what is the research objective in statistics

• Defining Research Objectives: How To  Write Them

Almost all industries use research for growth and development. Research objectives are how researchers ensure that their study has direction and makes a significant contribution to growing an industry or niche.

Research objectives provide a clear and concise statement of what the researcher wants to find out. As a researcher, you need to clearly outline and define research objectives to guide the research process and ensure that the study is relevant and generates the impact you want.

In this article, we will explore research objectives and how to leverage them to achieve successful research studies.

What Are Research Objectives?

Research objectives are what you want to achieve through your research study. They guide your research process and help you focus on the most important aspects of your topic.

You can also define the scope of your study and set realistic and attainable study goals with research objectives. For example, with clear research objectives, your study focuses on the specific goals you want to achieve and prevents you from spending time and resources collecting unnecessary data.

However, sticking to research objectives isn’t always easy, especially in broad or unconventional research. This is why most researchers follow the SMART criteria when defining their research objectives.

Understanding SMART Criteria in Research

Think of research objectives as a roadmap to achieving your research goals, with the SMART criteria as your navigator on the map.

SMART stands for Specific, Measurable, Achievable, Relevant, and Time-bound. These criteria help you ensure that your research objectives are clear, specific, realistic, meaningful, and time-bound.

Here’s a breakdown of the SMART Criteria:

Specific : Your research objectives should be clear: what do you want to achieve, why do you want to achieve it, and how do you plan to achieve it? Avoid vague or broad statements that don’t provide enough direction for your research.

Measurable : Your research objectives should have metrics that help you track your progress and measure your results. Also, ensure the metrics are measurable with data to verify them.

Achievable : Your research objectives should be within your research scope, timeframe, and budget. Also, set goals that are challenging but not impossible.

Relevant: Your research objectives should be in line with the goal and significance of your study. Also, ensure that the objectives address a specific issue or knowledge gap that is interesting and relevant to your industry or niche.

Time-bound : Your research objectives should have a specific deadline or timeframe for completion. This will help you carefully set a schedule for your research activities and milestones and monitor your study progress.

Characteristics of Effective Research Objectives

Clarity : Your objectives should be clear and unambiguous so that anyone who reads them can understand what you intend to do. Avoid vague or general terms that could be taken out of context.

Specificity : Your objectives should be specific and address the research questions that you have formulated. Do not use broad or narrow objectives as they may restrict your field of research or make your research irrelevant.

Measurability : Define your metrics with indicators or metrics that help you determine if you’ve accomplished your goals or not. This will ensure you are tracking the research progress and making interventions when needed.

Also, do use objectives that are subjective or based on personal opinions, as they may be difficult to accurately verify and measure.

Achievability : Your objectives should be realistic and attainable, given the resources and time available for your research project. You should set objectives that match your skills and capabilities, they can be difficult but not so hard that they are realistically unachievable.

For example, setting very difficult make you lose confidence, and abandon your research. Also, setting very simple objectives could demotivate you and prevent you from closing the knowledge gap or making significant contributions to your field with your research.

Relevance : Your objectives should be relevant to your research topic and contribute to the existing knowledge in your field. Avoid objectives that are unrelated or insignificant, as they may waste your time or resources.

Time-bound : Your objectives should be time-bound and specify when you will complete them. Have a realistic and flexible timeframe for achieving your objectives, and track your progress with it. 

Steps to Writing Research Objectives

Identify the research questions.

The first step in writing effective research objectives is to identify the research questions that you are trying to answer. Research questions help you narrow down your topic and identify the gaps or problems that you want to address with your research.

For example, if you are interested in the impact of technology on children’s development, your research questions could be:

• What is the relationship between technology use and academic performance among children?
• Are children who use technology more likely to do better in school than those who do not?
• What is the social and psychological impact of technology use on children?

Brainstorm Objectives

Once you have your research questions, you can brainstorm possible objectives that relate to them. Objectives are more specific than research questions, and they tell you what you want to achieve or learn in your research.

You can use verbs such as analyze, compare, evaluate, explore, investigate, etc. to express your objectives. Also, try to generate as many objectives as possible, without worrying about their quality or feasibility at this stage.

Prioritize Objectives

Once you’ve brainstormed your objectives, you’ll need to prioritize them based on their relevance and feasibility. Relevance is how relevant the objective is to your research topic and how well it fits into your overall research objective.

Feasibility is how realistic and feasible the objective is compared to the time, money, and expertise you have. You can create a matrix or ranking system to organize your objectives and pick the ones that matter the most.

Refine Objectives

The next step is to refine and revise your objectives to ensure clarity and specificity. Start by ensuring that your objectives are consistent and coherent with each other and with your research questions. 

Make Objectives SMART

A useful way to refine your objectives is to make them SMART, which stands for specific, measurable, achievable, relevant, and time-bound. 

• Specific : Objectives should clearly state what you hope to achieve.
• Measurable : They should be able to be quantified or evaluated.
• Achievable : realistic and within the scope of the research study.
• Relevant : They should be directly related to the research questions.
• Time-bound : specific timeframe for research completion.

Review and Finalize Objectives

The final step is to review your objectives for coherence and alignment with your research questions and aim. Ensure your objectives are logically connected and consistent with each other and with the purpose of your study.

You also need to check that your objectives are not too broad or too narrow, too easy or too hard, too many or too few. You can use a checklist or a rubric to evaluate your objectives and make modifications.

Examples of Well-Written Research Objectives

Example 1- Psychology

Research question: What are the effects of social media use on teenagers’ mental health?

Objective : To determine the relationship between the amount of time teenagers in the US spend on social media and their levels of anxiety and depression before and after using social media.

What Makes the Research Objective SMART?

The research objective is specific because it clearly states what the researcher hopes to achieve. It is measurable because it can be quantified by measuring the levels of anxiety and depression in teenagers. 

Also, the objective is achievable because the researcher can collect enough data to answer the research question. It is relevant because it is directly related to the research question. It is time-bound because it has a specific deadline for completion.

Example 2- Marketing

Research question : How can a company increase its brand awareness by 10%?

Objective : To develop a marketing strategy that will increase the company’s sales by 10% within the next quarter.

How Is this Research Objective SMART?

The research states what the researcher hopes to achieve ( Specific ). You can also measure the company’s reach before and after the marketing plan is implemented ( Measurable ).

The research objective is also achievable because you can develop a marketing plan that will increase awareness by 10% within the timeframe. The objective is directly related to the research question ( Relevant ). It is also time-bound because it has a specific deadline for completion.

Research objectives are a well-designed roadmap to completing and achieving your overall research goal. 

However, research goals are only effective if they are well-defined and backed up with the best practices such as the SMART criteria. Properly defining research objectives will help you plan and conduct your research project effectively and efficiently.

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Home » Research Objectives – Types, Examples and Writing Guide

Research Objectives – Types, Examples and Writing Guide

Table of Contents

Research Objectives

Research objectives refer to the specific goals or aims of a research study. They provide a clear and concise description of what the researcher hopes to achieve by conducting the research . The objectives are typically based on the research questions and hypotheses formulated at the beginning of the study and are used to guide the research process.

