larger values of one tend to be accompanied by smaller values of the other (Moore 208).

An example of a strong positive correlation would be the correlation between age and job experience. Typically, the longer people are alive, the more job experience they might have.

An example of a strong negative relationship might occur between the strength of people's party affiliations and their willingness to vote for a candidate from different parties. In many elections, Democrats are unlikely to vote for Republicans, and vice versa.

Regression analysis attempts to determine the best "fit" between two or more variables. The independent variable in a regression analysis is a continuous variable, and thus allows you to determine how one or more independent variables predict the values of a dependent variable.

Simple Linear Regression is the simplest form of regression. Like a correlation, it determines the extent to which one independent variables predicts a dependent variable. You can think of a simple linear regression as a correlation line. Regression analysis provides you with more information than correlation does, however. It tells you how well the line "fits" the data. That is, it tells you how closely the line comes to all of your data points. The line in the figure indicates the regression line drawn to find the best fit among a set of data points. Each dot represents a person and the axes indicate the amount of job experience and the age of that person. The dotted lines indicate the distance from the regression line. A smaller total distance indicates a better fit. Some of the information provided in a regression analysis, as a result, indicates the slope of the regression line, the R value (or correlation), and the strength of the fit (an indication of the extent to which the line can account for variations among the data points).

Multiple Linear Regression allows one to determine how well multiple independent variables predict the value of a dependent variable. A researcher might examine, for instance, how well age and experience predict a person's salary. The interesting thing here is that one would no longer be dealing with a regression "line." Instead, since the study deals with three dimensions (age, experience, and salary), it would be dealing with a plane, that is, with a two-dimensional figure. If a fourth variable was added to the equations, one would be dealing with a three-dimensional figure, and so on.

Misuses of Statistics

Statistics consists of tests used to analyze data. These tests provide an analytic framework within which researchers can pursue their research questions. This framework provides one way of working with observable information. Like other analytic frameworks, statistical tests can be misused, resulting in potential misinterpretation and misrepresentation. Researchers decide which research questions to ask, which groups to study, how those groups should be divided, which variables to focus upon, and how best to categorize and measure such variables. The point is that researchers retain the ability to manipulate any study even as they decide what to study and how to study it.

Potential Misuses:

Manipulating scale to change the appearance of the distribution of data
Eliminating high/low scores for more coherent presentation
Inappropriately focusing on certain variables to the exclusion of other variables
Presenting correlation as causation

Measures Against Potential Misuses:

Testing for reliability and validity
Testing for statistical significance
Critically reading statistics

Annotated Bibliography

Dear, K. (1997, August 28). SurfStat australia . Available: http://surfstat.newcastle.edu.au/surfstat/main/surfstat-main.html

A comprehensive site contain an online textbook, links together statistics sites, exercises, and a hotlist for Java applets.

de Leeuw, J. (1997, May 13 ). Statistics: The study of stability in variation . Available: http://www.stat.ucla.edu/textbook/ [1997, December 8].

An online textbook providing discussions specifically regarding variability.

Ewen, R.B. (1988). The workbook for introductory statistics for the behavioral sciences. Orlando, FL: Harcourt Brace Jovanovich.

A workbook providing sample problems typical of the statistical applications in social sciences.

Glass, G. (1996, August 26). COE 502: Introduction to quantitative methods . Available: http://seamonkey.ed.asu.edu/~gene/502/home.html

Outline of a basic statistics course in the college of education at Arizona State University, including a list of statistic resources on the Internet and access to online programs using forms and PERL to analyze data.

Hartwig, F., Dearing, B.E. (1979). Exploratory data analysis . Newberry Park, CA: Sage Publications, Inc.

Hayes, J. R., Young, R.E., Matchett, M.L., McCaffrey, M., Cochran, C., and Hajduk, T., eds. (1992). Reading empirical research studies: The rhetoric of research . Hillsdale, NJ: Lawrence Erlbaum Associates.

A text focusing on the language of research. Topics vary from "Communicating with Low-Literate Adults" to "Reporting on Journalists."

Hinkle, Dennis E., Wiersma, W. and Jurs, S.G. (1988). Applied statistics for the behavioral sciences . Boston: Houghton.

This is an introductory text book on statistics. Each of 22 chapters includes a summary, sample exercises and highlighted main points. The book also includes an index by subject.

Kleinbaum, David G., Kupper, L.L. and Muller K.E. Applied regression analysis and other multivariable methods 2nd ed . Boston: PWS-KENT Publishing Company.

An introductory text with emphasis on statistical analyses. Chapters contain exercises.

Kolstoe, R.H. (1969). Introduction to statistics for the behavioral sciences . Homewood, ILL: Dorsey.

Though more than 25-years-old, this textbook uses concise chapters to explain many essential statistical concepts. Information is organized in a simple and straightforward manner.

Levin, J., and James, A.F. (1991). Elementary statistics in social research, 5th ed . New York: HarperCollins.

This textbook presents statistics in three major sections: Description, From Description to Decision Making and Decision Making. The first chapter underlies reasons for using statistics in social research. Subsequent chapters detail the process of conducting and presenting statistics.

Liebetrau, A.M. (1983). Measures of association . Newberry Park, CA: Sage Publications, Inc.

Mendenhall, W.(1975). Introduction to probability and statistics, 4th ed. North Scltuate, MA: Duxbury Press.

An introductory textbook. A good overview of statistics. Includes clear definitions and exercises.

Moore, David S. (1979). Statistics: Concepts and controversies , 2nd ed . New York: W. H. Freeman and Company.

Introductory text. Basic overview of statistical concepts. Includes discussions of concrete applications such as opinion polls and Consumer Price Index.

Mosier, C.T. (1997). MG284 Statistics I - notes. Available: http://phoenix.som.clarkson.edu/~cmosier/statistics/main/outline/index.html

Explanations of fundamental statistical concepts.

Newton, H.J., Carrol, J.H., Wang, N., & Whiting, D.(1996, Fall). Statistics 30X class notes. Available: http://stat.tamu.edu/stat30x/trydouble2.html [1997, December 10].

This site contains a hyperlinked list of very comprehensive course notes from and introductory statistics class. A large variety of statistical concepts are covered.

Runyon, R.P., and Haber, A. (1976). Fundamentals of behavioral statistics , 3rd ed . Reading, MA: Addison-Wesley Publishing Company.

This is a textbook that divides statistics into categories of descriptive statistics and inferential statistics. It presents statistical procedures primarily through examples. This book includes sectional reviews, reviews of basic mathematics and also a glossary of symbols common to statistics.

Schoeninger, D.W. and Insko, C.A. (1971). Introductory statistics for the behavioral sciences . Boston: Allyn and Bacon, Inc.

An introductory text including discussions of correlation, probability, distribution, and variance. Includes statistical tables in the appendices.

Stevens, J. (1986). Applied multivariate statistics for the social sciences . Hillsdale, NJ: Lawrence Erlbaum Associates.

Stockberger, D. W. (1996). Introductory statistics: Concepts, models and applications . Available: http://www.psychstat.smsu.edu/ [1997, December 8].

Describes various statistical analyses. Includes statistical tables in the appendix.

Local Resources

If you are a member of the Colorado State University community and seek more in-depth help with analyzing data from your research (e.g., from an undergraduate or graduate research project), please contact CSU's Graybill Statistical Laboratory for statistical consulting assistance at http://www.stat.colostate.edu/statlab.html .

Jackson, Shawna, Karen Marcus, Cara McDonald, Timothy Wehner, & Mike Palmquist. (2005). Statistics: An Introduction. Writing@CSU . Colorado State University. https://writing.colostate.edu/guides/guide.cfm?guideid=67

Short courses

Introduction to Research Methods and Statistics

9:30am to 5pm
Next start date: 13 Jan 2025

Book a place

13 January 2025 Book now

This five-day short course will give you a comprehensive introduction to the fundamental aspects of research methods and statistics . It's suitable for those new to quantitative research.

You'll look at topics ranging from study design, data type and graphs through to choice and interpretation of statistical tests - with a particular focus on standard errors, confidence intervals and p-values.

This course takes place over five days (9:30am to 5pm).

This course is delivered by UCL's Centre for Applied Statistics Courses (CASC), part of the UCL Great Ormond Street Institute of Child Health (ICH).

Course content

During this basic introductory course in research methodology and statistical analyses you'll cover a variety of topics.

This is a theory-led course, but you'll be given plenty of opportunities to apply the concepts via practical and interactive activities integrated throughout.

The topics covered include:

Introduction to quantitative research
Research question development
Study design, sampling and confounding
Types of data
Graphical displays of data and results
Summarising numeric and categorical data
Numeric and categorical differences between groups
Hypothesis testing
Confidence intervals and p-values
Parametric statistical tests
Non-parametric tests
Bootstrapping
Regression analysis

Many examples used in the course are related to health research, but the concepts you'll learn about can be applied to most other fields.

Eligibility

The course is suitable for those new to quantitative research.

Learning outcomes

By the end of this course you should have a good, practical understanding of:

research design considerations (question formulation, sample selection and randomisation, study design, and research protocols)
data types, and appropriate summaries and graphs of samples and differences
standard errors, confidence intervals and p-values
parametric and nonparametric assumptions and tests
how to select an appropriate statistical test

Cost and concessions

The fees are:

External delegates (non UCL) - £750
UCL staff, students, alumni - £375*
ICH/GOSH staff and doctoral students - free

* valid UCL email address and/or UCL alumni number required upon registration.

Certificates

You can request a certificate of attendance for all of our courses once you've completed it. Please send your request to [email protected]

Include the following in your email:

the name of the completed course for which you'd like a certificate
how you'd like your name presented on the certificate (if the name/format differs from the details you gave during registration)

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Read the cancellation policy for this course on the ICH website. Please send all cancellation requests to [email protected]

Find out about CASC's other statistics courses

CASC's stats courses are for anyone requiring an understanding of research methodology and statistical analyses. The courses will allow non-statisticians to interpret published research and/or undertake their own research studies.

Find out more about CASC's full range of statistics courses , and the continuing statistics training scheme (book six one-day courses and get a seventh free.)

Course team

Dr Eirini Koutoumanou

Eirini has a BSc in Statistics from Athens University of Economics and Business and an MSc in Statistics from Lancaster University (funded by the Engineering and Physical Sciences Research Council). She joined UCL GOS Institute of Child Health in 2008 to develop a range of short courses for anyone interested in learning new statistical skills. Soon after, CASC was born. In 2014, she was promoted to Senior Teaching Fellow. In 2019, she successfully passed her PhD viva on the topic of Copula models and their application within paediatric data. Since early 2020 she has been co-directing CASC with its founder, Emeritus Professor Angie Wade, and has been the sole Director of CASC since January 2022. Eirini was promoted to Associate Professor (Teaching) with effect from October 2022.

Dr Chibueze Ogbonnaya

Since joining the teaching team at CASC in February 2019, Chibueze has contributed to the teaching and development of short courses. He currently leads and co-leads short courses on MATLAB, missing data, regression analysis and survival analysis. Chibueze has a BSc in Statistics from the University of Nigeria, where he briefly worked as a teaching assistant after graduation. He then moved to the University of Nottingham for his MSc and PhD in Statistics. His research interests include functional data analysis, applied machine learning and distribution theory.

Dr Catalina Rivera Suarez

Catalina has been an Associate Lecturer (Teaching) at CASC since January 2021. She has a PhD in Psychology and an MSc in Applied Statistics from Indiana University. She’s passionate about teaching courses in research methods, statistics, and statistical software. Catalina’s research focuses on studying how caregivers support the development of children's attentional control and language. She implements multilevel modeling techniques to investigate the moment-to-moment dynamics of shared joint visual engagement, as well as the quality of the language input, influencing infant learning and sustained attention at multiple timescales.

Dr Manolis Bagkeris

Manolis has a BSc in Statistics and Actuarial-Financial Mathematics from the University of the Aegean and an MSc in Medical Statistics from the Athens University of Economics and Business (AUEB). He’s worked as a research assistant at University of Crete, UCL and Imperial College London. He’s been working at CASC since November 2021, providing short courses in research methods and statistics for people who want to develop or enhance their knowledge in interpreting and undertaking their own research. His interests include paediatric epidemiology, clinical and population health, HIV, mental health and development. He was awarded a PhD from UCL in 2021 on the topic of frailty, falls, bone mineral density and fractures among HIV-positive and HIV-negative controls in England and Ireland.

"All sessions were exceptionally organised and presented in a clear and engaging style. The lecturers were incredibly knowledgeable and flexible and patient to the different levels of understanding in the room. The key concepts of making inferences set out at the beginning and carried throughout were especially helpful.

"Explaining the visual representation of data was very useful, as was having examples in the workbooks to learn from and 'correct'."

"The most memorable session for me was the one about significance testing. I am sure it will be very useful in my practice."

Course information last modified: 29 Aug 2024, 09:49

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Course length: 5 days

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Research Methods, Statistics, and Applications

Student resources, welcome to the sage edge site for research methods, statistics, and applications , third edition.

The third edition of Research Methods, Statistics, and Applications by Kathrynn A. Adams and Eva K. McGuire consistently integrates the interrelated concepts of research methods and statistics to better explain how the research process requires a combination of these two elements. This best-selling combined text includes numerous examples and practical applications from the latest research across the social and behavioral sciences. The conversational tone and emphasis on decision-making engages students in the research process and demonstrates the value of rigorous research in academic settings and beyond. The end goal of this book is to spark students' interest in conducting research and to increase their ability to critically analyze research in their daily lives. The third edition includes a new chapter on measurement to better highlight the critical importance of this topic, updates for the 7th edition of the Publication Manual of the American Psychological Association , new examples related to social justice, a new section on case studies, and more thorough integration of research ethics information and tips throughout each chapter.

This site features an array of free resources you can access anytime, anywhere.

Acknowledgments

We gratefully acknowledge Kathrynn A. Adams and Eva K. McGuire for writing an excellent text. Special thanks are also due to Kathrynn A. Adams and Eva K. McGuire of Guilford College for developing the resources on this site.

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Knowledge Base

The Beginner's Guide to Statistical Analysis | 5 Steps & Examples

Statistical analysis means investigating trends, patterns, and relationships using quantitative data . It is an important research tool used by scientists, governments, businesses, and other organisations.

To draw valid conclusions, statistical analysis requires careful planning from the very start of the research process . You need to specify your hypotheses and make decisions about your research design, sample size, and sampling procedure.

After collecting data from your sample, you can organise and summarise the data using descriptive statistics . Then, you can use inferential statistics to formally test hypotheses and make estimates about the population. Finally, you can interpret and generalise your findings.

This article is a practical introduction to statistical analysis for students and researchers. We’ll walk you through the steps using two research examples. The first investigates a potential cause-and-effect relationship, while the second investigates a potential correlation between variables.

Step 1: write your hypotheses and plan your research design, step 2: collect data from a sample, step 3: summarise your data with descriptive statistics, step 4: test hypotheses or make estimates with inferential statistics, step 5: interpret your results, frequently asked questions about statistics.

To collect valid data for statistical analysis, you first need to specify your hypotheses and plan out your research design.

Writing statistical hypotheses

The goal of research is often to investigate a relationship between variables within a population . You start with a prediction, and use statistical analysis to test that prediction.

A statistical hypothesis is a formal way of writing a prediction about a population. Every research prediction is rephrased into null and alternative hypotheses that can be tested using sample data.

While the null hypothesis always predicts no effect or no relationship between variables, the alternative hypothesis states your research prediction of an effect or relationship.

Null hypothesis: A 5-minute meditation exercise will have no effect on math test scores in teenagers.
Alternative hypothesis: A 5-minute meditation exercise will improve math test scores in teenagers.
Null hypothesis: Parental income and GPA have no relationship with each other in college students.
Alternative hypothesis: Parental income and GPA are positively correlated in college students.

Planning your research design

A research design is your overall strategy for data collection and analysis. It determines the statistical tests you can use to test your hypothesis later on.

First, decide whether your research will use a descriptive, correlational, or experimental design. Experiments directly influence variables, whereas descriptive and correlational studies only measure variables.

In an experimental design , you can assess a cause-and-effect relationship (e.g., the effect of meditation on test scores) using statistical tests of comparison or regression.
In a correlational design , you can explore relationships between variables (e.g., parental income and GPA) without any assumption of causality using correlation coefficients and significance tests.
In a descriptive design , you can study the characteristics of a population or phenomenon (e.g., the prevalence of anxiety in U.S. college students) using statistical tests to draw inferences from sample data.

Your research design also concerns whether you’ll compare participants at the group level or individual level, or both.

In a between-subjects design , you compare the group-level outcomes of participants who have been exposed to different treatments (e.g., those who performed a meditation exercise vs those who didn’t).
In a within-subjects design , you compare repeated measures from participants who have participated in all treatments of a study (e.g., scores from before and after performing a meditation exercise).
In a mixed (factorial) design , one variable is altered between subjects and another is altered within subjects (e.g., pretest and posttest scores from participants who either did or didn’t do a meditation exercise).
Experimental
Correlational

First, you’ll take baseline test scores from participants. Then, your participants will undergo a 5-minute meditation exercise. Finally, you’ll record participants’ scores from a second math test.