Types of Research Objectives

Here are the different types of research objectives in research:

• Exploratory Objectives: These objectives are used to explore a topic, issue, or phenomenon that has not been studied in-depth before. The aim of exploratory research is to gain a better understanding of the subject matter and generate new ideas and hypotheses .
• Descriptive Objectives: These objectives aim to describe the characteristics, features, or attributes of a particular population, group, or phenomenon. Descriptive research answers the “what” questions and provides a snapshot of the subject matter.
• Explanatory Objectives : These objectives aim to explain the relationships between variables or factors. Explanatory research seeks to identify the cause-and-effect relationships between different phenomena.
• Predictive Objectives: These objectives aim to predict future events or outcomes based on existing data or trends. Predictive research uses statistical models to forecast future trends or outcomes.
• Evaluative Objectives : These objectives aim to evaluate the effectiveness or impact of a program, intervention, or policy. Evaluative research seeks to assess the outcomes or results of a particular intervention or program.
• Prescriptive Objectives: These objectives aim to provide recommendations or solutions to a particular problem or issue. Prescriptive research identifies the best course of action based on the results of the study.
• Diagnostic Objectives : These objectives aim to identify the causes or factors contributing to a particular problem or issue. Diagnostic research seeks to uncover the underlying reasons for a particular phenomenon.
• Comparative Objectives: These objectives aim to compare two or more groups, populations, or phenomena to identify similarities and differences. Comparative research is used to determine which group or approach is more effective or has better outcomes.
• Historical Objectives: These objectives aim to examine past events, trends, or phenomena to gain a better understanding of their significance and impact. Historical research uses archival data, documents, and records to study past events.
• Ethnographic Objectives : These objectives aim to understand the culture, beliefs, and practices of a particular group or community. Ethnographic research involves immersive fieldwork and observation to gain an insider’s perspective of the group being studied.
• Action-oriented Objectives: These objectives aim to bring about social or organizational change. Action-oriented research seeks to identify practical solutions to social problems and to promote positive change in society.
• Conceptual Objectives: These objectives aim to develop new theories, models, or frameworks to explain a particular phenomenon or set of phenomena. Conceptual research seeks to provide a deeper understanding of the subject matter by developing new theoretical perspectives.
• Methodological Objectives: These objectives aim to develop and improve research methods and techniques. Methodological research seeks to advance the field of research by improving the validity, reliability, and accuracy of research methods and tools.
• Theoretical Objectives : These objectives aim to test and refine existing theories or to develop new theoretical perspectives. Theoretical research seeks to advance the field of knowledge by testing and refining existing theories or by developing new theoretical frameworks.
• Measurement Objectives : These objectives aim to develop and validate measurement instruments, such as surveys, questionnaires, and tests. Measurement research seeks to improve the quality and reliability of data collection and analysis by developing and testing new measurement tools.
• Design Objectives : These objectives aim to develop and refine research designs, such as experimental, quasi-experimental, and observational designs. Design research seeks to improve the quality and validity of research by developing and testing new research designs.
• Sampling Objectives: These objectives aim to develop and refine sampling techniques, such as probability and non-probability sampling methods. Sampling research seeks to improve the representativeness and generalizability of research findings by developing and testing new sampling techniques.

How to Write Research Objectives

Writing clear and concise research objectives is an important part of any research project, as it helps to guide the study and ensure that it is focused and relevant. Here are some steps to follow when writing research objectives:

• Identify the research problem : Before you can write research objectives, you need to identify the research problem you are trying to address. This should be a clear and specific problem that can be addressed through research.
• Define the research questions : Based on the research problem, define the research questions you want to answer. These questions should be specific and should guide the research process.
• Identify the variables : Identify the key variables that you will be studying in your research. These are the factors that you will be measuring, manipulating, or analyzing to answer your research questions.
• Write specific objectives: Write specific, measurable objectives that will help you answer your research questions. These objectives should be clear and concise and should indicate what you hope to achieve through your research.
• Use the SMART criteria: To ensure that your research objectives are well-defined and achievable, use the SMART criteria. This means that your objectives should be Specific, Measurable, Achievable, Relevant, and Time-bound.
• Revise and refine: Once you have written your research objectives, revise and refine them to ensure that they are clear, concise, and achievable. Make sure that they align with your research questions and variables, and that they will help you answer your research problem.

Example of Research Objectives

Examples of research objectives Could be:

Research Objectives for the topic of “The Impact of Artificial Intelligence on Employment”:

• To investigate the effects of the adoption of AI on employment trends across various industries and occupations.
• To explore the potential for AI to create new job opportunities and transform existing roles in the workforce.
• To examine the social and economic implications of the widespread use of AI for employment, including issues such as income inequality and access to education and training.
• To identify the skills and competencies that will be required for individuals to thrive in an AI-driven workplace, and to explore the role of education and training in developing these skills.
• To evaluate the ethical and legal considerations surrounding the use of AI for employment, including issues such as bias, privacy, and the responsibility of employers and policymakers to protect workers’ rights.

When to Write Research Objectives

• At the beginning of a research project : Research objectives should be identified and written down before starting a research project. This helps to ensure that the project is focused and that data collection and analysis efforts are aligned with the intended purpose of the research.
• When refining research questions: Writing research objectives can help to clarify and refine research questions. Objectives provide a more concrete and specific framework for addressing research questions, which can improve the overall quality and direction of a research project.
• After conducting a literature review : Conducting a literature review can help to identify gaps in knowledge and areas that require further research. Writing research objectives can help to define and focus the research effort in these areas.
• When developing a research proposal: Research objectives are an important component of a research proposal. They help to articulate the purpose and scope of the research, and provide a clear and concise summary of the expected outcomes and contributions of the research.
• When seeking funding for research: Funding agencies often require a detailed description of research objectives as part of a funding proposal. Writing clear and specific research objectives can help to demonstrate the significance and potential impact of a research project, and increase the chances of securing funding.
• When designing a research study : Research objectives guide the design and implementation of a research study. They help to identify the appropriate research methods, sampling strategies, data collection and analysis techniques, and other relevant aspects of the study design.
• When communicating research findings: Research objectives provide a clear and concise summary of the main research questions and outcomes. They are often included in research reports and publications, and can help to ensure that the research findings are communicated effectively and accurately to a wide range of audiences.
• When evaluating research outcomes : Research objectives provide a basis for evaluating the success of a research project. They help to measure the degree to which research questions have been answered and the extent to which research outcomes have been achieved.
• When conducting research in a team : Writing research objectives can facilitate communication and collaboration within a research team. Objectives provide a shared understanding of the research purpose and goals, and can help to ensure that team members are working towards a common objective.

Purpose of Research Objectives

Some of the main purposes of research objectives include:

• To clarify the research question or problem : Research objectives help to define the specific aspects of the research question or problem that the study aims to address. This makes it easier to design a study that is focused and relevant.
• To guide the research design: Research objectives help to determine the research design, including the research methods, data collection techniques, and sampling strategy. This ensures that the study is structured and efficient.
• To measure progress : Research objectives provide a way to measure progress throughout the research process. They help the researcher to evaluate whether they are on track and meeting their goals.
• To communicate the research goals : Research objectives provide a clear and concise description of the research goals. This helps to communicate the purpose of the study to other researchers, stakeholders, and the general public.

Advantages of Research Objectives

Here are some advantages of having well-defined research objectives:

• Focus : Research objectives help to focus the research effort on specific areas of inquiry. By identifying clear research questions, the researcher can narrow down the scope of the study and avoid getting sidetracked by irrelevant information.
• Clarity : Clearly stated research objectives provide a roadmap for the research study. They provide a clear direction for the research, making it easier for the researcher to stay on track and achieve their goals.
• Measurability : Well-defined research objectives provide measurable outcomes that can be used to evaluate the success of the research project. This helps to ensure that the research is effective and that the research goals are achieved.
• Feasibility : Research objectives help to ensure that the research project is feasible. By clearly defining the research goals, the researcher can identify the resources required to achieve those goals and determine whether those resources are available.
• Relevance : Research objectives help to ensure that the research study is relevant and meaningful. By identifying specific research questions, the researcher can ensure that the study addresses important issues and contributes to the existing body of knowledge.

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Research Aims, Objectives & Questions

The “Golden Thread” Explained Simply (+ Examples)

By: David Phair (PhD) and Alexandra Shaeffer (PhD) | June 2022

The research aims , objectives and research questions (collectively called the “golden thread”) are arguably the most important thing you need to get right when you’re crafting a research proposal , dissertation or thesis . We receive questions almost every day about this “holy trinity” of research and there’s certainly a lot of confusion out there, so we’ve crafted this post to help you navigate your way through the fog.

Overview: The Golden Thread

• What is the golden thread
• What are research aims ( examples )
• What are research objectives ( examples )
• What are research questions ( examples )
• The importance of alignment in the golden thread

What is the “golden thread”?  

The golden thread simply refers to the collective research aims , research objectives , and research questions for any given project (i.e., a dissertation, thesis, or research paper ). These three elements are bundled together because it’s extremely important that they align with each other, and that the entire research project aligns with them.

Importantly, the golden thread needs to weave its way through the entirety of any research project , from start to end. In other words, it needs to be very clearly defined right at the beginning of the project (the topic ideation and proposal stage) and it needs to inform almost every decision throughout the rest of the project. For example, your research design and methodology will be heavily influenced by the golden thread (we’ll explain this in more detail later), as well as your literature review.

The research aims, objectives and research questions (the golden thread) define the focus and scope ( the delimitations ) of your research project. In other words, they help ringfence your dissertation or thesis to a relatively narrow domain, so that you can “go deep” and really dig into a specific problem or opportunity. They also help keep you on track , as they act as a litmus test for relevance. In other words, if you’re ever unsure whether to include something in your document, simply ask yourself the question, “does this contribute toward my research aims, objectives or questions?”. If it doesn’t, chances are you can drop it.

Alright, enough of the fluffy, conceptual stuff. Let’s get down to business and look at what exactly the research aims, objectives and questions are and outline a few examples to bring these concepts to life.

Research Aims: What are they?

Simply put, the research aim(s) is a statement that reflects the broad overarching goal (s) of the research project. Research aims are fairly high-level (low resolution) as they outline the general direction of the research and what it’s trying to achieve .

Research Aims: Examples  

True to the name, research aims usually start with the wording “this research aims to…”, “this research seeks to…”, and so on. For example:

“This research aims to explore employee experiences of digital transformation in retail HR.”   “This study sets out to assess the interaction between student support and self-care on well-being in engineering graduate students”  

As you can see, these research aims provide a high-level description of what the study is about and what it seeks to achieve. They’re not hyper-specific or action-oriented, but they’re clear about what the study’s focus is and what is being investigated.

Need a helping hand?

Research Objectives: What are they?

The research objectives take the research aims and make them more practical and actionable . In other words, the research objectives showcase the steps that the researcher will take to achieve the research aims.

The research objectives need to be far more specific (higher resolution) and actionable than the research aims. In fact, it’s always a good idea to craft your research objectives using the “SMART” criteria. In other words, they should be specific, measurable, achievable, relevant and time-bound”.

Research Objectives: Examples  

Let’s look at two examples of research objectives. We’ll stick with the topic and research aims we mentioned previously.  

For the digital transformation topic:

To observe the retail HR employees throughout the digital transformation. To assess employee perceptions of digital transformation in retail HR. To identify the barriers and facilitators of digital transformation in retail HR.

And for the student wellness topic:

To determine whether student self-care predicts the well-being score of engineering graduate students. To determine whether student support predicts the well-being score of engineering students. To assess the interaction between student self-care and student support when predicting well-being in engineering graduate students.

  As you can see, these research objectives clearly align with the previously mentioned research aims and effectively translate the low-resolution aims into (comparatively) higher-resolution objectives and action points . They give the research project a clear focus and present something that resembles a research-based “to-do” list.

Research Questions: What are they?

Finally, we arrive at the all-important research questions. The research questions are, as the name suggests, the key questions that your study will seek to answer . Simply put, they are the core purpose of your dissertation, thesis, or research project. You’ll present them at the beginning of your document (either in the introduction chapter or literature review chapter) and you’ll answer them at the end of your document (typically in the discussion and conclusion chapters).  

The research questions will be the driving force throughout the research process. For example, in the literature review chapter, you’ll assess the relevance of any given resource based on whether it helps you move towards answering your research questions. Similarly, your methodology and research design will be heavily influenced by the nature of your research questions. For instance, research questions that are exploratory in nature will usually make use of a qualitative approach, whereas questions that relate to measurement or relationship testing will make use of a quantitative approach.  

Let’s look at some examples of research questions to make this more tangible.

Research Questions: Examples  

Again, we’ll stick with the research aims and research objectives we mentioned previously.  

For the digital transformation topic (which would be qualitative in nature):

How do employees perceive digital transformation in retail HR? What are the barriers and facilitators of digital transformation in retail HR?  

And for the student wellness topic (which would be quantitative in nature):

Does student self-care predict the well-being scores of engineering graduate students? Does student support predict the well-being scores of engineering students? Do student self-care and student support interact when predicting well-being in engineering graduate students?  

You’ll probably notice that there’s quite a formulaic approach to this. In other words, the research questions are basically the research objectives “converted” into question format. While that is true most of the time, it’s not always the case. For example, the first research objective for the digital transformation topic was more or less a step on the path toward the other objectives, and as such, it didn’t warrant its own research question.  

So, don’t rush your research questions and sloppily reword your objectives as questions. Carefully think about what exactly you’re trying to achieve (i.e. your research aim) and the objectives you’ve set out, then craft a set of well-aligned research questions . Also, keep in mind that this can be a somewhat iterative process , where you go back and tweak research objectives and aims to ensure tight alignment throughout the golden thread.