In this experiment, the independent variable is the 5-minute meditation exercise, and the dependent variable is the math test score from before and after the intervention. Example: Correlational research design In a correlational study, you test whether there is a relationship between parental income and GPA in graduating college students. To collect your data, you will ask participants to fill in a survey and self-report their parents’ incomes and their own GPA.

Measuring variables

When planning a research design, you should operationalise your variables and decide exactly how you will measure them.

For statistical analysis, it’s important to consider the level of measurement of your variables, which tells you what kind of data they contain:

Categorical data represents groupings. These may be nominal (e.g., gender) or ordinal (e.g. level of language ability).
Quantitative data represents amounts. These may be on an interval scale (e.g. test score) or a ratio scale (e.g. age).

Many variables can be measured at different levels of precision. For example, age data can be quantitative (8 years old) or categorical (young). If a variable is coded numerically (e.g., level of agreement from 1–5), it doesn’t automatically mean that it’s quantitative instead of categorical.

Identifying the measurement level is important for choosing appropriate statistics and hypothesis tests. For example, you can calculate a mean score with quantitative data, but not with categorical data.

In a research study, along with measures of your variables of interest, you’ll often collect data on relevant participant characteristics.

Variable	Type of data
Age	Quantitative (ratio)
Gender	Categorical (nominal)
Race or ethnicity	Categorical (nominal)
Baseline test scores	Quantitative (interval)
Final test scores	Quantitative (interval)


Parental income	Quantitative (ratio)
GPA	Quantitative (interval)

In most cases, it’s too difficult or expensive to collect data from every member of the population you’re interested in studying. Instead, you’ll collect data from a sample.

Statistical analysis allows you to apply your findings beyond your own sample as long as you use appropriate sampling procedures . You should aim for a sample that is representative of the population.

Sampling for statistical analysis

There are two main approaches to selecting a sample.

Probability sampling: every member of the population has a chance of being selected for the study through random selection.
Non-probability sampling: some members of the population are more likely than others to be selected for the study because of criteria such as convenience or voluntary self-selection.

In theory, for highly generalisable findings, you should use a probability sampling method. Random selection reduces sampling bias and ensures that data from your sample is actually typical of the population. Parametric tests can be used to make strong statistical inferences when data are collected using probability sampling.

But in practice, it’s rarely possible to gather the ideal sample. While non-probability samples are more likely to be biased, they are much easier to recruit and collect data from. Non-parametric tests are more appropriate for non-probability samples, but they result in weaker inferences about the population.

If you want to use parametric tests for non-probability samples, you have to make the case that:

your sample is representative of the population you’re generalising your findings to.
your sample lacks systematic bias.

Keep in mind that external validity means that you can only generalise your conclusions to others who share the characteristics of your sample. For instance, results from Western, Educated, Industrialised, Rich and Democratic samples (e.g., college students in the US) aren’t automatically applicable to all non-WEIRD populations.

If you apply parametric tests to data from non-probability samples, be sure to elaborate on the limitations of how far your results can be generalised in your discussion section .

Create an appropriate sampling procedure

Based on the resources available for your research, decide on how you’ll recruit participants.

Will you have resources to advertise your study widely, including outside of your university setting?
Will you have the means to recruit a diverse sample that represents a broad population?
Do you have time to contact and follow up with members of hard-to-reach groups?

Your participants are self-selected by their schools. Although you’re using a non-probability sample, you aim for a diverse and representative sample. Example: Sampling (correlational study) Your main population of interest is male college students in the US. Using social media advertising, you recruit senior-year male college students from a smaller subpopulation: seven universities in the Boston area.

Calculate sufficient sample size

Before recruiting participants, decide on your sample size either by looking at other studies in your field or using statistics. A sample that’s too small may be unrepresentative of the sample, while a sample that’s too large will be more costly than necessary.

There are many sample size calculators online. Different formulas are used depending on whether you have subgroups or how rigorous your study should be (e.g., in clinical research). As a rule of thumb, a minimum of 30 units or more per subgroup is necessary.

To use these calculators, you have to understand and input these key components:

Significance level (alpha): the risk of rejecting a true null hypothesis that you are willing to take, usually set at 5%.
Statistical power : the probability of your study detecting an effect of a certain size if there is one, usually 80% or higher.
Expected effect size : a standardised indication of how large the expected result of your study will be, usually based on other similar studies.
Population standard deviation: an estimate of the population parameter based on a previous study or a pilot study of your own.

Once you’ve collected all of your data, you can inspect them and calculate descriptive statistics that summarise them.

Inspect your data

There are various ways to inspect your data, including the following:

Organising data from each variable in frequency distribution tables .
Displaying data from a key variable in a bar chart to view the distribution of responses.
Visualising the relationship between two variables using a scatter plot .

By visualising your data in tables and graphs, you can assess whether your data follow a skewed or normal distribution and whether there are any outliers or missing data.

A normal distribution means that your data are symmetrically distributed around a center where most values lie, with the values tapering off at the tail ends.

Mean, median, mode, and standard deviation in a normal distribution

In contrast, a skewed distribution is asymmetric and has more values on one end than the other. The shape of the distribution is important to keep in mind because only some descriptive statistics should be used with skewed distributions.

Extreme outliers can also produce misleading statistics, so you may need a systematic approach to dealing with these values.

Calculate measures of central tendency

Measures of central tendency describe where most of the values in a data set lie. Three main measures of central tendency are often reported:

Mode : the most popular response or value in the data set.
Median : the value in the exact middle of the data set when ordered from low to high.
Mean : the sum of all values divided by the number of values.

However, depending on the shape of the distribution and level of measurement, only one or two of these measures may be appropriate. For example, many demographic characteristics can only be described using the mode or proportions, while a variable like reaction time may not have a mode at all.

Calculate measures of variability

Measures of variability tell you how spread out the values in a data set are. Four main measures of variability are often reported:

Range : the highest value minus the lowest value of the data set.
Interquartile range : the range of the middle half of the data set.
Standard deviation : the average distance between each value in your data set and the mean.
Variance : the square of the standard deviation.

Once again, the shape of the distribution and level of measurement should guide your choice of variability statistics. The interquartile range is the best measure for skewed distributions, while standard deviation and variance provide the best information for normal distributions.

Using your table, you should check whether the units of the descriptive statistics are comparable for pretest and posttest scores. For example, are the variance levels similar across the groups? Are there any extreme values? If there are, you may need to identify and remove extreme outliers in your data set or transform your data before performing a statistical test.

	Pretest scores	Posttest scores
Mean	68.44	75.25
Standard deviation	9.43	9.88
Variance	88.96	97.96
Range	36.25	45.12
	30

From this table, we can see that the mean score increased after the meditation exercise, and the variances of the two scores are comparable. Next, we can perform a statistical test to find out if this improvement in test scores is statistically significant in the population. Example: Descriptive statistics (correlational study) After collecting data from 653 students, you tabulate descriptive statistics for annual parental income and GPA.

It’s important to check whether you have a broad range of data points. If you don’t, your data may be skewed towards some groups more than others (e.g., high academic achievers), and only limited inferences can be made about a relationship.

	Parental income (USD)	GPA
Mean	62,100	3.12
Standard deviation	15,000	0.45
Variance	225,000,000	0.16
Range	8,000–378,000	2.64–4.00
	653

A number that describes a sample is called a statistic , while a number describing a population is called a parameter . Using inferential statistics , you can make conclusions about population parameters based on sample statistics.

Researchers often use two main methods (simultaneously) to make inferences in statistics.

Estimation: calculating population parameters based on sample statistics.
Hypothesis testing: a formal process for testing research predictions about the population using samples.

You can make two types of estimates of population parameters from sample statistics:

A point estimate : a value that represents your best guess of the exact parameter.
An interval estimate : a range of values that represent your best guess of where the parameter lies.

If your aim is to infer and report population characteristics from sample data, it’s best to use both point and interval estimates in your paper.

You can consider a sample statistic a point estimate for the population parameter when you have a representative sample (e.g., in a wide public opinion poll, the proportion of a sample that supports the current government is taken as the population proportion of government supporters).

There’s always error involved in estimation, so you should also provide a confidence interval as an interval estimate to show the variability around a point estimate.

A confidence interval uses the standard error and the z score from the standard normal distribution to convey where you’d generally expect to find the population parameter most of the time.

Hypothesis testing

Using data from a sample, you can test hypotheses about relationships between variables in the population. Hypothesis testing starts with the assumption that the null hypothesis is true in the population, and you use statistical tests to assess whether the null hypothesis can be rejected or not.

Statistical tests determine where your sample data would lie on an expected distribution of sample data if the null hypothesis were true. These tests give two main outputs:

A test statistic tells you how much your data differs from the null hypothesis of the test.
A p value tells you the likelihood of obtaining your results if the null hypothesis is actually true in the population.

Statistical tests come in three main varieties:

Comparison tests assess group differences in outcomes.
Regression tests assess cause-and-effect relationships between variables.
Correlation tests assess relationships between variables without assuming causation.

Your choice of statistical test depends on your research questions, research design, sampling method, and data characteristics.

Parametric tests

Parametric tests make powerful inferences about the population based on sample data. But to use them, some assumptions must be met, and only some types of variables can be used. If your data violate these assumptions, you can perform appropriate data transformations or use alternative non-parametric tests instead.

A regression models the extent to which changes in a predictor variable results in changes in outcome variable(s).

A simple linear regression includes one predictor variable and one outcome variable.
A multiple linear regression includes two or more predictor variables and one outcome variable.

Comparison tests usually compare the means of groups. These may be the means of different groups within a sample (e.g., a treatment and control group), the means of one sample group taken at different times (e.g., pretest and posttest scores), or a sample mean and a population mean.

A t test is for exactly 1 or 2 groups when the sample is small (30 or less).
A z test is for exactly 1 or 2 groups when the sample is large.
An ANOVA is for 3 or more groups.

The z and t tests have subtypes based on the number and types of samples and the hypotheses:

If you have only one sample that you want to compare to a population mean, use a one-sample test .
If you have paired measurements (within-subjects design), use a dependent (paired) samples test .
If you have completely separate measurements from two unmatched groups (between-subjects design), use an independent (unpaired) samples test .
If you expect a difference between groups in a specific direction, use a one-tailed test .
If you don’t have any expectations for the direction of a difference between groups, use a two-tailed test .

The only parametric correlation test is Pearson’s r . The correlation coefficient ( r ) tells you the strength of a linear relationship between two quantitative variables.

However, to test whether the correlation in the sample is strong enough to be important in the population, you also need to perform a significance test of the correlation coefficient, usually a t test, to obtain a p value. This test uses your sample size to calculate how much the correlation coefficient differs from zero in the population.

You use a dependent-samples, one-tailed t test to assess whether the meditation exercise significantly improved math test scores. The test gives you:

a t value (test statistic) of 3.00
a p value of 0.0028

Although Pearson’s r is a test statistic, it doesn’t tell you anything about how significant the correlation is in the population. You also need to test whether this sample correlation coefficient is large enough to demonstrate a correlation in the population.

A t test can also determine how significantly a correlation coefficient differs from zero based on sample size. Since you expect a positive correlation between parental income and GPA, you use a one-sample, one-tailed t test. The t test gives you:

a t value of 3.08
a p value of 0.001

The final step of statistical analysis is interpreting your results.

Statistical significance

In hypothesis testing, statistical significance is the main criterion for forming conclusions. You compare your p value to a set significance level (usually 0.05) to decide whether your results are statistically significant or non-significant.

Statistically significant results are considered unlikely to have arisen solely due to chance. There is only a very low chance of such a result occurring if the null hypothesis is true in the population.

This means that you believe the meditation intervention, rather than random factors, directly caused the increase in test scores. Example: Interpret your results (correlational study) You compare your p value of 0.001 to your significance threshold of 0.05. With a p value under this threshold, you can reject the null hypothesis. This indicates a statistically significant correlation between parental income and GPA in male college students.

Note that correlation doesn’t always mean causation, because there are often many underlying factors contributing to a complex variable like GPA. Even if one variable is related to another, this may be because of a third variable influencing both of them, or indirect links between the two variables.

Effect size

A statistically significant result doesn’t necessarily mean that there are important real life applications or clinical outcomes for a finding.

In contrast, the effect size indicates the practical significance of your results. It’s important to report effect sizes along with your inferential statistics for a complete picture of your results. You should also report interval estimates of effect sizes if you’re writing an APA style paper .

With a Cohen’s d of 0.72, there’s medium to high practical significance to your finding that the meditation exercise improved test scores. Example: Effect size (correlational study) To determine the effect size of the correlation coefficient, you compare your Pearson’s r value to Cohen’s effect size criteria.

Decision errors

Type I and Type II errors are mistakes made in research conclusions. A Type I error means rejecting the null hypothesis when it’s actually true, while a Type II error means failing to reject the null hypothesis when it’s false.

You can aim to minimise the risk of these errors by selecting an optimal significance level and ensuring high power . However, there’s a trade-off between the two errors, so a fine balance is necessary.

Frequentist versus Bayesian statistics

Traditionally, frequentist statistics emphasises null hypothesis significance testing and always starts with the assumption of a true null hypothesis.

However, Bayesian statistics has grown in popularity as an alternative approach in the last few decades. In this approach, you use previous research to continually update your hypotheses based on your expectations and observations.

Bayes factor compares the relative strength of evidence for the null versus the alternative hypothesis rather than making a conclusion about rejecting the null hypothesis or not.

Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.

The research methods you use depend on the type of data you need to answer your research question .

If you want to measure something or test a hypothesis , use quantitative methods . If you want to explore ideas, thoughts, and meanings, use qualitative methods .
If you want to analyse a large amount of readily available data, use secondary data. If you want data specific to your purposes with control over how they are generated, collect primary data.
If you want to establish cause-and-effect relationships between variables , use experimental methods. If you want to understand the characteristics of a research subject, use descriptive methods.

Statistical analysis is the main method for analyzing quantitative research data . It uses probabilities and models to test predictions about a population from sample data.

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T-Distribution | What It Is and How To Use It (With Examples)
The Standard Normal Distribution | Calculator, Examples & Uses
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Understanding Confidence Intervals | Easy Examples & Formulas
Variability | Calculating Range, IQR, Variance, Standard Deviation
What is Effect Size and Why Does It Matter? (Examples)
What Is Interval Data? | Examples & Definition
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What Is the Mode in Statistics? | Definition, Examples & Calculator

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Research Methods and Statistics in Psychology

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Description

Research Methods and Statistics in Psychology provides a seamless introduction to the subject, identifying various research areas and analyzing how one can approach them statistically. The text provides a solid empirical foundation for undergraduate psychology majors, and it prepares the reader to think critically and evaluate psychological research and claims they might hear in the news or popular press. This second edition features updated examples of research and new illustrations of important principles. It also includes updated coverage of ethical…

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Key features

Presents the pitfalls of research so students can avoid them and understand the problem solving aspect of research.
Includes 'living' research examples that are contemporary and interesting to capture student interest in the topic
Offers guidelines for creating American Psychological Association-style papers, presentations and posters

About the book

DOI https://doi.org/10.1017/9781108399555
Subjects Psychology, Psychology Research Methods and Statistics, Qualitative Research Methods
Publication date: 14 March 2019
ISBN: 9781108423113
Dimensions (mm): 253 x 203 mm
Weight: 1.44kg
Contains: 52 b/w illus.
Page extent: 530 pages
Availability: In stock
ISBN: 9781108436243
Weight: 1.24kg
Availability: Available
Publication date: 12 December 2018
ISBN: 9781108399555

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Bernard C. Beins is Professor of Psychology at Ithaca College, New York. He received the Charles Brewer Excellence in Teaching Award from the American Psychological Foundation of American Psychological Association. He has authored, co-authored, or co-edited 17 traditional and electronic books on research, critical thinking, and pedagogy; 50 peer-reviewed articles and book chapters; over 275 presentations; and overseen over 100 student presentations. He is a Fellow of the Association for Psychological Science; American Psychological Association Divisions 1 (Society for General Psychology), 2 (Society for the Teaching of Psychology), 3 (Society for Experimental and Cognitive Science), and 52 (International Psychology); and the Eastern Psychological Association.

Maureen A. McCarthy is Dean of the College of Sciences and Humanities and Professor of Psychological Science at Ball State University, Indiana. She is a fellow of the Association for Psychological Science, the American Psychological Association (Division 2), and the Eastern Psychological Association. She has authored more than 50 publications including refereed journal articles, book chapters, edited books, policy documents, and books.

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Statistical methods in research

Affiliation.

1 The Sackler Institute of Pulmonary Pharmacology, School of Biomedical Science, King's College London, 5th Floor Franklin Wilkins Building, SEI9NH Waterloo Campus, London, UK. [email protected]
PMID: 21607874
DOI: 10.1007/978-1-61779-126-0_26

Statistical methods appropriate in research are described with examples. Topics covered include the choice of appropriate averages and measures of dispersion to summarize data sets, and the choice of tests of significance, including t-tests and a one- and a two-way ANOVA plus post-tests for normally distributed (Gaussian) data and their non-parametric equivalents. Techniques for transforming non-normally distributed data to more Gaussian distributions are discussed. Concepts of statistical power, errors and the use of these in determining the optimal size of experiments are considered. Statistical aspects of linear and non-linear regression are discussed, including tests for goodness-of-fit to the chosen model and methods for comparing fitted lines and curves.