The importance of strong alignment 

Alignment is the keyword here and we have to stress its importance . Simply put, you need to make sure that there is a very tight alignment between all three pieces of the golden thread. If your research aims and research questions don’t align, for example, your project will be pulling in different directions and will lack focus . This is a common problem students face and can cause many headaches (and tears), so be warned.

Take the time to carefully craft your research aims, objectives and research questions before you run off down the research path. Ideally, get your research supervisor/advisor to review and comment on your golden thread before you invest significant time into your project, and certainly before you start collecting data .  

Recap: The golden thread

In this post, we unpacked the golden thread of research, consisting of the research aims , research objectives and research questions . You can jump back to any section using the links below.

As always, feel free to leave a comment below – we always love to hear from you. Also, if you’re interested in 1-on-1 support, take a look at our private coaching service here.

Psst... there’s more!

This post was based on one of our popular Research Bootcamps . If you're working on a research project, you'll definitely want to check this out ...

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39 Comments

Thank you very much for your great effort put. As an Undergraduate taking Demographic Research & Methodology, I’ve been trying so hard to understand clearly what is a Research Question, Research Aim and the Objectives in a research and the relationship between them etc. But as for now I’m thankful that you’ve solved my problem.

Well appreciated. This has helped me greatly in doing my dissertation.

An so delighted with this wonderful information thank you a lot.

so impressive i have benefited a lot looking forward to learn more on research.

I am very happy to have carefully gone through this well researched article.

Infact,I used to be phobia about anything research, because of my poor understanding of the concepts.

Now,I get to know that my research question is the same as my research objective(s) rephrased in question format.

I please I would need a follow up on the subject,as I intends to join the team of researchers. Thanks once again.

Thanks so much. This was really helpful.

I know you pepole have tried to break things into more understandable and easy format. And God bless you. Keep it up

i found this document so useful towards my study in research methods. thanks so much.

This is my 2nd read topic in your course and I should commend the simplified explanations of each part. I’m beginning to understand and absorb the use of each part of a dissertation/thesis. I’ll keep on reading your free course and might be able to avail the training course! Kudos!

Thank you! Better put that my lecture and helped to easily understand the basics which I feel often get brushed over when beginning dissertation work.

This is quite helpful. I like how the Golden thread has been explained and the needed alignment.

This is quite helpful. I really appreciate!

The article made it simple for researcher students to differentiate between three concepts.

Very innovative and educational in approach to conducting research.

I am very impressed with all these terminology, as I am a fresh student for post graduate, I am highly guided and I promised to continue making consultation when the need arise. Thanks a lot.

A very helpful piece. thanks, I really appreciate it .

Very well explained, and it might be helpful to many people like me.

Wish i had found this (and other) resource(s) at the beginning of my PhD journey… not in my writing up year… 😩 Anyways… just a quick question as i’m having some issues ordering my “golden thread”…. does it matter in what order you mention them? i.e., is it always first aims, then objectives, and finally the questions? or can you first mention the research questions and then the aims and objectives?

Thank you for a very simple explanation that builds upon the concepts in a very logical manner. Just prior to this, I read the research hypothesis article, which was equally very good. This met my primary objective.

My secondary objective was to understand the difference between research questions and research hypothesis, and in which context to use which one. However, I am still not clear on this. Can you kindly please guide?

In research, a research question is a clear and specific inquiry that the researcher wants to answer, while a research hypothesis is a tentative statement or prediction about the relationship between variables or the expected outcome of the study. Research questions are broader and guide the overall study, while hypotheses are specific and testable statements used in quantitative research. Research questions identify the problem, while hypotheses provide a focus for testing in the study.

Exactly what I need in this research journey, I look forward to more of your coaching videos.

This helped a lot. Thanks so much for the effort put into explaining it.

What data source in writing dissertation/Thesis requires?

What is data source covers when writing dessertation/thesis

This is quite useful thanks

I’m excited and thankful. I got so much value which will help me progress in my thesis.

where are the locations of the reserch statement, research objective and research question in a reserach paper? Can you write an ouline that defines their places in the researh paper?

Very helpful and important tips on Aims, Objectives and Questions.

Thank you so much for making research aim, research objectives and research question so clear. This will be helpful to me as i continue with my thesis.

Thanks much for this content. I learned a lot. And I am inspired to learn more. I am still struggling with my preparation for dissertation outline/proposal. But I consistently follow contents and tutorials and the new FB of GRAD Coach. Hope to really become confident in writing my dissertation and successfully defend it.

As a researcher and lecturer, I find splitting research goals into research aims, objectives, and questions is unnecessarily bureaucratic and confusing for students. For most biomedical research projects, including ‘real research’, 1-3 research questions will suffice (numbers may differ by discipline).

Awesome! Very important resources and presented in an informative way to easily understand the golden thread. Indeed, thank you so much.

Well explained

The blog article on research aims, objectives, and questions by Grad Coach is a clear and insightful guide that aligns with my experiences in academic research. The article effectively breaks down the often complex concepts of research aims and objectives, providing a straightforward and accessible explanation. Drawing from my own research endeavors, I appreciate the practical tips offered, such as the need for specificity and clarity when formulating research questions. The article serves as a valuable resource for students and researchers, offering a concise roadmap for crafting well-defined research goals and objectives. Whether you’re a novice or an experienced researcher, this article provides practical insights that contribute to the foundational aspects of a successful research endeavor.

A great thanks for you. it is really amazing explanation. I grasp a lot and one step up to research knowledge.

I really found these tips helpful. Thank you very much Grad Coach.

I found this article helpful. Thanks for sharing this.

thank you so much, the explanation and examples are really helpful

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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.

More From Abdishakur Hassan The 7 Best Thematic Map Types for Geospatial Data

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.

Recent Expert Contributors Articles

Statistics Made Easy

The Importance of Statistics in Research (With Examples)

The field of statistics is concerned with collecting, analyzing, interpreting, and presenting data.

In the field of research, statistics is important for the following reasons:

Reason 1 : Statistics allows researchers to design studies such that the findings from the studies can be extrapolated to a larger population.

Reason 2 : Statistics allows researchers to perform hypothesis tests to determine if some claim about a new drug, new procedure, new manufacturing method, etc. is true.

Reason 3 : Statistics allows researchers to create confidence intervals to capture uncertainty around population estimates.

In the rest of this article, we elaborate on each of these reasons.

Reason 1: Statistics Allows Researchers to Design Studies

Researchers are often interested in answering questions about populations like:

• What is the average weight of a certain species of bird?
• What is the average height of a certain species of plant?
• What percentage of citizens in a certain city support a certain law?

One way to answer these questions is to go around and collect data on every single individual in the population of interest.

However, this is typically too costly and time-consuming which is why researchers instead take a  sample  of the population and use the data from the sample to draw conclusions about the population as a whole.

There are many different methods researchers can potentially use to obtain individuals to be in a sample. These are known as  sampling methods .

There are two classes of sampling methods:

• Probability sampling methods : Every member in a population has an equal probability of being selected to be in the sample.
• Non-probability sampling methods : Not every member in a population has an equal probability of being selected to be in the sample.

By using probability sampling methods, researchers can maximize the chances that they obtain a sample that is representative of the overall population.