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Accounting for Competing Risks in Clinical Research

1 Institute for Clinical Evaluative Sciences (ICES), Toronto, Ontario, Canada
2 Institute of Health Policy, Management and Evaluation, University of Toronto, Toronto, Ontario, Canada
3 Sunnybrook Research Institute, Toronto, Ontario, Canada
4 NHS Blood and Transplant, Bristol, United Kingdom
5 Department of Biomedical Data Sciences, Leiden University Medical Center, Leiden, the Netherlands
Original Investigation Metformin or Sulfonylurea Use in Kidney Disease Christianne L. Roumie, MD, MPH; Jonathan Chipman, PhD; Jea Young Min, PharmD, MPH, PhD; Amber J. Hackstadt, PhD; Adriana M. Hung, MD, MPH; Robert A. Greevy Jr, PhD; Carlos G. Grijalva, MD, MPH; Tom Elasy, MD, MPH; Marie R. Griffin, MD, MPH JAMA

Survival analyses are statistical methods for the analysis of time-to-event outcomes. 1 An example is time from study entry to death. A competing risk is an event whose occurrence precludes the occurrence of the primary event of interest. In a study whose outcome is time to death due to cardiovascular causes, for instance, death due to a noncardiovascular cause is a competing risk. Conventional statistical methods for the analysis of survival data typically aim to estimate the probability of the event of interest over time or the effect of a risk factor or treatment on that probability or on the intensity with which events occur. These methods require modification in the presence of competing risks. A key feature of survival analysis is the ability to properly account for censoring, which occurs when the outcome event is not observed before the end of the study participant’s follow-up period.

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Postgraduate study
Postgraduate taught courses

Psychological Research Methods with Advanced Statistics

Explore this course:.

Applications for 2024 entry closed at 5pm on Friday 6 September. Applications for 2025 entry open on Monday 16 September.

School of Psychology, Faculty of Science

Student conducting eye tracking experiment

Course description

Through our advanced statistical training program, you’ll learn the latest research methods that are needed to handle and interpret large datasets documenting human behaviour, preparing you for clinical training, a PhD or an exciting psychological career.

Our advanced statistical training program will equip you with the latest modelling techniques, ranging from generalised and multilevel models to the intricacies of structural equation modelling. We'll teach you essential skills and provide hands-on opportunities to apply these techniques using the R statistical environment.

Whether your interests lie in cognitive and developmental psychology, or you're drawn to social and clinical psychology, our course is tailored so you can apply advanced statistical methods across the breadth of the discipline.

Alongside your statistical training you'll learn a broad range of research techniques such as neuroimaging (EEG, fMRI), behavioural genetics, clinical trial design, qualitative interview, diary study methodologies and specialist methods for working with infants, children and clinical populations.

We’ll also train you in a range of skills that are important for psychologists in academia and professional roles: you'll understand ethical issues in research, learn how to write a grant proposal, and develop your presentation skills ready to take part in our summer postgraduate students' conference

The research project and literature review elements of the course, which include coverage of meta-analysis, give you the opportunity to focus on a chosen psychological research question in detail under the supervision of one of our world-class researchers. You can choose a supervisor from an area of psychology that matches your research interests and future career aspirations within cognitive, developmental, social or clinical psychology.

This project gives you the opportunity to put your new statistical skills and research methods knowledge into practice while addressing an issue at the cutting edge of psychological research.

MSc research projects and literature reviews often form the basis of publications in peer-reviewed journals.

Identifying subtypes of autism
Relationships between drinking motives and alcohol consumption: secondary data analysis of the Offending, Crime and Justice Survey
Comparing the characteristics of child psychopathology reported by self, parent and teacher: Analysis of the British Child and Adolescent Mental Health Survey.
Simmonds-Buckley, M., Osivwemu, E. O., Kellett, S., & Taylor, C. (2022). The acceptability of cognitive analytic therapy (CAT): Meta-analysis and benchmarking of treatment refusal and treatment dropout rates . Clinical Psychology Review , 96 , 102187.
Griffin, B., Conner, M., & Norman, P. (2022). Applying an extended protection motivation theory to predict Covid-19 vaccination intentions and uptake in 50–64 year olds in the UK . Social Science & Medicine, 298 , 114819.
Tait, J., Edmeade, L., & Delgadillo, J. (2022). Are depressed patients’ coping strategies associated with psychotherapy treatment outcomes? Psychology and Psychotherapy: Theory, Research and Practice, 95 , 98–112.
Vaci, N., Stafford, T., Ren, Y., & Habgood, J. (2024). Experiments in games: Modding the Zool Redimensioned warning system to support players’ skill acquisition and attrition rate . Proceedings of the Annual Meeting of the Cognitive Science Society, 46(0).

Psychological Research Methods at Sheffield

In addition to Psychological Research Methods with Advanced Statistics, at Sheffield we offer two other specialist masters courses in this area that allow you to specialise further and develop the skills you need for a successful career:

MSc Psychological Research Methods
MSc Psychological Research Methods with Data Science

Book a 15-minute online meeting with our director of postgraduate recruitment to find out more information and ask further questions.

Book an appointment with Dr Vanessa Loaiza

An open day gives you the best opportunity to hear first-hand from our current students and staff about our courses.

You may also be able to pre-book a department/school visit as part of a campus tour. Open days and campus tours

1 year full-time
2 years part-time

You’ll learn through hands-on laboratory sessions, problem-solving classes, lectures, seminars and individual projects.

Your individual research project is the biggest part of your course, where you’ll be working alongside PhD students and experienced postdoctoral researchers. Here you’ll gain extensive first-hand experience as a researcher, and will have access to the outstanding research facilities in Sheffield.

You'll be assessed through formal examinations and coursework which may include essays, poster presentations, coding assignments, and a dissertation.

Regular feedback is also provided, so you can understand your own development throughout the course.

Your career

This course is great preparation for a PhD, and our graduates have gone on to PhD training with an advanced quantitative dimension in neuroimaging, health psychology and social psychology. Others have started their career in the higher education, health or charity sectors working as:

Graduate Statistical Analyst or Programme Analyst in Higher Education.
Psychological Wellbeing Practitioner, Assistant Psychologist or Research Assistant in NHS trusts or other public health organisations.
Psychological Researcher or Lecturer in academia.

Learn more about where your psychology masters could take you here .

By choosing the School of Psychology for your postgraduate study, you'll join our global alumni network, where hundreds of our employed graduates are working across academia, healthcare, and related fields, and completing further study around the world. Explore our interactive map of graduate destinations:

School of Psychology

The School of Psychology at Sheffield is focused on exploring the science behind the human brain and human behaviour.

Our teaching is informed by cutting-edge scientific research, which ranges from cognitive and neural processes across the lifespan to the wellbeing of individuals and society . All of this has an impact on the population.

Our work explores child development, psychological therapies, health and wellbeing, lifestyle choices, cognitive behavioural therapy, safe driving, mother-baby interaction, autism, Parkinson's disease, and reducing prejudice and inequality. It’s research like this that our students are able to get involved in throughout their course.

At Sheffield, we have a range of practical teaching and research facilities where you can get hands-on, applying the knowledge you’ve gained in your masters.

For your statistical training, we have computer labs where you can access industry standard statistical analysis software SPSS, computational modelling software MATLAB, as well as flexible programming languages Python and R.

You’ll also have the chance to access a range of tools for testing participants during your research projects. Depending on your project, these may include eye-tracking technology used in perception studies, TMS and TDCS equipment for experiments involving brain stimulation, and our state-of-the-art EEG suite for measuring brain activity. Individual and group testing rooms are also available.

Student profiles

My dissertation supervisor was enthusiastic and engaging, providing guidance and support

Peter Carr Statistical Analyst in Higher Education, MSc Psychological Research Methods with Advanced Statistics

Peter began studying the MSc Psychological Research Methods with Advanced Statistics course to help him to develop the strong statistical and data science skills to be able to pursue a career in this area.

Entry requirements

Minimum 2:1 undergraduate honours degree in a relevant subject with relevant modules.

Subject requirements

We accept degrees in the following subject areas:

Experimental Psychology
Psychology with Research Methods
Quantitative Psychology

We may be able to consider degrees relating to Statistics for Psychology.

Module requirements

You should have studied at least one module from the following areas:

Advanced Research Methods in Psychology
Data Analysis in Psychology
Experimental Design
Psychology of Research
Quantitative Research Methods
Research Ethics in Psychology
Research Methods in Psychology
Research Skills for Psychology
Scientific Writing for Psychology
Statistics for Psychology

IELTS 6.5 (with 6 in each component) or University equivalent

If you're an international student who does not meet the entry requirements for this course, you have the opportunity to apply for a pre-masters programme in Science and Engineering at the University of Sheffield International College . This course is designed to develop your English language and academic skills. Upon successful completion, you can progress to degree level study at the University of Sheffield.

If you have any questions about entry requirements, please contact the school/department .

Fees and funding

Each year we offer a select number of bursaries to students on our courses. If you're awarded a bursary you'll receive a £1,500 reduction in your tuition fees. These bursaries are awarded on a competitive basis, based on:

academic performance as indicated by a grade point average and transcript
other relevant skills and knowledge (for example, programming courses outside the degree or relevant work experience)
research activity (co-authoring papers, conference presentations, etc)
personal statement, which should include information on why you want to do the course you have applied for and how it fits with your aspirations

To be considered for a bursary in the year that you intend to start your course, submit your application to study with us by 31 May. All applications received before this deadline will automatically be considered for a bursary.

Applications for 2024 entry closed at 5pm on Friday 6 September. Applications for 2025 open on Monday 16 September.

More information

[email protected] +44 114 222 6533

Quantitative Methodology: Measurement and Statistics, P.B.C.

Spring

June 30, 2025

The Quantitative Methodology: Measurement and Statistics—Post-Baccalaureate Certificate program is designed for doctoral students enrolled at the University of Maryland who seek specialized training in quantitative methods to complement their primary area of study. This highly ranked certificate program equips you with essential skills and knowledge in advanced statistical analysis, providing a valuable quantitative specialization applicable to many academic and professional pursuits.

Key Features

Customized Curriculum : Tailor your course selection to align with your research interests and career goals in consultation with your assigned QMMS certificate advisor.
Core Course Foundation : Build a strong quantitative foundation through completion of four common core courses, covering applied measurement, general linear models, causal inference, and evaluation methods.
Interdisciplinary Opportunities : Collaborate with faculty and students from diverse academic backgrounds, enriching your learning experience and broadening your perspective on quantitative research methodologies.
Demonstrate proficiency in the application of general and generalized linear models for analyzing data across various research contexts.
Understand and critically evaluate different research designs, ensuring the selection of appropriate methodologies to address research questions effectively.
Gain a solid understanding of the fundamentals of measurement, including reliability, validity, and scale construction, to inform data collection and interpretation.
Acquire practical skills in utilizing data analytics software packages to conduct statistical analysis and interpret research findings accurately.

If you are a prospective student who has questions about this program, please contact a QMMS faculty member or Dr. Gregory R. Hancock, [email protected]

Complete the Enrollment Form

Per University policy , you cannot graduate and obtain a Ph.D. before completing the QMMS certificate. However, they can be completed within the same semester.

Yi Feng, student, Quantitative Methodology: Measurement and Statistics

Courses in this certificate are carefully selected. Your specific program of study will be structured to take into account your background and goals.

QMMS Graduate Student Handbook Program of Study The certificate requires completion of 21 credits, including the following four common core courses:

QMMS 623 Applied Measurement: Issues and Practices (3)
QMMS 646 General Linear Models I (3)
QMMS 647 Causal Inference and Evaluation Methods (3)
QMMS 651 General Linear Models II (3)

The courses to be taken for the remaining nine credits should be chosen in consultation with your assigned QMMS certificate advisor.

You must maintain a grade point average of at least 3.5 in courses taken for the certificate. Also, you must complete each course in the certificate with a grade of B or better. If a lower grade is obtained in a given course, then the course in question must be repeated until this grade requirement is achieved or not counted in the certificate and another course substituted.

Sep 17 Graduate Fair Expo Sep 17, 2024 4:00 – 6:00 pm

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Active funding opportunity

Nsf 24-587: research on the science and technology enterprise: indicators, statistics, and methods (ncses s&t), program solicitation, document information, document history.

Posted: June 30, 2024
Replaces: NSF 21-627

Program Solicitation NSF 24-587

Directorate for Social, Behavioral and Economic Sciences
National Center for Science and Engineering Statistics

Full Proposal Deadline(s) (due by 5 p.m. submitting organization’s local time):

January 21, 2025

Third Tuesday in January, Annually Thereafter

June 17, 2025

Third Tuesday in June, Annually Thereafter

Important Information And Revision Notes

Any proposal submitted in response to this solicitation should be submitted in accordance with the NSF Proposal & Award Policies & Procedures Guide (PAPPG) that is in effect for the relevant due date to which the proposal is being submitted. The NSF PAPPG is regularly revised and it is the responsibility of the proposer to ensure that the proposal meets the requirements specified in this solicitation and the applicable version of the PAPPG. Submitting a proposal prior to a specified deadline does not negate this requirement.

Summary Of Program Requirements

General information.

Program Title:

Research on the Science and Technology Enterprise: Indicators, Statistics, and Methods (NCSES S&T)

The National Center for Science and Engineering Statistics (NCSES) of the National Science Foundation (NSF) is one of the thirteen principal federal statistical agencies within the United States. It is responsible for the collection, acquisition, analysis, reporting and dissemination of objective, statistical data related to the science and technology (S&T) enterprise in the United States and other nations that is relevant and useful to practitioners, researchers, policymakers and the public. NCSES uses this information to prepare a number of statistical data reports including Women, Minorities and Persons with Disabilities in Science and Engineering and the National Science Board's biennial report, Science and Engineering (S&E) Indicators . The Center would like to enhance its efforts to support analytic and methodological research in support of its surveys as well as promote the education and training of researchers in the use of large-scale nationally representative datasets. NCSES welcomes efforts by the research community to use NCSES or other data to conduct research on the S&T enterprise, develop improved survey methodologies that could benefit NCSES surveys, explore alternate data sources that could supplement NCSES data, create and improve indicators of S&T activities and resources, strengthen methodologies to analyze S&T statistical data, and explore innovative ways to communicate S&T statistics. To that end, NCSES invites proposals for individual or multi-investigator research projects, doctoral dissertation improvement awards, conferences, experimental research, survey research and data collection, and dissemination projects under its program for Research on the Science and Technology Enterprise: Indicators, Statistics, and Methods (NCSES S&T).

Broadening Participation In STEM:

NSF recognizes the unique lived experiences of individuals from communities that are underrepresented and/or underserved in science, technology, engineering, and mathematics (STEM) and the barriers to inclusion and access to STEM education and careers. NSF highly encourages the leadership, partnership, and contributions in all NSF opportunities of individuals who are members of such communities supported by NSF. This includes leading and designing STEM research and education proposals for funding; serving as peer reviewers, advisory committee members, and/or committee of visitor members; and serving as NSF leadership, program, and/or administrative staff. NSF also highly encourages demographically diverse institutions of higher education (IHEs) to lead, partner, and contribute to NSF opportunities on behalf of their research and education communities. NSF expects that all individuals, including those who are members of groups that are underrepresented and/or underserved in STEM, are treated equitably and inclusively in the Foundation's proposal and award process.

NSF encourages IHEs that enroll, educate, graduate, and employ individuals who are members of groups underrepresented and/or underserved in STEM education programs and careers to lead, partner, and contribute to NSF opportunities, including leading and designing STEM research and education proposals for funding. Such IHEs include, but may not be limited to, community colleges and two-year institutions, mission-based institutions such as Historically Black Colleges and Universities (HBCUs), Tribal Colleges and Universities (TCUs), women's colleges, and institutions that primarily serve persons with disabilities, as well as institutions defined by enrollment such as Predominantly Undergraduate Institutions (PUIs), Minority-Serving Institutions (MSIs), and Hispanic Serving Institutions (HSIs).

"Broadening participation in STEM" is the comprehensive phrase used by NSF to refer to the Foundation's goal of increasing the representation and diversity of individuals, organizations, and geographic regions that contribute to STEM teaching, research, and innovation. To broaden participation in STEM, it is necessary to address issues of equity, inclusion, and access in STEM education, training, and careers. Whereas all NSF programs might support broadening participation components, some programs primarily focus on supporting broadening participation research and projects. Examples can be found on the NSF Broadening Participation in STEM website.

Cognizant Program Officer(s):

Please note that the following information is current at the time of publishing. See program website for any updates to the points of contact.