This allows researchers to extrapolate the findings from the sample to the overall population.

Read more about the two classes of sampling methods here .

Reason 2: Statistics Allows Researchers to Perform Hypothesis Tests

Another way that statistics is used in research is in the form of hypothesis tests .

These are tests that researchers can use to determine if there is a statistical significance between different medical procedures or treatments.

For example, suppose a scientist believes that a new drug is able to reduce blood pressure in obese patients. To test this, he measures the blood pressure of 30 patients before and after using the new drug for one month.

He then performs a paired samples t- test using the following hypotheses:

• H 0 : μ after = μ before (the mean blood pressure is the same before and after using the drug)
• H A : μ after < μ before (the mean blood pressure is less after using the drug)

If the p-value of the test is less than some significance level (e.g. α = .05), then he can reject the null hypothesis and conclude that the new drug leads to reduced blood pressure.

Note : This is just one example of a hypothesis test that is used in research. Other common tests include a one sample t-test , two sample t-test , one-way ANOVA , and two-way ANOVA .

Reason 3: Statistics Allows Researchers to Create Confidence Intervals

Another way that statistics is used in research is in the form of confidence intervals .

A confidence interval is a range of values that is likely to contain a population parameter with a certain level of confidence.

For example, suppose researchers are interested in estimating the mean weight of a certain species of turtle.

Instead of going around and weighing every single turtle in the population, researchers may instead take a simple random sample of turtles with the following information:

• Sample size  n = 25
• Sample mean weight  x  = 300
• Sample standard deviation  s = 18.5

Using the confidence interval for a mean formula , researchers may then construct the following 95% confidence interval:

95% Confidence Interval:  300 +/-  1.96*(18.5/√ 25 ) =  [292.75, 307.25]

The researchers would then claim that they’re 95% confident that the true mean weight for this population of turtles is between 292.75 pounds and 307.25 pounds.

Additional Resources

The following articles explain the importance of statistics in other fields:

The Importance of Statistics in Healthcare The Importance of Statistics in Nursing The Importance of Statistics in Business The Importance of Statistics in Economics The Importance of Statistics in Education

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Hey there. My name is Zach Bobbitt. I have a Masters of Science degree in Applied Statistics and I’ve worked on machine learning algorithms for professional businesses in both healthcare and retail. I’m passionate about statistics, machine learning, and data visualization and I created Statology to be a resource for both students and teachers alike.  My goal with this site is to help you learn statistics through using simple terms, plenty of real-world examples, and helpful illustrations.

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You may have heard someone say, “Research shows that…” What this means is that an experimenter used the scientific method to test a Research Hypothesis, and either supported that Research Hypothesis or did not support that Research Hypothesis. However, much of what you read online is not supported by research using the scientific method. Instead, people who don’t know what an IV or DV is try to convince you that their ideas are correct.

As a group, scientists seem to be bizarrely fixated on running statistical tests on everything. In fact, we use statistics so often that we sometimes forget to explain to people why we do. It’s a kind of article of faith among scientists – and especially social scientists – that your findings can’t be trusted until you’ve done some stats. Undergraduate students might be forgiven for thinking that we’re all completely mad, because no one takes the time to answer one very simple question:

Why do you do statistics? Why don’t scientists just use common sense?

There’s a lot of good answers to it, 1 but a really simple answer is: we don’t trust ourselves enough. Scientists, especially psychologists, worry that we’re human, and susceptible to all of the biases, temptations and frailties that humans suffer from. Much of statistics is basically a safeguard. Using “common sense” to evaluate evidence means trusting gut instincts, relying on verbal arguments and on using the raw power of human reason to come up with the right answer. Most scientists don’t think this approach is likely to work.

In fact, come to think of it, this sounds a lot like a psychological question. In this behavioral statistics textbook, it seems like a good idea to dig a little deeper here. Is it really plausible to think that this “common sense” approach is very trustworthy? Verbal arguments have to be constructed in language, and all languages have biases – some things are harder to say than others, and not necessarily because they’re false (e.g., quantum electrodynamics is a good theory, but hard to explain in words). The instincts of our “gut” aren’t designed to solve scientific problems, they’re designed to handle day to day inferences – and given that biological evolution is slower than cultural change, we should say that our gut is designed to solve the day to day problems for a different world than the one we live in. Most fundamentally, reasoning sensibly requires people to engage in “induction”, making wise guesses and going beyond the immediate evidence of the senses to make generalizations about the world. If you think that you can do that without being influenced by various distractors, well, I have a bridge in Brooklyn I’d like to sell you.

The Curse of Belief Bias

People are mostly pretty smart. Our minds are quite amazing things, and we seem to be capable of the most incredible feats of thought and reason. That doesn’t make us perfect though. And among the many things that psychologists have shown over the years is that we really do find it hard to be neutral, to evaluate evidence impartially and without being swayed by pre-existing biases.

But first, suppose that people really are perfectly able to set aside their pre-existing beliefs about what is true and what isn’t, and evaluate an argument purely on its logical merits. We’d expect 100% of people to say that the valid arguments are valid, and 0% of people to say that the invalid arguments are valid. So if you ran an experiment looking at this, you’d expect to see data like this:

If the data looked like this (or even a good approximation to this), we might feel safe in just trusting our gut instincts. That is, it’d be perfectly okay just to let scientists evaluate data based on their common sense, and not bother with all this murky statistics stuff. However, you have taken classes, and might know where this is going . . .

In a classic study, Evans, Barston, and Pollard (1983) ran an experiment looking at exactly this. What they found is show in Table \(\PageIndex{2}\); when pre-existing biases (i.e., beliefs) were in agreement with the structure of the data, everything went the way you’d hope (in bold). Not perfect, but that’s pretty good. But look what happens when our intuitive feelings about the truth of the conclusion run against the logical structure of the argument (the not-bold percentages):

Almost all people continue to believe something that isn't true, even with a valid argument against it. Also, almost half of people continue to believe that true arguments are false (if they started out not believing it).

Oh dear, that’s not as good. Apparently, when we are presented with a strong argument that contradicts our pre-existing beliefs, we find it pretty hard to even perceive it to be a strong argument (people only did so 46% of the time). Even worse, when people are presented with a weak argument that agrees with our pre-existing biases, almost no-one can see that the argument is weak (people got that one wrong 92% of the time!).

Overall, people did do better than a chance at compensating for their prior biases, since about 60% of people’s judgments were correct (you’d expect 50% by chance). Even so, if you were a professional “evaluator of evidence”, and someone came along and offered you a magic tool that improves your chances of making the right decision from 60% to (say) 95%, you’d probably jump at it, right? Of course you would. Thankfully, we actually do have a tool that can do this. But it’s not magic, it’s statistics. So that’s reason #1 why scientists love statistics. It’s just too easy for us humans to continue to “believe what we want to believe”; so if we want to “believe in the data” instead, we’re going to need a bit of help to keep our personal biases under control. That’s what statistics does: it helps keep us honest.