Sharon A. Boivin, telephone: (703) 292-4263, email: [email protected]

47.075 --- Social Behavioral and Economic Sciences

Award Information

Anticipated Type of Award: Standard Grant or Continuing Grant

Based on the quality of proposals and the availability of funds, NSF expects to make 5 to 10 awards each year.

subject to the availability of funds

Eligibility Information

Who May Submit Proposals:

Proposals may only be submitted by the following: Standard research proposals: Institutions of Higher Education (IHEs): Two- and four-year IHEs (including community colleges) accredited in, and having a campus located in the US, acting on behalf of their faculty members. Special Instructions for International Branch Campuses of US IHEs: If the proposal includes funding to be provided to an international branch campus of a US institution of higher education (including through use of subawards and consultant arrangements), the proposer must explain the benefit(s) to the project of performance at the international branch campus, and justify why the project activities cannot be performed at the US campus. Non-profit, non-academic organizations: Independent museums, observatories, research laboratories, professional societies and similar organizations located in the U.S. that are directly associated with educational or research activities. Tribal Nations: An American Indian or Alaska Native tribe, band, nation, pueblo, village, or community that the Secretary of the Interior acknowledges as a federally recognized tribe pursuant to the Federally Recognized Indian Tribe List Act of 1994, 25 U.S.C. §§ 5130-5131. Doctoral Dissertation Research Improvement Grant proposals: Doctoral Degree granting IHEs accredited in, and having a campus located in, the US acting on behalf of their faculty members.

Who May Serve as PI:

Standard research proposals: No special restrictions or limits. Doctoral Dissertation Research Improvement Grant proposals: The dissertation advisor must be listed as the Principal Investigator and the student must be listed as the co-Principal Investigator.

Limit on Number of Proposals per Organization:

There are no restrictions or limits.

Limit on Number of Proposals per PI or co-PI:

Proposal Preparation and Submission Instructions

A. proposal preparation instructions.

Letters of Intent: Not required
Preliminary Proposal Submission: Not required

Full Proposals:

Full Proposals submitted via Research.gov: NSF Proposal and Award Policies and Procedures Guide (PAPPG) guidelines apply. The complete text of the PAPPG is available electronically on the NSF website at: https://www.nsf.gov/publications/pub_summ.jsp?ods_key=pappg .
Full Proposals submitted via Grants.gov: NSF Grants.gov Application Guide: A Guide for the Preparation and Submission of NSF Applications via Grants.gov guidelines apply (Note: The NSF Grants.gov Application Guide is available on the Grants.gov website and on the NSF website at: https://www.nsf.gov/publications/pub_summ.jsp?ods_key=grantsgovguide ).

B. Budgetary Information

Cost Sharing Requirements:

Inclusion of voluntary committed cost sharing is prohibited.

Indirect Cost (F&A) Limitations:

Not Applicable

Other Budgetary Limitations:

C. Due Dates

Proposal review information criteria.

Merit Review Criteria:

National Science Board approved criteria. Additional merit review criteria apply. Please see the full text of this solicitation for further information.

Award Administration Information

Award Conditions:

Additional award conditions apply. Please see the full text of this solicitation for further information.

Reporting Requirements:

Standard NSF reporting requirements apply.

I. Introduction

The National Center for Science and Engineering Statistics (NCSES) of the National Science Foundation (NSF) is responsible for the collection, acquisition, analysis, reporting and dissemination of objective, statistical data related to the science and technology (S&T) enterprise in the United States and other nations. This information should be relevant and useful to practitioners, researchers, policymakers and the public. NCSES uses this information to prepare a number of statistical data reports as well as analytical reports including Women, Minorities and Persons with Disabilities in Science and Engineering and the National Science Board's biennial report, Science and Engineering (S&E) Indicators.

The America COMPETES Reauthorization Act codifies the role of NCSES in supporting research using the data that it collects and its role in research methodologies related to its work. The legislation specifies the responsibilities of NCSES in supporting the education and training of researchers who use large-scale data sets, such as the ones NCSES now collects. The following activities form the core of NCSES work:

The collection, acquisition, analysis, reporting, and dissemination of statistical data related to the United States and other nations;
Support of research that uses NCSES data;
Methodological research in areas related to its work; and
Education and training of researchers in the use of large-scale nationally representative data sets.

II. Program Description

NCSES welcomes proposals for research, conferences, and studies to advance the understanding of the S&T enterprise and encourage development of methods that will improve the quality of our data. Research could include: improved approaches to indicator construction and presentation, new S&T indicator development, strengthening of data collection methodologies and privacy protection to improve surveys that collect S&T data, investigations of alternate data sources to study S&T topics, analyses to inform STEM education and workforce policy, and innovations in the communication of S&T statistics. NCSES encourages proposals that analyze NCSES data or NCSES data in conjunction with those from other sources but does not limit the work to the analysis of the data it collects.

A. AREAS OF INTEREST

Potential topics for consideration include but are not limited to:

Improving analytical techniques to produce better indicators of issues related to: (1) the education and retention of scientists and engineers including minorities, women, or persons with disabilities as described in the NCSES publication Diversity and STEM: Women, Minorities, and Persons with Disabilities 2023 | NSF - National Science Foundation , (2) the demand, supply, career pathways, and/or characteristics of science and engineering personnel, including those without bachelor’s degrees (3) outcomes and impacts of research and development (R&D) expenditures in various sectors, countries, and fields including emerging science and technology fields, (4) estimates of current and near-term future S&T resources; and (5) measures of U.S. competitiveness in S&T.

Developing new and/or improved methods of measuring the inputs, outputs, interactions, and social or economic impacts of S&T activities. These methods could involve the use of administrative records, social media, or novel data extraction methods.

Developing new data, analyses, and/or indicators of the globalization of science, engineering, and technology, as well as analyses leading to a better understanding of the changing global economy. This could include: international comparisons of S&T capabilities and activities, indicators of international education and mobility of scientists and engineers, and foreign investment in S&T activities.
Improving data collection methodologies for S&T surveys and censuses, including those conducted by NCSES. Such studies could research improvements in the target population, sample frame, and sample design, focusing on coverage and sampling error. Also included are developments of new data collection techniques and operational efficiencies such as adaptive survey design and passive data collection. Studies focused on the respondent experience and reduction in respondent burden such as modular survey design are also relevant.
Improving analysis and data processing methodologies for NCSES data by researching topics such as imputation techniques, privacy protections, or data consistency with related surveys or administrative data. This research could also involve investigations of linkage of alternate data sources to supplement NCSES data and reporting.

Pursuing innovations in the dissemination of S&T statistics to encourage communication of the information in a timely and user-friendly fashion. This could include interactive visualizations, studies of user needs, and new reporting formats for indicators.

B. DATA AVAILABILITY

NCSES encourages proposers to use NCSES data for their research. NCSES conducts the following surveys for which data are available:

STEM Education

Survey of Graduate Students and Postdoctorates in Science and Engineering (GSS)

Survey of Earned Doctorates (SED)

Science and Engineering Workforce

Early Career Doctorates Survey (ECDS)

Survey of Doctorate Recipients (SDR)

National Survey of College Graduates (NSCG)

National Training, Education, and Workforce Survey (NTEWS)

Survey of Postdocs at Federally Funded Research and Development Centers

Government Funding for Science and Engineering

S urvey of Federal Funds for Research and Development

Survey of Federal Science and Engineering Support to Universities, Colleges, and Nonprofit Institutions

Survey of State Research and Development Expenditures

Higher Education Research and Development

Higher Education Research and Development Survey (HERD)

Survey of Science and Engineering Research Facilities

Research and Development

Annual Business Survey (ABS)

Business Enterprise Research and Development Survey (BERD)

Federal Facilities Research and Development Survey

FFRDS Research and Development Survey

Nonprofit Research Activities Survey (NPRA)

For a broad overview of all of the surveys see: https://www.nsf.gov/statistics/srvyoverview/overview.cfm

To explore public use data, see: https://ncsesdata.nsf.gov/explorer .

C. DATA ACQUISITION

If proposers expect to use existing datasets, the proposal should indicate what those datasets are and whether the proposer expects to be able to acquire the data. Some NCSES datasets do require special procedures to acquire data. Information about data access can be found here: Explore Data | NSF - National Science Foundation .

Restricted Use Data Licensing

NCSES grants licenses to securely access restricted use microdata files under certain conditions. Licenses are only needed for microdata not available in public use files .

Restricted use microdata licenses are available from NCSES for the following:

Early Career Doctorate Survey (ECDS)
National Survey of Recent College Graduates (NSRCG)
Scientists and Engineers Statistical Data System (SESTAT) Integrated File
Survey of Doctorate Recipients (SDR)/SDR Longitudinal (LSDR)
Survey of Earned Doctorates (SED)/Doctorate Record File (DRF)

The process of applying for access to NCSES data is evolving. The Foundations for Evidence-Based Policymaking Act of 2018 called for the federal government to establish a standard application process (SAP) through which agencies; the Congressional Budget Office; state, local, and tribal governments; researchers; and other individuals, as appropriate, may apply for access to restricted use microdata. In response, the federal statistical system developed the SAP Portal at www.researchdatagov.org .

The SAP Portal is a Web-based metadata catalog and application portal that serves as the “front door” to apply for restricted use data from any of the 16 principal federal statistical agencies and units for evidence building purposes. To learn more about the SAP, please visit the SAP overview Web page.

The SAP Portal provides prospective applicants with a comprehensive metadata catalog for over 1,300 restricted use data assets from the federal statistical agencies and accepts applications requesting access to these assets. Users with questions about arrangements for use of restricted use data or questions about existing applications should contact NCSES directly at [email protected] .

How to Request Access to Restricted Use Data from NCSES

Prior to beginning the restricted use application process, we encourage individuals to explore NCSES’s publicly available data products. NCSES makes data available through our online data tools, data tables, data profiles, and public use microdata files. For more information about all these publicly available options, please visit NCSES's Explore Data Web page.

If an individual’s research or policy questions cannot be informed using publicly available data products, NCSES allows individuals employed at a U.S. based institution or organization the opportunity to apply for access, through the SAP Portal , to restricted use data files for select statistical research projects at NCSES’s Secure Data Access Facility and through the Federal Statistical Research Data Centers. Below are the steps associated with requesting access to NCSES restricted use data.

Discover data: Explore the SAP Portal metadata catalog to identify available NCSES microdata to inform research and policy questions.
Submit an application: Submit a request for access to NCSES restricted use data through the SAP Portal . The Application Instruction Manual provides step-by-step instructions to submit an application requesting access to restricted use data. The manual is available through the SAP Portal's “Help” dropdown menu.
Receive an application determination: After an application is submitted through the SAP Portal, NCSES will review the application in adherence with the review criteria outlined in the SAP policy . Applicants will receive an application determination notification through the SAP Portal.
Submit data security requirements: For approved applications, NCSES will contact the applicant to provide instructions on the data security requirements needed to gain access to the restricted use data. The completion and submission of the NCSES data security requirements will take place outside of the SAP Portal.
Obtain help: For questions about the data or the application process, please contact NCSES at [email protected] .

Researchers are often interested in matching NCSES data to other non-NCSES data sources. Individuals interested in matching data should review the NCSES Policy on Matching Non-NCSES Data to Restricted Use Data Sets (35 KB) to better understand how NCSES considers these requests.

The goal of having a restricted-use data License is to maximize the use of statistical information while protecting individually identifiable information from disclosure.

D. GENERAL INFORMATION

NCSES' core mission areas are:

The collection, acquisition, analysis, reporting, and dissemination of statistical data on science, engineering, technology and research and development related to the United States and other nations;
Education and training of researchers in the use of large-scale nationally representative data sets

Alignment with NCSES Mission

Proposals that do not target one or more of NCSES' core mission areas will be returned without review. The NCSES program overlaps with many other research activities and areas at NSF. Researchers with projects that do not meet specific NCSES criteria might consider other NSF programs and activities. Those programs that may be of particular interest to NCSES researchers are: Science of Science: Discovery, Communication, and Impact (SoS: DCI), Methodology, Measurement and Statistics (MMS), Science of Organizations (SoO), Science and Technology Studies (STS), SBE Science of Broadening Participation (SBE SBP), and Partnerships for Innovation (PFI).

Interaction with NCSES

As noted in the section on Award Conditions, recipients will make a virtual presentation to the National Center for Science and Engineering Statistics to report on their activities at the conclusion of their work.

Dissertation Awards

NCSES Doctoral Dissertation Research Improvement Grants (DDRIGs) help to defray direct costs associated with conducting research, including data set acquisition, original data collection, additional statistical or methodological training, meeting with scholars associated with original datasets, and fieldwork away from the student's home campus.

Dissertation Advice to Students

As a general rule, proposals that review well are those that clearly state a central research question, make an argument that engages and/or debates relevant literature, specifies the data the student will gather and the analytic procedures the student will apply to those data. Additionally, strong proposals state what the researcher expects to find or show through the research.

When preparing the proposal, write clearly and concisely. Reviewers will be selected from a variety of specialty areas so it is possible that one or more reviewers will not specialize in your particular area of research. Defining key terms and keeping your proposal free of jargon will ensure that all reviewers will be able to understand your proposal and evaluate it fairly.

III. Award Information

Iv. eligibility information, v. proposal preparation and submission instructions.

Full Proposal Preparation Instructions : Proposers may opt to submit proposals in response to this Program Solicitation via Research.gov or Grants.gov.

Full Proposals submitted via Research.gov: Proposals submitted in response to this program solicitation should be prepared and submitted in accordance with the general guidelines contained in the NSF Proposal and Award Policies and Procedures Guide (PAPPG). The complete text of the PAPPG is available electronically on the NSF website at: https://www.nsf.gov/publications/pub_summ.jsp?ods_key=pappg . Paper copies of the PAPPG may be obtained from the NSF Publications Clearinghouse, telephone (703) 292-8134 or by e-mail from [email protected] . The Prepare New Proposal setup will prompt you for the program solicitation number.
Full proposals submitted via Grants.gov: Proposals submitted in response to this program solicitation via Grants.gov should be prepared and submitted in accordance with the NSF Grants.gov Application Guide: A Guide for the Preparation and Submission of NSF Applications via Grants.gov . The complete text of the NSF Grants.gov Application Guide is available on the Grants.gov website and on the NSF website at: ( https://www.nsf.gov/publications/pub_summ.jsp?ods_key=grantsgovguide ). To obtain copies of the Application Guide and Application Forms Package, click on the Apply tab on the Grants.gov site, then click on the Apply Step 1: Download a Grant Application Package and Application Instructions link and enter the funding opportunity number, (the program solicitation number without the NSF prefix) and press the Download Package button. Paper copies of the Grants.gov Application Guide also may be obtained from the NSF Publications Clearinghouse, telephone (703) 292-8134 or by e-mail from [email protected] .

In determining which method to utilize in the electronic preparation and submission of the proposal, please note the following:

Collaborative Proposals. All collaborative proposals submitted as separate submissions from multiple organizations must be submitted via Research.gov. PAPPG Chapter II.E.3 provides additional information on collaborative proposals.

See PAPPG Chapter II.D.2 for guidance on the required sections of a full research proposal submitted to NSF. Please note that the proposal preparation instructions provided in this program solicitation may deviate from the PAPPG instructions.

Data Management and Sharing Plan

To ensure efficient accessibility of new data, metrics and indicators that are developed via this solicitation, all research proposals that develop new data must include a Data Management and Sharing Plan. Proposers must adhere to NSF's general data policy (see Data Management and Sharing Plan for SBE Proposals ). Data developed from NCSES restricted-use datasets may not be shared publicly and will reside with NCSES at the end of the research period for additional dissemination by NCSES. Proposers should also apply the following requirements as appropriate.

Requirements for the Data Management and Sharing Plan for data developed from NCSES datasets:

Statement regarding where any new or linked data will be archived. At a minimum, the proposal should include a letter of support from the specified data center.
Identification of the data management point of contact and the person who is responsible for submitting the data, metadata and other documentation.
Clear indication of which data are to be shared in the research community. Such data must be made available through an openly accessible data management system as soon as data are collected and verified.

In some cases, the data that are developed or linked to NCSES data will be sensitive in nature. Proposers may request an exemption from the NCSES NSF program officer for those data. The request for exemption must clearly state why the data cannot be disseminated. In some cases, proposers might indicate a reasonable time period within which the data must be privately held.

Doctoral Dissertation Research Improvement Grant Proposals

Doctoral Dissertation Research Improvement Grant proposals submitted to NCSES should be prepared in accordance with the guidelines for regular research proposals specified in the PAPPG. NCSES DDRIG proposals have additional requirements that are specified below. Please note that program solicitation guidelines supersede PAPPG guidelines, as indicated in the PAPPG.