Before you “like” or share news articles or posts online, try to get to get as close to the original study as you can get, and figure out what the IV, DV, sample, and population is so that you can decide if their clam is actually supported by research. Was the IV created (not just measured)? Does the way that the DV was measured make sense for that outcome? Does the sample really represent the population that they are saying it does? Science is hard to do well, but it’s the best way to learn new things about the world.

1 Including the suggestion that common sense is in short supply among scientists.

Evans, J. St. B. T., Barston, J. L., & Pollard, P. (1983). On the conflict between logic and belief in syllogistic reasoning. Memory & Cognition, 11 , 295-306.

Quantitative and Qualitative Research

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What is Quantitative Research?

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Quantitative methodology is the dominant research framework in the social sciences. It refers to a set of strategies, techniques and assumptions used to study psychological, social and economic processes through the exploration of numeric patterns . Quantitative research gathers a range of numeric data. Some of the numeric data is intrinsically quantitative (e.g. personal income), while in other cases the numeric structure is  imposed (e.g. ‘On a scale from 1 to 10, how depressed did you feel last week?’). The collection of quantitative information allows researchers to conduct simple to extremely sophisticated statistical analyses that aggregate the data (e.g. averages, percentages), show relationships among the data (e.g. ‘Students with lower grade point averages tend to score lower on a depression scale’) or compare across aggregated data (e.g. the USA has a higher gross domestic product than Spain). Quantitative research includes methodologies such as questionnaires, structured observations or experiments and stands in contrast to qualitative research. Qualitative research involves the collection and analysis of narratives and/or open-ended observations through methodologies such as interviews, focus groups or ethnographies.

Coghlan, D., Brydon-Miller, M. (2014).  The SAGE encyclopedia of action research  (Vols. 1-2). London, : SAGE Publications Ltd doi: 10.4135/9781446294406

What is the purpose of quantitative research?

The purpose of quantitative research is to generate knowledge and create understanding about the social world. Quantitative research is used by social scientists, including communication researchers, to observe phenomena or occurrences affecting individuals. Social scientists are concerned with the study of people. Quantitative research is a way to learn about a particular group of people, known as a sample population. Using scientific inquiry, quantitative research relies on data that are observed or measured to examine questions about the sample population.

Allen, M. (2017).  The SAGE encyclopedia of communication research methods  (Vols. 1-4). Thousand Oaks, CA: SAGE Publications, Inc doi: 10.4135/9781483381411

How do I know if the study is a quantitative design?  What type of quantitative study is it?

Quantitative Research Designs: Descriptive non-experimental, Quasi-experimental or Experimental?

Studies do not always explicitly state what kind of research design is being used.  You will need to know how to decipher which design type is used.  The following video will help you determine the quantitative design type.

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Research Methodology

Methodology refers to the overarching strategy and rationale of your research. Developing your methodology involves studying the research methods used in your field and the theories or principles that underpin them, in order to choose the approach that best matches your research objectives. Methodology is the first step in planning a research project.

Qualitative Data Coding

What Is a Focus Group?

Reviewed by Olivia Guy-Evans, MSc

Cross-Cultural Research Methodology In Psychology

What is internal validity in research.

Reviewed by Saul Mcleod, PhD

Scientific Method

Qualitative research, experiments.

The scientific method is a step-by-step process used by researchers and scientists to determine if there is a relationship between two or more variables. Psychologists use this method to conduct psychological research, gather data, process information, and describe behaviors.

Learn More: Steps of the Scientific Method

Variables apply to experimental investigations. The independent variable is the variable the experimenter manipulates or changes. The dependent variable is the variable being tested and measured in an experiment, and is 'dependent' on the independent variable.

Learn More: Independent and Dependent Variables

When you perform a statistical test a p-value helps you determine the significance of your results in relation to the null hypothesis. A p-value less than 0.05 (typically ≤ 0.05) is statistically significant.

Learn More: P-Value and Statistical Significance

Qualitative research is a process used for the systematic collection, analysis, and interpretation of non-numerical data. Qualitative research can be used to gain a deep contextual understanding of the subjective social reality of individuals.

The experimental method involves the manipulation of variables to establish cause-and-effect relationships. The key features are controlled methods and the random allocation of participants into controlled and experimental groups.

Learn More: How the Experimental Method Works in Psychology

Frequent Asked Questions

What does p-value of 0.05 mean?

A p-value less than 0.05 (typically ≤ 0.05) is statistically significant. It indicates strong evidence against the null hypothesis, as there is less than a 5% probability the results have occurred by random chance rather than a real effect. Therefore, we reject the null hypothesis and accept the alternative hypothesis.

However, it is important to note that the p-value is not the only factor that should be considered when interpreting the results of a hypothesis test. Other factors, such as effect size, should also be considered.

Learn More: What A p-Value Tells You About Statistical Significance

What does z-score tell you?

A  z-score  describes the position of a raw score in terms of its distance from the mean when measured in standard deviation units. It is also known as a standard score because it allows the comparison of scores on different variables by standardizing the distribution. The z-score is positive if the value lies above the mean and negative if it lies below the mean.

Learn More: Z-Score: Definition, Calculation, Formula, & Interpretation

What is an independent vs dependent variable?

The independent variable is the variable the experimenter manipulates or changes and is assumed to have a direct effect on the dependent variable. For example, allocating participants to either drug or placebo conditions (independent variable) to measure any changes in the intensity of their anxiety (dependent variable).

Learn More : What are Independent and Dependent Variables?

What is the difference between qualitative and quantitative?

Quantitative data is numerical information about quantities and qualitative data is descriptive and regards phenomena that can be observed but not measured, such as language.

Learn More: What’s the difference between qualitative and quantitative research?

Explore Research Methodology

What Is Face Validity In Research? Importance & How To Measure

Criterion Validity: Definition & Examples

Convergent Validity: Definition and Examples

Content Validity in Research: Definition & Examples

Construct Validity In Psychology Research

Concurrent Validity In Psychology

Internal vs. External Validity In Psychology

Qualitative Research: Characteristics, Design, Methods & Examples

Demand Characteristics In Psychology: Definition, Examples & Control

Between-Subjects vs. Within-Subjects Study Design

Random Assignment in Psychology: Definition & Examples

Double-Blind Experimental Study And Procedure Explained

Observer Bias: Definition, Examples & Prevention

Sampling Bias: Types, Examples & How to Avoid It

What is The Null Hypothesis & When Do You Reject The Null Hypothesis

Between-Subjects Design: Overview & Examples

What Is A Case Control Study?

Case Study Research Method in Psychology

Cohort Study: Definition, Designs & Examples

Cluster Sampling: Definition, Method and Examples

Convenience Sampling: Definition, Method and Examples

Confounding Variables in Psychology: Definition & Examples

Control Group vs Experimental Group

Controlled Experiment

Correlation in Psychology: Meaning, Types, Examples & coefficient

Extraneous Variables In Research: Types & Examples

Ethnocentrism In Psychology: Examples, Disadvantages, & Cultural Relativism

Ethical Considerations In Psychology Research

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Objectives of Statistics

The Objectives of Statistics :

The main objective of statistics is to study the various facts and problems in the research field and to evaluate the causes and results of the changes occurring in them.