Project Duration: 12 months with possibility of renewal (with additional funding) based on progress toward completion.
Project Budget: Dissertation grants are generally for $15,000 or less although higher levels of funding are possible with justification. Funds are for expenses associated with conducting the dissertation research (e.g., data collection, field work, payment to subjects, survey expenses, software, microfilm, data transcription, file creation and data merging, travel, and expenses incurred at sites away from the student’s home institution). The grant does not support stipend, salary, or tuition reimbursement. Neither the PI (the dissertation advisor) nor any of the co-PIs (including the dissertation student) should be listed in Section A (Senior/Key Personnel) on the Budget, since DDRIG proposals do not provide funds for salaries or stipends for the doctoral student, the dissertation advisor, or other faculty advisors. Therefore, their names should be manually removed from Section A on the budget to avoid construal as voluntary committed cost sharing, which is not permitted.
Proposal Title: This should begin with, "Doctoral Dissertation Research: ...”
PI: The dissertation advisor must be listed as the Principal Investigator. The dissertation student must be listed as the co-Principal Investigator.
Project Summary: Each proposal must contain a summary of the proposed project not more than one page in length. The Project Summary consists of an overview, a statement on the intellectual merit of the proposed activity, and a statement on the broader impacts of the proposed activity. The intellectual merit portion should include, minimally, background information on the research (theory, prior research), research hypotheses and/or questions, and a description of methods and expected findings. The broader impacts portion might address such questions as: How well does the activity advance discovery and understanding? How does the work promote teaching, training, or learning? What may be the benefits of the proposed activity to society?
Project Description: Must not exceed 10 single pages. Do not send transcripts and letters of recommendation but include any questionnaires or survey guides for original data collection as supplementary documents.
Results from Prior NSF Support section: Not required for DDRIG proposals.

Cost Sharing:

D. Research.gov/Grants.gov Requirements

For Proposals Submitted Via Research.gov:

To prepare and submit a proposal via Research.gov, see detailed technical instructions available at: https://www.research.gov/research-portal/appmanager/base/desktop?_nfpb=true&_pageLabel=research_node_display&_nodePath=/researchGov/Service/Desktop/ProposalPreparationandSubmission.html . For Research.gov user support, call the Research.gov Help Desk at 1-800-673-6188 or e-mail [email protected] . The Research.gov Help Desk answers general technical questions related to the use of the Research.gov system. Specific questions related to this program solicitation should be referred to the NSF program staff contact(s) listed in Section VIII of this funding opportunity.

For Proposals Submitted Via Grants.gov:

Before using Grants.gov for the first time, each organization must register to create an institutional profile. Once registered, the applicant's organization can then apply for any federal grant on the Grants.gov website. Comprehensive information about using Grants.gov is available on the Grants.gov Applicant Resources webpage: https://www.grants.gov/web/grants/applicants.html . In addition, the NSF Grants.gov Application Guide (see link in Section V.A) provides instructions regarding the technical preparation of proposals via Grants.gov. For Grants.gov user support, contact the Grants.gov Contact Center at 1-800-518-4726 or by email: [email protected] . The Grants.gov Contact Center answers general technical questions related to the use of Grants.gov. Specific questions related to this program solicitation should be referred to the NSF program staff contact(s) listed in Section VIII of this solicitation. Submitting the Proposal: Once all documents have been completed, the Authorized Organizational Representative (AOR) must submit the application to Grants.gov and verify the desired funding opportunity and agency to which the application is submitted. The AOR must then sign and submit the application to Grants.gov. The completed application will be transferred to Research.gov for further processing. The NSF Grants.gov Proposal Processing in Research.gov informational page provides submission guidance to applicants and links to helpful resources including the NSF Grants.gov Application Guide , Grants.gov Proposal Processing in Research.gov how-to guide , and Grants.gov Submitted Proposals Frequently Asked Questions . Grants.gov proposals must pass all NSF pre-check and post-check validations in order to be accepted by Research.gov at NSF. When submitting via Grants.gov, NSF strongly recommends applicants initiate proposal submission at least five business days in advance of a deadline to allow adequate time to address NSF compliance errors and resubmissions by 5:00 p.m. submitting organization's local time on the deadline. Please note that some errors cannot be corrected in Grants.gov. Once a proposal passes pre-checks but fails any post-check, an applicant can only correct and submit the in-progress proposal in Research.gov.

Proposers that submitted via Research.gov may use Research.gov to verify the status of their submission to NSF. For proposers that submitted via Grants.gov, until an application has been received and validated by NSF, the Authorized Organizational Representative may check the status of an application on Grants.gov. After proposers have received an e-mail notification from NSF, Research.gov should be used to check the status of an application.

VI. NSF Proposal Processing And Review Procedures

Proposals received by NSF are assigned to the appropriate NSF program for acknowledgement and, if they meet NSF requirements, for review. All proposals are carefully reviewed by a scientist, engineer, or educator serving as an NSF Program Officer, and usually by three to ten other persons outside NSF either as ad hoc reviewers, panelists, or both, who are experts in the particular fields represented by the proposal. These reviewers are selected by Program Officers charged with oversight of the review process. Proposers are invited to suggest names of persons they believe are especially well qualified to review the proposal and/or persons they would prefer not review the proposal. These suggestions may serve as one source in the reviewer selection process at the Program Officer's discretion. Submission of such names, however, is optional. Care is taken to ensure that reviewers have no conflicts of interest with the proposal. In addition, Program Officers may obtain comments from site visits before recommending final action on proposals. Senior NSF staff further review recommendations for awards. A flowchart that depicts the entire NSF proposal and award process (and associated timeline) is included in PAPPG Exhibit III-1.

A comprehensive description of the Foundation's merit review process is available on the NSF website at: https://www.nsf.gov/bfa/dias/policy/merit_review/ .

Proposers should also be aware of core strategies that are essential to the fulfillment of NSF's mission, as articulated in Leading the World in Discovery and Innovation, STEM Talent Development and the Delivery of Benefits from Research - NSF Strategic Plan for Fiscal Years (FY) 2022 - 2026 . These strategies are integrated in the program planning and implementation process, of which proposal review is one part. NSF's mission is particularly well-implemented through the integration of research and education and broadening participation in NSF programs, projects, and activities.

One of the strategic objectives in support of NSF's mission is to foster integration of research and education through the programs, projects, and activities it supports at academic and research institutions. These institutions must recruit, train, and prepare a diverse STEM workforce to advance the frontiers of science and participate in the U.S. technology-based economy. NSF's contribution to the national innovation ecosystem is to provide cutting-edge research under the guidance of the Nation's most creative scientists and engineers. NSF also supports development of a strong science, technology, engineering, and mathematics (STEM) workforce by investing in building the knowledge that informs improvements in STEM teaching and learning.

NSF's mission calls for the broadening of opportunities and expanding participation of groups, institutions, and geographic regions that are underrepresented in STEM disciplines, which is essential to the health and vitality of science and engineering. NSF is committed to this principle of diversity and deems it central to the programs, projects, and activities it considers and supports.

A. Merit Review Principles and Criteria

The National Science Foundation strives to invest in a robust and diverse portfolio of projects that creates new knowledge and enables breakthroughs in understanding across all areas of science and engineering research and education. To identify which projects to support, NSF relies on a merit review process that incorporates consideration of both the technical aspects of a proposed project and its potential to contribute more broadly to advancing NSF's mission "to promote the progress of science; to advance the national health, prosperity, and welfare; to secure the national defense; and for other purposes." NSF makes every effort to conduct a fair, competitive, transparent merit review process for the selection of projects.

1. Merit Review Principles

These principles are to be given due diligence by PIs and organizations when preparing proposals and managing projects, by reviewers when reading and evaluating proposals, and by NSF program staff when determining whether or not to recommend proposals for funding and while overseeing awards. Given that NSF is the primary federal agency charged with nurturing and supporting excellence in basic research and education, the following three principles apply:

All NSF projects should be of the highest quality and have the potential to advance, if not transform, the frontiers of knowledge.
NSF projects, in the aggregate, should contribute more broadly to achieving societal goals. These "Broader Impacts" may be accomplished through the research itself, through activities that are directly related to specific research projects, or through activities that are supported by, but are complementary to, the project. The project activities may be based on previously established and/or innovative methods and approaches, but in either case must be well justified.
Meaningful assessment and evaluation of NSF funded projects should be based on appropriate metrics, keeping in mind the likely correlation between the effect of broader impacts and the resources provided to implement projects. If the size of the activity is limited, evaluation of that activity in isolation is not likely to be meaningful. Thus, assessing the effectiveness of these activities may best be done at a higher, more aggregated, level than the individual project.

With respect to the third principle, even if assessment of Broader Impacts outcomes for particular projects is done at an aggregated level, PIs are expected to be accountable for carrying out the activities described in the funded project. Thus, individual projects should include clearly stated goals, specific descriptions of the activities that the PI intends to do, and a plan in place to document the outputs of those activities.

These three merit review principles provide the basis for the merit review criteria, as well as a context within which the users of the criteria can better understand their intent.

2. Merit Review Criteria

All NSF proposals are evaluated through use of the two National Science Board approved merit review criteria. In some instances, however, NSF will employ additional criteria as required to highlight the specific objectives of certain programs and activities.

The two merit review criteria are listed below. Both criteria are to be given full consideration during the review and decision-making processes; each criterion is necessary but neither, by itself, is sufficient. Therefore, proposers must fully address both criteria. (PAPPG Chapter II.D.2.d(i). contains additional information for use by proposers in development of the Project Description section of the proposal). Reviewers are strongly encouraged to review the criteria, including PAPPG Chapter II.D.2.d(i), prior to the review of a proposal.

When evaluating NSF proposals, reviewers will be asked to consider what the proposers want to do, why they want to do it, how they plan to do it, how they will know if they succeed, and what benefits could accrue if the project is successful. These issues apply both to the technical aspects of the proposal and the way in which the project may make broader contributions. To that end, reviewers will be asked to evaluate all proposals against two criteria:

Intellectual Merit: The Intellectual Merit criterion encompasses the potential to advance knowledge; and
Broader Impacts: The Broader Impacts criterion encompasses the potential to benefit society and contribute to the achievement of specific, desired societal outcomes.

The following elements should be considered in the review for both criteria:

Advance knowledge and understanding within its own field or across different fields (Intellectual Merit); and
Benefit society or advance desired societal outcomes (Broader Impacts)?
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Open Access

Peer-reviewed

Research Article

Deep autoencoder-based behavioral pattern recognition outperforms standard statistical methods in high-dimensional zebrafish studies

Roles Conceptualization, Formal analysis, Methodology, Validation, Writing – original draft, Writing – review & editing

* E-mail: [email protected]

Affiliations Bioinformatics Research Center, Department of Biological Sciences, NC State University, Raleigh, North Carolina, United States of America, Sciome LLC, Research Triangle Park, North Carolina, United States of America

Roles Data curation, Investigation, Validation, Writing – review & editing

Affiliation Department of Environmental and Molecular Toxicology, Oregon State University, Corvallis, Oregon, United States of America

Roles Formal analysis, Writing – review & editing

Affiliation Bioinformatics Research Center, Department of Biological Sciences, NC State University, Raleigh, North Carolina, United States of America

Roles Investigation, Validation, Writing – review & editing

Roles Funding acquisition, Resources, Supervision, Writing – review & editing

Roles Conceptualization, Funding acquisition, Project administration, Resources, Supervision, Writing – review & editing

Affiliations Bioinformatics Research Center, Department of Biological Sciences, NC State University, Raleigh, North Carolina, United States of America, Predictive Toxicology Branch, Division of Translational Toxicology, National Institute of Environmental Health Sciences, Durham, North Carolina, United States of America

Adrian J. Green,
Lisa Truong,
Preethi Thunga,
Connor Leong,
Melody Hancock,
Robyn L. Tanguay,
David M. Reif

Published: September 10, 2024
https://doi.org/10.1371/journal.pcbi.1012423
Peer Review
Reader Comments

This is an uncorrected proof.

Zebrafish have become an essential model organism in screening for developmental neurotoxic chemicals and their molecular targets. The success of zebrafish as a screening model is partially due to their physical characteristics including their relatively simple nervous system, rapid development, experimental tractability, and genetic diversity combined with technical advantages that allow for the generation of large amounts of high-dimensional behavioral data. These data are complex and require advanced machine learning and statistical techniques to comprehensively analyze and capture spatiotemporal responses. To accomplish this goal, we have trained semi-supervised deep autoencoders using behavior data from unexposed larval zebrafish to extract quintessential “normal” behavior. Following training, our network was evaluated using data from larvae shown to have significant changes in behavior (using a traditional statistical framework) following exposure to toxicants that include nanomaterials, aromatics, per- and polyfluoroalkyl substances (PFAS), and other environmental contaminants. Further, our model identified new chemicals (Perfluoro-n-octadecanoic acid, 8-Chloroperfluorooctylphosphonic acid, and Nonafluoropentanamide) as capable of inducing abnormal behavior at multiple chemical-concentrations pairs not captured using distance moved alone. Leveraging this deep learning model will allow for better characterization of the different exposure-induced behavioral phenotypes, facilitate improved genetic and neurobehavioral analysis in mechanistic determination studies and provide a robust framework for analyzing complex behaviors found in higher-order model systems.

Author summary

We demonstrate that a deep autoencoder using raw behavioral tracking data from zebrafish toxicity screens outperforms conventional statistical methods, resulting in a comprehensive evaluation of behavioral data. Our models can accurately distinguish between normal and abnormal behavior with near-complete overlap with existing statistical approaches, with many chemicals detectable at lower concentrations than with conventional statistical tests; this is a crucial finding for the protection of public health as exposure can lead to a range of neurodevelopmental disorders, including cognitive and other behavioral deficits. Our deep learning models enable the identification of new substances capable of inducing aberrant behavior, and we generated new data to demonstrate the reproducibility of these results. Thus, neurodevelopmentally active chemicals identified by our deep autoencoder models may represent previously undetectable signals of subtle individual response differences. Our method elegantly accounts for the high degree of behavioral variability associated with the genetic diversity found in a highly outbred population, as is typical for zebrafish research, thereby making it applicable to multiple laboratories generating similar data. Utilizing the vast quantities of control data generated during high-throughput screening is one of the most innovative aspects of this study and to our knowledge is the first study to explicitly develop a deep autoencoder model for anomaly detection in large-scale toxicological behavior studies.

Citation: Green AJ, Truong L, Thunga P, Leong C, Hancock M, Tanguay RL, et al. (2024) Deep autoencoder-based behavioral pattern recognition outperforms standard statistical methods in high-dimensional zebrafish studies. PLoS Comput Biol 20(9): e1012423. https://doi.org/10.1371/journal.pcbi.1012423

Editor: Samuel V. Scarpino, Northeastern University, UNITED STATES OF AMERICA

Received: April 12, 2023; Accepted: August 15, 2024; Published: September 10, 2024

This is an open access article, free of all copyright, and may be freely reproduced, distributed, transmitted, modified, built upon, or otherwise used by anyone for any lawful purpose. The work is made available under the Creative Commons CC0 public domain dedication.

Data Availability: The code and data required to replicate findings reported in the article are available at https://github.com/Tanguay-Lab/Manuscripts/tree/main/Green_et_al_(2024)_Manuscript .

Funding: This research was supported by the National Institutes of Health (NIH) grant awards ES030287 (RLT, LT), ES030007 (AJG, DMR), ES025128 (DMR), ES033243 (DMR), and CA161608 (AJG, DMR). This research was supported [in part] by the Intramural Research Program of the NIH, ZIAES103385 (DMR). The funders played no role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

Introduction

Significant progress continues to be made in our understanding of neurodevelopmental disorders such as autism spectrum disorder, attention deficit hyperactivity disorder (ADHD), developmental delay, learning disabilities, and other neurodevelopmental problems. As incidences continue to rise globally and affect 10–15% of all births, more work must be done to improve our understanding of these disorders [ 1 – 3 ]. Meta-analyses suggest strong and consistent epidemiological evidence that the developing nervous system is particularly vulnerable to low-level exposure to widespread environmental contaminants, as the anatomical and functional architecture of the human brain is mainly determined by developmental transcriptional processes during the prenatal period [ 3 – 7 ]. Therefore, identifying associations between developmental exposures and neurological effects is a core objective to improve public health by informing disease and disability prevention [ 1 , 8 ].

As the number of environmental contaminants grows to nearly one million, comprehensive data on the neurodevelopmental toxicity of these contaminants remain sparse or nonexistent [ 3 , 9 – 11 ]. In response, high-throughput screening (HTS) assays have been developed to expedite chemical toxicity testing using in vitro and in vivo systems [ 12 – 14 ]. However, in vitro cell and cell-free assays cannot fully capture systemic organismal responses in terms of anatomy, physiology, or behavior [ 15 ]. Zebrafish ( Danio rerio ) have emerged as an ideal model for studying low-level chemical exposure because of their high fecundity, rapid development, genetic tractability, and amenability to high-throughput data generation [ 12 , 16 , 17 ]. The zebrafish brain’s structural organization, cellular morphology, and neurotransmitter systems are very similar to other vertebrates, including chickens, rats, and humans [ 18 – 21 ]. Furthermore, zebrafish have behavioral patterns highly similar to mammals, and genetic homologs for 70% of human genes and 82% of human disease genes, making them a powerful model organism for revealing the neuronal developmental pathways underlying behavior [ 22 – 24 ].

Zebrafish larvae show swimming patterns essential for their survival following swim bladder development at four to five days post-fertilization (dpf), including exploration, foraging, and escape response which can be assessed using various locomotor behavioral assays [ 25 , 26 ] while more advanced continuous swimming, schooling, and reproductive behavior is still developing. One of these assays, the larval photomotor response (LPR), utilizes a sudden transition from light to dark, eliciting a stereotyped large-angle O-bend, followed by several minutes of increased movement, which gradually reduces [ 27 , 28 ]. Exposure to toxicants has been shown to alter this stereotypical behavioral response [ 24 , 29 ]. Current HTS for behavioral neurotoxicity focuses heavily on analyzing locomotor behavior using distance moved and population-based statistical methods [ 24 , 30 ]. However, while the behavior repertoire of larval zebrafish is less sophisticated when compared to that of adult zebrafish and other higher-order vertebrates, they are capable of numerous distinct behaviors [ 24 , 31 , 32 ]. These behaviors, such as thigmotaxis, and light avoidance cannot always be captured when using distance moved as a sole indicator of neurobehavioral toxicity in analyses of this data. Moreover, as most laboratory zebrafish populations feature significant genetic heterogeneity, individual responses to exotic toxicants cannot be expected to be homogeneous for simplistic measures such as distance moved [ 33 ].

Improved accessibility to computing resources and application interfaces, together with recent advances in deep-learning makes it possible to analyze complex behavioral data in novel ways and predict neurodevelopmental toxicity [ 34 – 36 ]. The volume and diversity of data generated during HTS experiments, combined with the variety in toxicological response within populations, present an opportunity that is well-suited for machine learning (ML). In particular, analysis of zebrafish HTS data from five dpf larvae exposed to 1,060 unique chemicals reveals that only 8% of chemical-concentration pairs (a unique combination of chemical and concentration, e.g. 6.4 μM Nicotine) exhibit changes in distance moved [ 30 ], which is low given the known toxicity profiles of the chemical set. The traditional methods for analyzing zebrafish behavior data are primarily based on measurement of distance moved and instances of variations in the movement patterns, velocity changes and spatial preference is lost due to the sheer volume of data and complexity. Additionally, the traditional analysis methods is unable to identify meaningful patterns due to the noise and variability. This challenge provides an opportunity to apply methods developed for anomaly detection from areas such as financial fraud [ 37 ], medical application faults [ 38 ], security systems intrusion [ 39 ], system faults [ 40 ], and others [ 41 , 42 ]. Such ML techniques would allow for a more holistic evaluation of zebrafish behavior by learning complex features such as movement patterns, velocity changes and spatial preferences associated with “normal” behavior and flagging subtle deviations. These intricate nuances could be indicative of chemical toxicity and can often be missed by traditional assays relying solely on measuring distance moved as a metric. In anomaly detection, we learn the pattern of a normal process, and anything that does not follow this pattern is classified as an anomaly. This learning model is particularly applicable, as many HTS data sets have large amounts of control data to analyze [ 30 ]. One intriguing approach to achieving this is by applying an autoencoder [ 43 – 48 ]. An autoencoder is a neural network of two modules, an encoder and a decoder [ 47 , 49 ]. The encoder learns the underlying features of a process, and these features are typically in a reduced dimension. The decoder then uses this reduced dimension to recreate the original data from these underlying features.

In the present study, we trained deep autoencoder models to recognize the pattern of quintessential larval zebrafish behavior and identify abnormal behavior following developmental chemical exposure. The performance of our deep autoencoders was compared against a two sample Kolmogorov–Smirnov test (K-S test), a standard for behavioral assessment. In addition to model development, we assessed the features driving performance through feature permutation and generated new confirmatory data to assess model reproducibility and confirm novel findings.

Statistical classification of behavior

A two sample Kolmogorov–Smirnov test (K-S test) was used to compared treated vs control distance moved and angular velocity in light/dark cycling in zebrafish larvae at five dpf. We identified 40 chemical-concentration combinations from nine chemicals and 28 chemical-concentration combinations from nine chemicals capable of inducing a significantly different (p < 0.05) behavioral response using both distance moved and angular velocity, respectively ( S2 Table ). While 10 chemicals were identified using both methods, nine chemicals were similar, with distance moved finding a significant difference in multi-walled carbon nanotubes at 75 and 100 μM and angular velocity finding a difference in sodium 2-(N-ethylperfluorooctane-1-sulfonamido)ethyl phosphate at 0.25 μM. Considering that distance moved revealed more chemical-concentration combinations in this screening application, we used this metric to identify abnormal larvae to ensure a sufficient number for training the autoencoder models. Using the 30 th and 70 th percentiles, we defined 227 individual larvae as abnormal ( Fig 1A ). These 227 larvae formed the validation set used to test the performance of our models.

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(A) Schematic representation of the differences in statistical and autoencoder based classification of behavioral response in larval zebrafish. (B) Venn diagram showing overlap between statistical and autoencoder classified abnormal zebrafish. (C) Evaluating the change in model performance when the values of a single feature are randomly shuffled. Kappa–Cohen’s Kappa statistic, AUROC—area under the receiver operating characteristic. Figure depicts means ± SEM. (D) Coefficients of variation for each of the main numerical features.

https://doi.org/10.1371/journal.pcbi.1012423.g001

Training performance

Autoencoder models were trained using only control data for each of the activity states (hypoactive, normal, and hyperactive) per phase of the second light cycle. This resulted in six trained models ( S1 Fig the training loss plots for the models). Table 1 shows the results for the six deep autoencoder models trained using control data and validated using data from zebrafish defined as abnormal using the K-S test. All the models performed well with values ranging from 0.615–0.867 and 0.740–0.922 for the Kappa and AUROC, respectively. As expected, the models consistently produced high specificity (SP) levels as this value indicated how well the models classify control data. There was greater variability in the sensitivity (SE) with the dark phase models matching or outperforming the light phase models for each activity state. Further, we observed a noteworthy trend across all models producing high positive predictive value (PPV). Overall, these results show that deep autoencoders trained using control data is capable of distinguishing between normal and abnormal larval zebrafish behavior with a high degree of accuracy.

Table showing performance of model trained using different activity states of the control data in both light and dark phases.

https://doi.org/10.1371/journal.pcbi.1012423.t001

Evaluation of unknowns

Using the six trained models, we evaluated the 2,719 treated zebrafish larvae ( Fig 1 ). The autoencoders correctly classified 156 of the 227 larvae that fell below or above the 30 th and 70 th percentiles, respectively. In addition, our deep autoencoders identified 463 larvae as abnormal from the 2,492 larvae defined as normal using the K-S test ( Fig 1B ). The majority (422) of these 619 larvae were from one of 66 chemical-concentration combinations from 13 chemicals ( Table 2 ). The deep autoencoders successfully identified nine of the ten statistically abnormal chemicals and identified these chemicals at or below the lowest concentration shown to be statistically significant. While the deep autoencoders did not identify Perfluorodecylphosphonic acid as capable of inducing abnormal behavior, but they did identify 3-Perfluoropentyl propanoic acid (5:3), Perfluoro-n-octadecanoic acid, 8-Chloroperfluorooctylphosphonic acid, and Nonafluoropentanamide, which were missed in the statistical testing framework. These results, summarized in Fig 2 , show that deep autoencoders can match the performance of the K-S test and are more sensitive at detecting abnormal behavior.

Utilizing our analysis pipeline produced six deep autoencoder models (three for the light phase and three for the dark phase) capable of classifying larval zebrafish behavior with high Kappa and AUROC values. The trained models were then used to classify the non-significant exposed larvae and identified Nonafluoropentanamide, Perfluorohexanesulfonic acid, (Heptafluoropropyl)trimethylsilane, 2-Methylphenanthrene, 8-Chloroperfluorooctylphosphonic acid, Perfluoro-n-octadecanoic acid, and others as capable of inducing abnormal behavior.

https://doi.org/10.1371/journal.pcbi.1012423.g002

Table showing chemicals and concentrations flagged for displaying abnormal behavioral effects when evaluated using Autoencoder. Compounds that were picked up by Autoencoder, but not KS test are highlighted in red.

https://doi.org/10.1371/journal.pcbi.1012423.t002

Features driving improved autoencoder performance

To determine the features in the model that were most important in driving classification performance, we employed permutation feature importance. This technique is a model agnostic inspection technique used for any fitted estimator to determine the importance of each feature in the model. Larger the decrease in model performance (Kappa or AUROC) when a single feature value is randomly shuffled, the more important the feature. Our results, shown in Fig 1C , indicate that phase, trial time, x position, and y position are the largest drivers of model performance, while distance moved and velocity contribute very little. Coefficients of variation show greater variability in the x and y positional data between control and exposed groups compared to either velocity or distance moved ( Fig 1D ). This trend is consistent irrespective of the larval activity state (hypoactive, normal activity, or hyperactive) relative to their respective controls ( Fig 3 ).

Coefficients of variation (CVs) for each of the main numerical features (A–C) in the light (D–F) and in the dark. Columns show CVs of larval zebrafish significantly (p < 0.05) (A, D) hypoactive, (B, E) normal activity, or (C, F) hyperactive relative to their respective controls.

https://doi.org/10.1371/journal.pcbi.1012423.g003

Experimental confirmation of autoencoder findings

To provide an unbiased evaluation of the final model fits, we generated new data using 2-Methylphenanthrene, and Nonafluoropentanamide. The data collected confirmed that our models accurately classified all controls as normal while detecting similar levels of abnormal behavior response across the concentration range ( Fig 4 ) (p > 0.15). These results show that the trained model is capable of producing similar results across experimental replicates.

Comparison of the performance of deep autoencoder models between the training set and two chemicals identified by the models to elicit abnormal larval zebrafish behavior. Percent of larval zebrafish classified as abnormal based on their behavioral response to developmental exposure to (A) 2-Methylphenanthrene and (B) Nonafluoropentanamide.

https://doi.org/10.1371/journal.pcbi.1012423.g004

Statistical analysis identified 39 chemical-concentration combinations from ten chemicals capable of inducing a significantly different (p < 0.05) behavioral response. Utilizing the 227 abnormal individuals identified by the statistical test as our validation set, we trained six deep autoencoder models using control data for each of the activity states (hypoactive, normal, and hyperactive). All of the resulting models performed well with values ranging from 0.615–0.867 and 0.740–0.922 for the Kappa and AUROC, respectively. All models achieved SP values above 94.8% and PPV values above 77.6% while SE values for all dark phase models outperformed the light phase models for each activity state ( Table 1 ). Assessment of permutation feature importance indicates that phase, trial time, x-position, and y-position are the largest drivers of model performance ( Fig 1C ). The calculated coefficients of variation shed some light on this surprising finding ( Fig 1D ). They show that variation in the x and y positional data is greater than observed for velocity or distance moved between control and exposed groups. These differences in variation likely make it easier for the models to distinguish between treated and exposed groups.

When we examined exposed larvae defined as normal using the K-S test ( Fig 1 ), our deep autoencoders identified 66 chemical-concentration combinations from 12 chemicals ( Table 2 ) with Perfluoro-n-octadecanoic acid, 8-Chloroperfluorooctylphosphonic acid, and Nonafluoropentanamide only identified by our autoencoders. These results show that a deep autoencoder-based model can classify larval zebrafish behavior as normal or abnormal with very good efficacy and often identified abnormal behaviors at lower concentrations than current statistical methods. Further, the models identified three novel chemicals, Perfluoro-n-octadecanoic acid, 8-Chloroperfluorooctylphosphonic acid, and Nonafluoropentanamide as capable of inducing abnormal behavior ( Fig 3 ). While making a definitive claim will require further experimentation, it does appear that the autoencoder method is particularly sensitive at detecting changes due to PFAS exposure. PFAS are associated with increased glutamate levels in the hippocampus and catecholamine levels in the hypothalamus, decreased dopamine in the whole brain after PFAS exposure, and increased extracellular glutamate has been observed in the hippocampus epileptic rats [ 50 , 51 ]. Thus, it is reasonable to infer that these neurochemical changes are capable of altering autoencoder-detectable patterns without changing locomotor magnitude or direction.

Recognition and categorization of swimming patterns in larvae is a challenging task and a number of approaches have been used. These can range from subjective analysis based on experienced observations [ 31 , 52 ] or through the application of unsupervised ML [ 27 , 32 , 53 – 57 ]. These studies have focused on the analysis and categorization of behavioral patterns in wild-type strains [ 27 , 57 ], mutant strains [ 32 , 53 ], or larvae exposed to neuroactive chemicals [ 32 ] but do not classify behavior as normal or abnormal. In addition, these unsupervised approaches have utilized highspeed camera systems which are medium to low throughput and have limited potential in the screening of tens of thousands of chemicals for behavioral effects. As introduced above, classification of behavior is one of the primary goals of toxicological screening and tends to result in highly imbalanced datasets and lend themselves to anomaly detection methodologies. While these methods are common in manufacturing [ 41 – 43 , 58 ], information systems [ 38 , 40 ], security systems [ 39 , 45 ], and financial fraud [ 37 ] they have only very recently been applied to biological data [ 44 , 59 , 60 ]. To the best of our knowledge, this is the first study to explicitly develop a deep autoencoder model for anomaly detection in toxicological behavior studies.

Overall, our results show that a deep autoencoder utilizing raw behavioral tracking data from five dpf zebrafish larvae can accurately distinguish between normal and abnormal behavior. We show that these results are reproducible and allow for the identification of new compounds capable of eliciting abnormal behavior. Further, our models were able to identify abnormal behavior following chemical exposure at lower concentrations than with traditional statistical tests such as the two sample Kolmogorov–Smirnov test (K-S test). Our approach accounts for the high degree of behavioral variability associated with the genetic diversity found within a highly outbred population typical of zebrafish studies, thereby making it extensible to use across labs. Our deep autoencoders only needed seven hundred controls and a three-minute light and three-minute dark cycle to identify differences. The majority of zebrafish labs have historical or the ability to generate similar data that can be used to train their own deep autoencoder models. Looking to the future, neurodevelopmentally active chemicals identified using our deep autoencoder models may represent heretofore undetectable signals of subtle differences in individual responses, suggesting chemicals that should be investigated further as eliciting differential population responses (i.e. interindividual susceptibility differences).

These findings will facilitate the application of behavioral characterization methods discussed above, such as ZebraZoom [ 32 ], using highspeed cameras to identify the behavioral traits most perturbed by the chemical exposure and allow for more mechanistic discovery. One of the key innovations presented in this study is leveraging vast amounts of control data generated as part of any high-throughput screening (HTS)–setting the stage for predictive toxicological applications and safety assessments for the enormous backlog of as-yet untested chemicals.

Materials and methods

This section describes the autoencoder models utilizing a semi-supervised ML algorithm and logistic regression (LR) to discriminate between normal and abnormal behavior in chemically exposed five dpf zebrafish. An overview of our approach is shown in Fig 2 . Briefly, we created and trained six autoencoder models for each phase of the assay; namely, hyperactive, normal, and hypoactive depending on the control movement in the light or dark phases of the assay. Finally, treated plates were tested on one of these, depending on which category, its controls fell under. We used experimental data collected on a large and diverse compound set of 30 chemicals including an insecticide, nanomaterial, perfluorinated chemicals, and aromatic pollutants at a range of concentrations (133 chemical-concentration pairs) to assess the neurotoxic effects of these chemicals following developmental exposure ( S1 Table ).

Ethics statement

This study was conducted in accordance with the guidelines and regulations set forth by the Institutional Animal Care and Use Committee (IACUC) at Oregon State University. The protocol was reviewed and approved by the IACUC under the approval number 2021–0227. All procedures involving animals were performed in compliance with the ethical standards of the institution and adhered to the principles of humane animal treatment.

Zebrafish husbandry

Tropical 5D wild-type zebrafish were housed at Oregon State University’s Sinnhuber Aquatic Research Laboratory (SARL, Corvallis, OR) in densities of 1000 fish per 100-gallon tank according to the Oregon State University Animal Use Care and Protocol: 2021–0227 [ 61 ]. Fish were maintained at 28°C on a 14:10 h light/dark cycle in recirculating filtered water, supplemented with Instant Ocean salts. Adult, larval and juvenile fish were fed with size-appropriate GEMMA Micro food 2–3 times a day (Skretting). Spawning funnels were placed in the tanks the night prior, and the following morning, embryos were collected and staged [ 62 , 63 ]. Embryos were maintained in embryo medium (EM) in an incubator at 28°C until further processing. EM consisted of 15 mM NaCl, 0.5 mM KCl, 1 mM MgSO 4 , 0.15 mM KH 2 PO 4 , 0.05 mM Na 2 HPO 4 , and 0.7 mM NaHCO 3 [ 63 ].

Developmental chemical exposure

The empirical data used to develop our model were gathered as described in Truong et al. and Noyes et al. [ 12 , 64 , 65 ]. The experimental design consisted of the 30 unique chemicals tested ( S1 Table ) with at least 7 replicates (an individual embryo in singular wells of a 96-well plate) at each concentration for each chemical. The concentrations evaluated were based on preliminary studies within the authors’ lab to span lethal and sub-lethal concentration range were possible based on physical chemicals properties including solubility.

Developmental toxicity assessments

Mortality and morphology..