Statistics is the science of gaining knowledge from data. You can collect data in the correct manner, perform detailed analyses, and effectively present the results if you have statistical knowledge.

Statistics teaches people how to make intelligent and accurate conclusions about a larger population by analysing a small and limited sample of data . The following are the major objectives of statistics:

• To draw conclusions (inferences) about a population followed by an analysis of information contained in sample data. This includes assessing the degree of uncertainty in these inferences.
• To plan the process and the extent of sampling so that the observations can be used to draw valid conclusions.
• To determine the type and quantity of data that must be collected.
• To organise and summarise the information.
• To analyse and draw conclusions from the data.
• To assess the conclusions’ strengths and evaluate their uncertainty.

According to Prof. Boddington , “The main objective of statistical research is to enable comparison between past and present results to ascertain the reasons for changes, which have taken place and the effect of such changes in future.

According to Johnson and Jackson , “The real purpose of statistical methods is to make proper sense out of facts and figures, to make discoveries about unknown and to cost light upon the situation.”

According to Robert W. Buges , “The fundamental principle of statistics is to remove the domain of ignorance, prejudice, rule of thumb, arbitrary and premature decisions, traditions and dogmatism and to increase the domain where decisions are made and principles are formulated on the basis of analysed quantitative facts.”

Hence, it is clear that statistics is an integral stage of national development, which helps us in solving various complex problems.

(Source – Various books of college library)

Tags: the objective of statistics, objectives of statistics, objectives of studying statistics, aims and objectives of statistics, explain the objectives of statistics

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Why Should the FDA Focus on Pragmatic Clinical Research?

• 1 US Food and Drug Administration, White Oak Campus, Silver Spring, Maryland
• Editor's Note Integrating Clinical Trials and Practice Gregory Curfman, MD JAMA
• Special Communication The Integration of Clinical Trials With the Practice of Medicine Derek C. Angus, MD, MPH; Alison J. Huang, MD, MAS; Roger J. Lewis, MD, PhD; Amy P. Abernethy, MD, PhD; Robert M. Califf, MD; Martin Landray, PhD; Nancy Kass, ScD; Kirsten Bibbins-Domingo, PhD, MD, MAS; JAMA Summit on Clinical Trials Participants; Ali B Abbasi; Kaleab Z Abebe; Amy P Abernethy; Stacey J. Adam; Derek C Angus; Jamy Ard; Rachel A Bender Ignacio ; Scott M Berry; Deepak L. Bhatt; Kirsten Bibbins-Domingo; Robert O. Bonow; Marc Bonten; Sharon A. Brangman; John Brownstein; Melinda J. B. Buntin; Atul J Butte; Robert M. Califf; Marion K Campbell; Anne R. Cappola; Anne C Chiang; Deborah Cook; Steven R Cummings; Gregory Curfman; Laura J Esserman; Lee A Fleisher; Joseph B Franklin; Ralph Gonzalez; Cynthia I Grossman; Tufia C. Haddad; Roy S. Herbst; Adrian F. Hernandez; Diane P Holder; Leora Horn; Grant D. Huang; Alison Huang; Nancy Kass; Rohan Khera; Walter J. Koroshetz; Harlan M. Krumholz; Martin Landray; Roger J. Lewis; Tracy A Lieu; Preeti N. Malani; Christa Lese Martin; Mark McClellan; Mary M. McDermott; Stephanie R. Morain; Susan A Murphy; Stuart G Nicholls; Stephen J Nicholls; Peter J. O'Dwyer; Bhakti K Patel; Eric Peterson; Sheila A. Prindiville; Joseph S. Ross; Kathryn M Rowan; Gordon Rubenfeld; Christopher W. Seymour; Rod S Taylor; Joanne Waldstreicher; Tracy Y. Wang JAMA

Traditional randomized clinical trials (RCTs) have long been a key tool underpinning drug and device development. The use of individual participant randomization and active or placebo controls in RCTs, combined with comprehensive collection of highly structured data, supports assay sensitivity. At the same time, focused enrollment criteria and careful attention to the collection of adverse events for specified follow-up periods promote detection of toxicities and risks. These trials support a system, regulated by the US Food and Drug Administration (FDA) and other global regulators, that allows the majority of candidate therapies whose risks outweigh benefits for intended use to be screened out while enabling safe and effective medical products to advance to market. However, the next stage—after product development and marketing authorization are completed and a therapy is integrated into clinical practice—needs serious attention.

• Editor's Note Integrating Clinical Trials and Practice JAMA

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Abbasi AB , Curtis LH , Califf RM. Why Should the FDA Focus on Pragmatic Clinical Research? JAMA. Published online June 03, 2024. doi:10.1001/jama.2024.6227

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• 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 ].

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

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

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:

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:

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:

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:

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

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 ].

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.

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

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

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:

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

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:

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:

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

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:

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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U.S. public, private and charter schools in 5 charts

While children in the United States are guaranteed a free education at their local public school through state constitutional law, many families weigh other educational options for their children. Even before the coronavirus pandemic upended families’ usual routines, 36% of parents with K-12 students say they considered multiple schools for their child in the 2018-19 school year.

Students’ school environments vary widely – sometimes even for children living in the same community – depending on whether they attend traditional public, private or charter schools.

Here are some key distinctions between these three types of schools, based on data from the National Center for Education Statistics (NCES). All figures reflect the most recent school year with data for all three types of schools.

Pew Research Center conducted this analysis to better understand how U.S. students’ school experiences might differ depending on whether they attend a traditional public school, a private school or a charter school.

Data comes from the Institute of Education Sciences’ National Center for Education Statistics . We used the most recent year in which data is available for all three school types.

Public, private and charter schools include those that teach students in kindergarten through 12th grade, unless otherwise specified. Racial categories used in this analysis include those who report being a single race and non-Hispanic. Hispanics are of any race. National School Lunch Program data for 2021-22 is not available for Alaska.

What’s the difference between public, private and charter schools?

Until a few decades ago, parents with kids in elementary, middle or high school could choose to send them to either a traditional public school or a private one. More recently, many states have added a third option: public charter schools.

• Traditional public schools are taxpayer funded, are tuition free and must adhere to standards set by a school district or state board of education. These are the most common schooling option in the U.S.
• Private schools are known for being selective, religiously affiliated or sometimes both, and charge tuition rather than receive public money. In addition to tuition dollars, private schools may be funded through a combination of donations, endowments or grants from other private sources. As a result, they have more autonomy when it comes to curriculum and other academic standards. During the 2021-22 school year, about three-quarters of private school K-12 students (77%) attended a religiously affiliated school. The largest share went to Catholic schools, which accounted for 35% of all private school enrollment. Another 23% of private school students attended secular institutions.
• Public charter schools are legally allowed to operate in nearly all states, plus the District of Columbia, as of 2024. Like traditional public schools, these are taxpayer funded and tuition free. They’re open to any student who wishes to enroll. But unlike their traditional counterparts, agreements – or charters – with the state or local government allow them flexibility when it comes to curriculum and other standards. They also may turn students away due to space constraints.