At 24 hours post-fertilization (hpf), embryos were screened for mortality, developmental delay, and spontaneous movement [ 12 ]. At 120 hpf, mortality, craniofacial abnormalities (eye, snout and jaw), body axis abnormalities, edema (yolk sac and pericardial edema), upright body abnormalities (swim bladder, somite and circulation), touch response brain abnormalities (brain, otic vesicle and pectoral fin), pigment, notochord, and trunk abnormalities (trunk and caudal fin) [ 12 , 66 , 67 ]. The incidence of abnormality across all morphology endpoints were evaluated as binary outcomes. Any individuals identified with a physical abnormality were excluded from any behavioral analysis as these abnormalities might confound the results.

Photomotor responses.

The larval photomotor response (LPR) assay was conducted at 120 hpf when the 96-round well plates of larvae were placed into a Zebrabox (Viewpoint LifeSciences) and larval movement was recorded. The recorded videos were then tracked with Ethovision XT v.11 analysis software for 24 min across 3 cycles of 3 min light: 3 min dark with an initial 6 minute dark acclimation period. The trial time(s), x-position, y-position, distance moved (μm), and velocity (mm/s) by each larva in the 2nd light/dark cycle were the features used for behavioral assessment ( S2 Fig ). The 2 nd light/dark cycle was chosen as it exhibited less noise than the 1 st cycle and was less influenced by any learning that might have occurred in the 3 rd cycle. For all assessments, data were collected from embryos exposed to nominal concentrations of chemical and uploaded under a unique well-plate identifier into a custom LIMS (Zebrafish Acquisition and Analysis Program [ZAAP])–a MySQL database and analyzed using custom R scripts that were executed in the LIMS background [ 29 ].

Data preprocessing and statistical analysis pipeline

Preprocessing..

All data processing, statistical analysis and ML were implemented in Python using the open source libraries Tensorflow [ 68 ], Keras [ 69 ], Scikit-learn [ 70 ], Pandas [ 71 ], and Numpy [ 72 ] within a purpose build Singularity container environment [ 73 ]. The x-position and y-position data was standardized relative to the center of each well and forward filled if datapoints were missing. Outliers were normalized to the maximum likely distance a zebrafish larva could move in 1/25 th of a second. Considering that the average length of a 5 dpf larval zebrafish is 3.9 mm and can move about 2.5 times it’s body length during a startle response (120 frames at 1000 frames/second) the threshold for distance moved in our system was set at 3.25 mm per frame [ 53 , 74 ]. This resulted in 5,445 of the 30,825,000 frames being normalized.

Statistical analysis

A two sample Kolmogorov–Smirnov test (K-S test), a non-parametric two-sided test with no adjustments for normality or multiple comparisons, was used to compare each chemical-concentration combination with their respective same plate controls (p < 0.05). Interexperimental zebrafish larval response to light/dark cycling is highly variable ( S2 Fig ). Therefore, it was essential to group the unexposed controls based on the mean from individual 96-well plates compared to mean movement for unexposed controls across all plates. Controls from individual plates with statistically significant (p < 0.01) differences in movement compared to the average of all controls were grouped together as hyperactive, normal, or hypoactive. Following grouping the K-S test was used to compare Individuals in the 30 th and 70 th percentiles of each chemical-concentration combination were defined as abnormal.

Autoencoder architecture

Deep autoencoders were developed using zebrafish control data to distinguish between normal and abnormal zebrafish behavior. The model was trained on a Dell R740 containing two Intel Xeon processors with 18 cores per processor, 512 GB RAM, and a Tesla-V100-PCIE (31.7 GB). The autoencoders consisted of an input and output layer of fixed-size based on the size of a single phase (25 frames per 180s) of the second light cycle (4500 frames by 5 features). The encoder network was composed of eight fully connected hidden layers using a normal kernel initialization, tanh activation, a dropout value of 0.2, L1 and L2 regularization values of 1e -05 , and an adadelta optimizer. The size of each hidden layer was reduced by increasing multiples of 15 and resulted in a compressed representation (bottleneck) size of 250. The decoder network was composed of six fully connected hidden layers using tanh activation, and a dropout value of 0.2. All hidden layers used an adadelta optimizer (learning_rate = 0.001, rho = 0.95, and epsilon = 1e-07) and mean squared error for the loss function [ 75 – 77 ]. For each model, we optimized the hyperparameters (i.e., the number of hidden layers, the number of nodes in the layers, loss functions, optimizers, regularization rates, and dropout rates) by grid search technique trained on all control data over 500 epochs using Cohens Kappa statistic as the objective metric. The final encoder models were trained over the course of 125000 epochs. The resulting compressed representation was used as input into a logistic regression layer trained using a 100 fold cross-validation with each fold consisting of 4000 epochs using a limited-memory BFGS solver. The code and dataset are available at GitHub [ https://github.com/Tanguay-Lab/Manuscripts/tree/main/Green_et_al_(2024)_Manuscript ].

Network performance and evaluation

The data showed strong normal vs abnormal class imbalance ( Fig 1 ). Classifiers may be biased towards the major class (normal) and therefore, show poor performance accuracy for the minor class (abnormal) [ 78 ]. Normal vs abnormal classification accuracy was evaluated using a confusion matrix, Cohen’s Kappa statistic, and area under the receiver operating characteristic (AUROC) as Kappa and AUROC measure model accuracy, while compensating for simple chance [ 79 ]. The primary metrics we used from the confusion matrix included sensitivity (SE), specificity (SP), and positive predictive value (PPV) as these parameters give us the true positive rate, true negative rate, and the proportion of true positives amongst all positive calls [ 80 – 82 ]. Chemical-concentration combinations were defined as abnormal if the autoencoders identified more individual as abnormal in the exposed than their respective controls and at least 25% of the individuals were abnormal. Permutation feature importance was used to evaluate which features are the most important for model performance. In brief, one feature (variable) is shuffled randomly and all features are fed into the model the resulting Kappa and AUROC values are calculated. This is repeated 1000 times per feature and average Kappa and AUROC are calculated across each shuffle [ 83 ]. To determine why one feature might be more important than another a coefficient of variation was calculated for each of the features in the control and exposed groups (variation() in the SciPy package).

Following model development two chemicals were identified for follow-up laboratory testing. We generated new data using 2-Methylphenanthrene, and Nonafluoropentanamide. 2-Methylphenanthrene was chosen as the autoencoder identified it was different from controls at a much lower concentration than a K-S test of distance moved and angular velocity while Nonafluoropentanamide was selected as it was not identified using either a K-S test of distance moved and angular velocity. Similarity between the results was determined by comparing fourth order polynomial curve fits with and a significance threshold of p < 0.05.

Supporting information

S1 table. study chemicals and their common use..

https://doi.org/10.1371/journal.pcbi.1012423.s001

S2 Table. Statistical results for behavioral response analysis.

https://doi.org/10.1371/journal.pcbi.1012423.s002

S1 Fig. Loss function results during training.

Changes of loss functions during the training of (A) light-hypoactive controls, (B) light-normal controls, (C) light-hyperactive controls, (D) dark-hypoactive controls, (E) dark-normal controls, (F) dark-hyperactive controls. Blue line–training data (controls-only), orange line–test data (abnormal-only).

https://doi.org/10.1371/journal.pcbi.1012423.s003

S2 Fig. Interexperimental behavioral response to light/dark cycling in control larval zebrafish.

Zebrafish larvae were statically exposed to a chemical from six hpf until five dpf. At five dpf, behavior was measured under environmental conditions of continuous light for three minutes (0–180) followed by three minutes of dark (180–360). This plot shows representative control behavior data (n = 7 per line) classified as hyperactive (blue line), normal (green line) or hypoactive (purple line). The insert shows an example of larval behavioral tracks produced by Ethovision XT software. Figure depicts means ± SEM.

https://doi.org/10.1371/journal.pcbi.1012423.s004

Acknowledgments

We would like to thank the staff at Sinnhuber Aquatic Research Laboratory, and John Lam for his contribution to reprocessing videos.

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http://orcid.org/0000-0001-9521-624X Jenifer Akoth Otieno 1 ,
Lisa Malesi Were 1 ,
http://orcid.org/0000-0002-7316-3340 Caleb Kimutai Sagam 1 ,
Simon Kariuki 1 ,
http://orcid.org/0000-0002-7951-3030 Eleanor Ochodo 1 , 2
1 Centre for Global Health Research, Kenya Medical Research Institute , Kisumu , Kenya
2 Centre for Evidence-Based Health Care, Division of Epidemiology and Biostatistics, Faculty of Medicine and Health Sciences , Stellenbosch University , Cape Town , South Africa
Correspondence to Ms. Jenifer Akoth Otieno; jenipherakoth15{at}gmail.com

Objective To perform critical methodological assessments on designs, outcomes, quality and implementation limitations of studies evaluating the impact of malaria rapid diagnostic tests (mRDTs) on patient-important outcomes in sub-Saharan Africa.

Design A systematic review of study methods.

Data sources MEDLINE, EMBASE, Cochrane Library, African Index Medicus and clinical trial registries were searched up to May 2022.

Eligibility criteria Primary quantitative studies that compared mRDTs to alternative diagnostic tests for malaria on patient-important outcomes within sub-Sahara Africa.

Data extraction and synthesis Studies were sought by an information specialist and two independent reviewers screened for eligible records and extracted data using a predesigned form using Covidence. Methodological quality was assessed using the National Institutes of Health tools. Descriptive statistics and thematic analysis guided by the Supporting the Use of Research Evidence framework were used for analysis. Findings were presented narratively, graphically and by quality ratings.

Results Our search yielded 4717 studies, of which we included 24 quantitative studies; (15, 62.5%) experimental, (5, 20.8%) quasi-experimental and (4, 16.7%) observational studies. Most studies (17, 70.8%) were conducted within government-owned facilities. Of the 24 included studies, (21, 87.5%) measured the therapeutic impact of mRDTs. Prescription patterns were the most reported outcome (20, 83.3%). Only (13, 54.2%) of all studies reported statistically significant findings, in which (11, 45.8%) demonstrated mRDTs’ potential to reduce over-prescription of antimalarials. Most studies (17, 70.8%) were of good methodological quality; however, reporting sample size justification needs improvement. Implementation limitations reported were mostly about health system constraints, the unacceptability of the test by the patients and low trust among health providers.

Conclusion Impact evaluations of mRDTs in sub-Saharan Africa are mostly randomised trials measuring mRDTs’ effect on therapeutic outcomes in real-life settings. Though their methodological quality remains good, process evaluations can be incorporated to assess how contextual concerns influence their interpretation and implementation.

PROSPERO registration number CRD42018083816.

INFECTIOUS DISEASES
Tropical medicine

Data availability statement

Data are available upon reasonable request. Our reviews’ data on the data extraction template forms, including data extracted from the included studies, will be availed by the corresponding author, JAO, upon reasonable request.

This is an open access article distributed in accordance with the Creative Commons Attribution 4.0 Unported (CC BY 4.0) license, which permits others to copy, redistribute, remix, transform and build upon this work for any purpose, provided the original work is properly cited, a link to the licence is given, and indication of whether changes were made. See: https://creativecommons.org/licenses/by/4.0/ .

https://doi.org/10.1136/bmjopen-2023-077361

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STRENGTHS AND LIMITATIONS OF THIS STUDY

We conducted a robust literature search to get a recent representative sample of articles to assess the methodology.

In addition to the methodology of studies, we evaluated the implementation challenges that limit the effect of the tests.

We only included studies published in English which might have limited the generalisability of study findings, but we believe this is a representative sample to investigate the methods used to assess the impact of malaria rapid diagnostic tests.

Introduction

The malaria burden remains high in sub-Saharan Africa despite several interventions deployed to control. 1 Interventions include but are not limited to the adoption of parasitological confirmation of malaria infection using malaria rapid diagnostic tests (mRDTs) and effective treatment using artemisinin-based combination therapies. 2 3 In 2021, there were 247 million cases of malaria reported globally, an increase of 2 million cases from 245 million cases reported in 2020. 4 This estimated increase in 2021 was mainly reported in sub-Saharan Africa. 4 Of all global malaria cases in 2021, 48.1% were reported in sub-Saharan Africa—Nigeria (26.6%), the Democratic Republic of the Congo (DRC) (12.3%), Uganda (5.1%) and Mozambique (4.1%). 4–6 Similarly, 51.9% of the worldwide malaria deaths were reported in sub-Saharan African—Nigeria (31.3%), the DRC (12.6%), the United Republic of Tanzania (4.1%) and Niger (3.9%). 4–6

Following the 2010 WHO’s policy on recommending parasitological diagnosis of malaria before treatment, the availability and access to mRDTs have significantly increased. 7 For instance, globally, manufacturers sold 3.5 billion mRDTs for malaria between 2010 and 2021, with almost 82% of these sales being in sub-Saharan African countries. 4 In the same period, National Malaria Control Programmes distributed 2.4 billion mRDTs globally, with 88% of the distribution being in sub-Saharan Africa. 4 This demonstrates impressive strides in access to diagnostic services in the public sector but does not effectively reveal the extent of test access in the private and retail sectors. Published literature indicates that over-the-counter (OTC) malaria medications or treatment in private retail drug stores are often the first point of care for fever or acute illness in African adults and children. 7–9 Using mRDTs in private drug outlets remains low, leading to overprescribing antimalarials. Increased access to mRDTs may minimise the overuse of OTC medicines to treat malaria.

Universal access to malaria diagnosis using quality-assured diagnostic tests is a crucial pillar of the WHO’s Global Technical Strategy (GTS) for malaria control and elimination. 4 10 11 Assessing the role of mRDTs in achieving the GTS goals and their impact on patient-important outcomes is essential in effectively guiding their future evaluation and programmatic scale-up. 12 Rapidly and accurately identifying those with the disease in a population is crucial to administering timely and appropriate treatment. It plays a key role in effective disease management, control and surveillance.

Impact evaluations determine if and how well a programme or intervention works. If impact evaluations are well conducted, they are expected to inform the scale-up of interventions such as mRDTs, including the cost associated with the implementation. Recent secondary research (systematic reviews on the impact of mRDTs on patient-important outcomes) 13 is only based on assessing mRDTs’ effect and does not consider how well the individual studies were conducted. Odaga et al conducted a Cochrane review comparing mRDTs to clinical diagnosis. They included seven trials where mRDTs substantially reduced antimalarial prescription and improved patient health outcomes. However, they did not assess the contextual factors that influence the effective implementation of the studies. There is a need to access the methodological implementation of studies that evaluate the impact of mRDTs. To our knowledge, no study has investigated the implementation methods of studies evaluating the impact of mRDTs.

We aimed to perform critical methodological assessments on the designs, outcomes, quality and implementation limitations of studies that evaluate the impact of mRDTs compared with other malaria diagnostic tests on patient-important outcomes among persons suspected of malaria in sub-Saharan Africa. We defined patient-important outcomes as; characteristics valued by patients which directly reflect how they feel, function or survive (direct downstream health outcomes such as morbidity, mortality and quality of life) and those that lie on the causal pathway through which a test can affect a patient’s health, and thus predict patient health outcomes (indirect upstream outcomes such as time to diagnosis, prescription patterns of antimalarials and antimicrobials, patient adherence). 14

We prepared this manuscript according to the reporting guideline: Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA-2020) 15 ( online supplemental files 1; 2 ). The protocol is registered with the International Prospective Register of Systematic Reviews and was last updated in June 2022. The protocol is also available as a preprint in the Open Science Network repositories. 12

Supplemental material

Patient and public involvement, criteria for including studies in this review, study designs.

We included primary quantitative studies published in English. We included observational and experimental studies in either controlled or uncontrolled settings. We did not limit trials to the unit of randomisation (individual or cluster). We extracted qualitative data from quantitative studies on implementation limitations. We excluded studies, which only provided test accuracy statistics without evaluating the tests’ impact on patient-important outcomes and modelling studies. We also excluded editorials, opinion pieces, non-research reports, theoretical studies, secondary quantitative studies, reports, case studies, case series or abstracts with insufficient information or no full texts available, as the methodology of the studies could not be fully appraised.

Population and setting

We defined our population as people suspected of having malaria infection caused by any of the four human malaria parasites ( Plasmodium falciparum, P. malariae, P. ovale and P. vivax ) who reside in any sub-Saharan African country, regardless of age, sex or disease severity.

Intervention

We restricted studies for inclusion to those assessing mRDTs, regardless of the test type or the manufacturer.

We included studies comparing mRDTs to microscopy, molecular diagnosis (PCR) or clinical/presumptive/routine diagnosis.

We included studies reporting on at least one or more patient-important outcomes. We adopted the conceptual framework for the classification of these outcomes as described by Schumacher et al . 16 Further details regarding the classification are available in our protocol. 12

Measures of the diagnostic impact that indirectly assess the effect of mRDTs on the diagnostic process, such as time to diagnosis/turn-around time and prediagnostic loss to follow-up.

Measures of the therapeutic impact that indirectly assess the effect of mRDTs on treatment decisions, such as time to treatment, pretreatment loss to follow-up, antimalarial/antibiotics prescription patterns and patient adherence to the test results.

Measures of the health impact that directly assess the effect of mRDTs on the patient’s health, such as mortality, morbidity, symptom resolution, quality of life and patient health costs.

Search methods for identifying studies

Electronic searches.

Given the review’s purpose to assess the methodology of existing studies, we searched the following electronic databases for a representative sample till May 2022; MEDLINE, EMBASE, Cochrane Library and African Index Medicus. We also searched clinical trial registries, including clinicaltrials.gov, the meta-register of controlled trials, the WHO trials register and the Pan African Clinical Trials Registry. We applied a broad search strategy that included the following key terms: “Malaria”, “Diagnosis”, “Rapid diagnostic test”, “Impact”, “Outcome” and their associated synonyms. The full search strategy is provided in online supplemental file 2 .

Study selection

Two reviewers independently screened the titles and abstracts of the search output and identified potentially eligible full texts using Covidence—an online platform for systematic reviews. 17 We resolved any differences or conflicts through discussion among the reviewers or consulting a senior reviewer.

Data extraction

Two reviewers independently extracted data from studies included using a predesigned and standard data extraction form in Covidence. 17 We piloted the form on two potentially eligible studies before its use and resolved any differences or conflicts through a discussion among the reviewers or consulting a senior reviewer. The study information that was extracted included the following:

General study details include the first author, year, title, geographical location(s), population, target condition and disease seasonality.

Study design details such as the type of study, intervention, comparator, prediagnostic, pretreatment and post-treatment loss to follow-up, outcome measures and results for outcome measures (effect size and precision). Study design issues were also considered, including sample size, study setting, inclusion criteria and study recruitment.

The quality assessment of the included studies was also performed using the National Institute for Health (NIH) quality assessment tools 18 ( online supplemental file 3 ).

The implementation challenges, as reported by study authors in the methods and the discussion sections, were extracted according to the four main domains of the Supporting the Use of Research Evidence (SURE) framework for identifying barriers and enablers to health systems: recipient of care, providers of care, health system constraints and sociopolitical constraints 19 ( online supplemental file 4 ).

Quality assessment

We assessed the methodological quality of included studies in Covidence. 17 We adopted two NIH quality assessment tools 18 for experimental and observational designs. Two reviewers independently assessed the methodological quality of studies as stratified by study design. We resolved any differences or conflicts by discussing among the reviewers or consulting a senior reviewer. Our quality evaluation was based on the number of quality criteria a study reported about its internal validity. The overall score was used to gauge the study’s methodological quality. We did not exclude studies based on the evaluation of methodological quality. Instead, we used our assessment to explain the methodological issues affecting impact studies of mRDTs.

We did not pool results from included individual studies, but we conducted descriptive statistics by synthesising our results narratively and graphically, as this was a methodological review. All included studies were thereby considered during narrative synthesis.

Quantitative data

We started our analysis by listing and classifying identified study designs and patient-important outcomes according to similarities. Stratified by study design, we used descriptive statistics for summarising key study characteristics. Descriptive analysis was done using STATA V.17 (Stata Corp, College Station, TX).

Qualitative data

We used the thematic framework analysis approach to analyse and synthesise the qualitative data to enhance our understanding of why the health stakeholders thought, felt and behaved as they did. 20 We applied the following steps: familiarisation with data, selection of a thematic framework (SURE), 19 coding themes, charting, mapping and interpreting identified themes.

A summary of our study selection has been provided in figure 1 . Our search yielded 4717 records as of June 2022. After removing 17 duplicates, we screened 4700 studies based on their titles and abstracts and excluded 4566 records. After that, we retrieved 134 full texts and screened them against the eligibility criteria. We excluded 110 studies. The characteristics of excluded studies are shown in online supplemental file 5 . Therefore, we included 24 studies in this systematic review.

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Preferred Reporting Items for Systematic Reviews and Meta-Analyses 2020 flow diagram showing the study selection process.

General characteristics of included studies

Study characteristics have been summarised in online supplemental file 6 . Studies included in this review were done in Ghana (7, 29.2%), Uganda (7, 29.2%), Tanzania (6, 25%), Burkina Faso (3, 12.5%), Nigeria (2, 8.3%) and Zambia (1, 4.2%). Most studies (16, 66.7%) were done on mixed populations of children and adults, while the remaining (8, 33.3%) were done on children alone. All studies (24, 100%) tested mRDTs as the intervention. Most studies (18, 75%) compared mRDTs to presumptive treatment/clinical diagnosis/clinical judgement, while the remaining (7, 29.2%) had microscopy and routine care (1, 4.2%) as their comparator. No study reported on PCR as a control.

Of all included studies, (17, 70.8%) were carried out in rural areas within government-owned facilities, (7, 29.2%) in urban areas and (2, 8.3%) in peri-urban areas. Few studies (6, 25%) were conducted in privately owned propriety facilities. Most studies (15, 62.5%) were conducted in health facilities and only (9, 37.5%) were within the communities. Studies conducted within health centres were (9, 37.5%), while those conducted in hospitals were (7, 29.2%). Most studies (15, 62.5%) were conducted during the high malaria transmission season, (9, 37.5%) during the low malaria season and (4, 16.7%) during the moderate malaria season. P. falciparum was the most common malaria parasite species (21, 87.5%)

We included multiple-armed studies with an intervention and a comparator ( online supplemental file 6 ). Of the 24 studies, (15, 62.5%) were experimental designs in which, (10, 41.7%) were cluster randomised controlled trials (4, 16.7%) were individual randomised controlled trials and (1, 4.2%) was a randomised crossover trial. Of the remaining studies, (5, 20.8%) were quasi-experimental designs (non-randomised studies of intervention) in which (4, 16.7%) were pre-post/before and after studies and (1, 4.2%) was non-randomised crossover trials. The remaining studies (4, 16.7%) were observational where, (3, 12.5%) were cross-sectional designs and (1, 4.2%) was a cohort study.

Patient-important outcomes

Patient-important outcome measures and individual study findings are summarised in online supplemental file 7 . Of the 24 included studies, (21, 87.5%) measured the therapeutic impact of mRDTs, while (13, 54.2%) evaluated its health impact and only (1, 4.2%) assessed its diagnostic impact. Only (13, 54.2%) of all studies reported statistically significant findings.

Measures of therapeutic impact

Of the included studies, (20, 83.3%) reported on either antimalarials or antibiotics prescription patterns. The patient’s adherence to test results was reported by (3, 12.5%) studies, and the time taken to initiate treatment was reported by (2, 8.3%). In contrast, the pretreatment loss to follow-up was reported by (1, 4.2%) study. Studies reporting statistically significant findings on prescription patterns were (12, 50%), in which (11, 45.8%) demonstrated mRDTs’ potential to reduce over-prescription of antimalarials. In contrast, (1, 4.2%) study reported increased antimalarial prescription in the mRDT arm. Other statistically significant findings were reported by two studies where (1, 4.2%) reported that patients’ adherence to test results was poor in the malaria RDT arm. In contrast, the other (1, 4.2%) reported that mRDTs reduced the time to offer treatment.

Measures of health impact

Of the included studies, (6, 25%) reported on mortality, while (5, 20.8%) reported on symptom resolution. Patient health cost was reported by (4, 16.7%) studies, while patient referral and clinical re-attendance rates were reported by (2, 8.3%) each. Few (3, 12.5%) studies reported statistically significant findings on measuring the health impact that mRDTs improved the patient’s health outcomes by reducing morbidity.

Measures of diagnostic impact

Time taken to diagnose patients with malaria was reported by (1, 4.2%) study where diagnosis using mRDTs reduced the time to diagnose patients, but the findings were not statistically significant.

Implementation challenges

The themes identified among included studies according to the SURE framework 19 are presented in table 1 . Most themes (n=7, 50%) emerged from the health system constraints domain while only one theme was reported under the domain, social and political constraints. Two themes, human resources and patient’s attitude were dominant. Lack of qualified staff in some study sites and patient’s preference for alternative diagnostic tests other than mRDTs hindered effective implementation of five studies.

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Implementation challenge reported by the included studies

Methodological quality of included studies

The methodological quality of the included studies is summarised in figures 2 and 3 . All studies assessed their outcomes validly and reliably and consistently implemented them across all participants. Some studies did not provide adequate information about loss-to-follow-up. Overall, (17, 70.8%) were of good methodological quality in which (11, 45.8%) were experimental, (3, 12.5%) were quasi-experimental and (3, 12.5%) were observational studies; however, blinding was not feasible. Concerns regarding patient non-adherence to treatment were reported in some studies. Sample size justification which is crucial when detecting differences in the measured primary outcomes was poorly reported among most studies. A detailed summary of each study’s performance is available in online supplemental files 8 and 9 .

Quality assessment of controlled intervention study designs. NIH, National Institute for Health.

Quality assessment of observational study designs. NIH, National Institute for Health.

In this methodological systematic review, we assessed the designs, patient-important outcomes, implementation challenges and the methodological quality of studies evaluating the impact of mRDTs on patient-important outcomes within sub-Saharan Africa. We found evidence of mRDTs’ impact on patient-important outcomes came from just a few (six) from Western, Eastern and Southern African countries. Few studies were done on children, while most enrolled mixed populations in rural settings within government-owned hospitals. Few studies were conducted within the community health posts. Included studies assessed mRDTs’ impact compared with either microscopy/clinical diagnosis, with a majority being carried out during the high malaria transmission seasons in areas predominated by P. falciparum . Studies included were primary comparative designs, with experimental designs being the majority, followed by quasi-experimental and observational designs.

While most studies evaluated the therapeutic impact of mRDTs by measuring the prescription patterns of antimalarials/antibiotics, few assessed the test’s health and diagnostic impact. Few studies reported statistically significant findings, mainly on reduced antimalarial prescription patterns due to mRDTs. Most studies were of good quality, but quality concerns were lack of adequate information about loss-to-follow-up, inability to blind participants/providers/investigators, patient’s poor adherence to treatment options provided as guided by the predefined study protocols and lack of proper sample size justification. Key implementation limitations included inadequate human resources, lack of facilities, patients’ unacceptability of mRDTs, little consumer knowledge of the test and the providers’ low confidence in mRDTs’ negative results.

Schumacher et al conducted a similar study focusing on the impact of tuberculosis molecular tests, but unlike ours, they did not focus on implementation challenges. Similar to our results, Schumacher et al 16 identified that evidence of the impact of diagnostic tests comes from just a small number of countries within a particular setting. 16 Likewise, most studies evaluating the impact of diagnostic tests are done in health facilities like hospitals rather than in the community. 16 Our finding that the choice of study design in diagnostic research is coupled with trade-offs is in line with Schumacher’s review. 16 In the same way, experimental designs are mostly preferred in assessing diagnostic test impact, followed by quasi-experimental studies—majorly pre-post studies—conducted before and after the introduction of the intervention. 16 Our findings also agree that observational designs are the least adopted in evaluating diagnostic impact. 16 Similarly, our review’s finding concur with Schumacher et al that it may be worthwhile to explore other designs 16 that use qualitative and quantitative methods, that is, the mixed-methods design, as this can create a better understanding of the test’s impact in a pragmatic way.

Our findings that studies indirectly assess the impact of diagnostic tests on patients by measuring the therapeutic impact rather than the direct health impact agree with Schumacher et al . 16 However, in this systematic review, the ‘prescription patterns’ were most reported in contrast to Schumacher et al , where the ‘time to treatment’ was by far the most common. 16 Similar to our finding, Schumacher et al determined that there is a trade-off in the choice of design and the fulfilment of criteria set forth to protect the study’s internal validity. 16 While Schumacher et al investigated the risk of bias, our review focused on methodological quality. 16

Diagnostic impact studies are complex to implement despite being crucial to any health system seeking to roll-out the universal health coverage programmes. 21 Unlike therapeutic interventions that directly affect outcomes, several factors influence access to and effective implementation of diagnostic testing. 22 While it is easier to measure indirect upstream outcomes to quantify mRDTs’ impact on diagnosis and treatment options, it is crucial to understand the downstream measures such as morbidity (symptom resolution, clinical re-attendance and referrals), mortality, patient health costs 22 are key to improving value-based care. Contextual factors such as the provider’s lack of trust in the test’s credibility can negate the positive effects of the test, such as good performance. This is a problem facing health systems that are putting up initiatives to roll out mRDTs as the providers often perceive that negative mRDTs’ results are false positives. 16 22 Consequently, lacking essential facilities and human resources can hinder the true estimation of the value mRDTs contribute to the patient’s health in resource-limited areas.

Strengths and limitations

We conducted a robust literature search to get a recent representative sample of articles to assess the methodology. In addition to the methodology of studies, we evaluated the implementation challenges that limit the effect of the tests. Although we only included studies published in English which could affect generalisability of these findings, we believe this is a representative sample. Included studies were just from a few countries with sub-Sahara which could limit generalisability to other countries within the region. Since the overall sample size may not be an adequate representative of the entire population, the findings presented herein should be interpreted with caution. Additionally, considerations of the limited diversity in terms of study populations, interventions and outcome measures due to the few countries represented in the review should be included when interpreting our findings.

Health system concerns in both anglophone and francophone countries in sub-Saharan Africa are similar. 23 Studies did not report on blinding, but this did not affect their methodological quality since prior knowledge of the test and the intervention itself calls for having prior knowledge of the test. Our study was limited by reporting of study items such as randomisation and blinding of participants, providers and outcome assessors. This limited our quality assessment in quasi-experimental studies. Therefore, authors are encouraged to report the study findings according to the relevant reporting guidelines. 24 Most studies did not justify their sample sizes which could have compromised the validity of findings by influencing the precision and reliability of estimates. In cases where the sample size is inadequate, the reliability and generalisability of the findings becomes limited due to imprecise estimates with broad CIs. Studies reported poor adherence to protocols which could have reduced the sample size and the overall statistical power which could limit validity.

Implications for practice, policy and future research

Controlling the malaria epidemic in high-burden settings in sub-Saharan Africa will require the effective implementation of tests that do more than provide incremental benefit over current testing strategies. Contextual factors affecting the test performance need to be considered a priori and factors introduced to mitigate their effect on implementing mRDTs. Process evaluations 25 can be incorporated into quantitative studies or done alongside quantitative studies to determine whether the tests have been implemented as intended and resulted in certain outputs. Process evaluations 25 can be incorporated into experimental studies to assess contextual challenges that could influence the design. Process evaluations can help decision-makers ascertain whether the mRDTs could similarly impact the people if adopted in a different context. Therefore, not only should process evaluations be performed but they should also be performed in a variety of contexts. It is prudent that patient-important outcomes be measured alongside process evaluations to better understand how to implement mRDTs. It may be worthwhile to focus on methodological research that guides impact evaluation reporting, particularly those that consider contextual factors. Future studies on the impact of mRDTs could improve by conducting mixed-methods designs which might provide richer data interpretation and insights into implementation challenges. Future studies could also consider providing clear justification for the sample size to ensure there is enough power to detect a significant difference.

Most studies evaluating mRDTs’ impact on patient-important outcomes in sub-Saharan Africa are randomised trials of good methodological quality conducted in real-life settings. The therapeutic effect of mRDTs is by far the most common measure of mRDTs’ impact. Quality issues include poor reporting on sample size justification and reporting of statistically significant findings. Effective studies of patient-important outcome measures need to account for contextual factors such as inadequate resources, patients’ unacceptability of mRDTs, and the providers’ low confidence in mRDTs’ negative results, which hinder the effective implementation of impact-evaluating studies. Process evaluations can be incorporated into experimental studies to assess contextual challenges that could influence the design.

Ethics statements

Patient consent for publication.

Not applicable.

Ethics approval

Acknowledgments.

We also acknowledge the information search specialist Vittoria Lutje for designing the search strategy and conducting the literature searches.

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X @AkothJenifer, @sagamcaleb1

Contributors Concept of the study: EO. Drafting of the initial manuscript: JAO. Intellectual input on versions of the manuscript: JAO, LMW, CKS, SK, EO. Study supervision: SK, EO. Approving final draft of the manuscript: JAO, LMW, CKS, SK, EO. Guarantor: JAO.

Funding EO is funded under the UK MRC African Research Leaders award (MR/T008768/1). This award is jointly funded by the UK Medical Research Council (MRC) and the UK Foreign, Commonwealth & Development Office (FCDO) under the MRC/FCDO Concordat agreement. It is also part of the EDCTP2 programme supported by the European Union. This publication is associated with the Research, Evidence and Development Initiative (READ-It). READ-It (project number 300342-104) is funded by UK aid from the UK government; however, the views expressed do not necessarily reflect the UK government’s official policies. The funding organisations had no role in the development of this review.

Competing interests None declared.

Patient and public involvement Patients and/or the public were not involved in the design, or conduct, or reporting, or dissemination plans of this research.

Provenance and peer review Not commissioned; externally peer reviewed.

Supplemental material This content has been supplied by the author(s). It has not been vetted by BMJ Publishing Group Limited (BMJ) and may not have been peer-reviewed. Any opinions or recommendations discussed are solely those of the author(s) and are not endorsed by BMJ. BMJ disclaims all liability and responsibility arising from any reliance placed on the content. Where the content includes any translated material, BMJ does not warrant the accuracy and reliability of the translations (including but not limited to local regulations, clinical guidelines, terminology, drug names and drug dosages), and is not responsible for any error and/or omissions arising from translation and adaptation or otherwise.

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