Differences exist in the size and locale of each type of school, NCES data from the 2021-22 school year shows.

Traditional public schools tend to be larger than the other types. For instance, 39% of public schools enroll 500 or more students, compared with 32% of charter schools and 8% of private schools. And while 31% of public schools have fewer than 300 students, 44% of charter schools and 82% of private schools do.

Public schools are relatively evenly distributed across urban, suburban and rural areas, while most charter and private school campuses are located in either cities or suburbs.

(Traditional public and charter school environment data includes prekindergarten students, who account for less than 1% of enrollment at these types of schools.)

Where is enrollment growing and shrinking?

During the 2021-22 school year, the vast majority of the country’s roughly 54.6 million public, private and charter school students in pre-K through 12th grade (83%) attended traditional public schools. Another 10% were enrolled in private schools, and 7% went to public charter schools.

Enrollment numbers have shifted over the last decade:

• Traditional public school enrollment has declined. In fall 2011, about 47.2 million students attended public elementary, middle and secondary schools, accounting for 87% of all school enrollment. By fall 2021, the number of public school students dropped to about 45.4 million, resulting in a small drop in public schools’ share of total enrollment.
• The popularity of charter schools has grown. Minnesota became the first state to pass legislation allowing charter schools in 1991. In the last 10 years alone, enrollment has risen from about 2.1 million students in fall 2011 to nearly 3.7 million in fall 2021, an increase from 4% to 7% of total enrollment.
• Private school enrollment has held relatively steady. Private school students have consistently made up about 10% of school enrollment, with numbers that have fluctuated from a 10-year low of fewer than 5.3 million in 2011 to a peak of almost 5.8 million in 2015.

How does enrollment look at the state level?

Nationwide, the vast majority of students in pre-K through 12th grade attend traditional public schools – but shares vary somewhat from state to state. In Wyoming, for example, nearly all students (97%) attend public school, while 45% do in D.C.

The states with the highest percentages of public school enrollment include some of those with the lowest population density . In addition to Wyoming, West Virginia (95%), Montana (93%), Kansas and Alaska (91% each) round out the top five states by share of public school enrollment.

In most states, students are more likely to attend a private school than a charter school. Charter school students make up a larger share of enrollment than private school students in just 12 states and D.C. (Data is unavailable for seven states because they did not have any charter schools or legislation allowing them in fall 2021.)

Among the places where students are the least likely to attend traditional public schools:

• D.C. has the highest share of charter school students, at 36%. Just 45% of K-12 students there attend traditional public schools. Another 19% attend private schools.
• D.C. and Hawaii have the largest percentage of students in private schools, at 19% each. In Hawaii, another 76% of students are enrolled in public school, and 6% are enrolled in charter schools.

How do student demographics vary by school type?

Charter schools had the most racial and ethnic diversity during the 2021-22 school year. Hispanic students make up the largest share of enrollment there (36%), followed by White (29%), Black (24%) and Asian American students (4%).

In contrast, 47% of traditional public school students and 65% of private school students are White. Smaller shares are Hispanic, Black or Asian.

Differences also exist by household income level. Nearly all public and charter schools are part of the National School Lunch Program , which provides free or reduced-price meals to students based on family income.

In general, charter school students are more likely than public school kids to qualify for the program. For instance, 31% of charter students and 21% of traditional public school students are enrolled at a school where more than three-quarters of their peers qualify for free or reduced-price lunch.

Because a relatively small share of private schools participate in this program, 2021-22 data is not available for them. However, research shows that private school enrollment rates are highest among upper-income families .

What does the teaching staff look like at each type of school?

More than 4.2 million full- and part-time teachers worked at public, private and charter schools during the 2020-21 school year, the most recent year with available data. That year, about 3.5 million teachers (83%) taught at traditional public schools. Another 466,000 (11%) worked in private schools, and 251,000 (6%) taught at public charters.

The teaching force in each environment varies based on race and ethnicity, age, experience, and educational attainment.

• Charter school teachers are the most racially and ethnically diverse: 69% of charter school teachers are White, compared with about eight-in-ten at both traditional public and private schools. Charters also employ the largest shares of Black and Hispanic teachers.
• Private school teachers skew slightly older, while charter school teachers are the youngest: About 17% of private school teachers are ages 60 and older, compared with 8% in public schools and 7% in charter schools. And in charter schools, 21% of teachers are under 30, compared with 14% each in public and private schools.
• Charters employ a larger share of teachers with fewer years of experience: For instance, 13% of both private and charter school teachers have fewer than three years of experience, compared with 7% of public school teachers. And 43% of charter school teachers have between three and nine years of experience, compared with 28% each in public and private schools.
• Public school teachers are the most likely to have a master’s degree: 52% of public school teachers have a master’s degree, compared with about 41% each in charter and private schools.

Katherine Schaeffer is a research analyst at Pew Research Center .

A quarter of U.S. teachers say AI tools do more harm than good in K-12 education

Most americans think u.s. k-12 stem education isn’t above average, but test results paint a mixed picture, about 1 in 4 u.s. teachers say their school went into a gun-related lockdown in the last school year, about half of americans say public k-12 education is going in the wrong direction, what public k-12 teachers want americans to know about teaching, most popular.

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Forced labour is a severe violation of human rights affecting 28 million of men, women and children in all countries and all economic sectors. It is rooted in poverty, discrimination and lack of social protection, and it disrupts fair competition between businesses. The issue has been at the heart of the ILO mandate to promote Fundamental Principles and Rights at Work, leaving no one behind.

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The state of AI in early 2024: Gen AI adoption spikes and starts to generate value

If 2023 was the year the world discovered generative AI (gen AI) , 2024 is the year organizations truly began using—and deriving business value from—this new technology. In the latest McKinsey Global Survey  on AI, 65 percent of respondents report that their organizations are regularly using gen AI, nearly double the percentage from our previous survey just ten months ago. Respondents’ expectations for gen AI’s impact remain as high as they were last year , with three-quarters predicting that gen AI will lead to significant or disruptive change in their industries in the years ahead.

About the authors

This article is a collaborative effort by Alex Singla , Alexander Sukharevsky , Lareina Yee , and Michael Chui , with Bryce Hall , representing views from QuantumBlack, AI by McKinsey, and McKinsey Digital.

Organizations are already seeing material benefits from gen AI use, reporting both cost decreases and revenue jumps in the business units deploying the technology. The survey also provides insights into the kinds of risks presented by gen AI—most notably, inaccuracy—as well as the emerging practices of top performers to mitigate those challenges and capture value.

AI adoption surges

Interest in generative AI has also brightened the spotlight on a broader set of AI capabilities. For the past six years, AI adoption by respondents’ organizations has hovered at about 50 percent. This year, the survey finds that adoption has jumped to 72 percent (Exhibit 1). And the interest is truly global in scope. Our 2023 survey found that AI adoption did not reach 66 percent in any region; however, this year more than two-thirds of respondents in nearly every region say their organizations are using AI. 1 Organizations based in Central and South America are the exception, with 58 percent of respondents working for organizations based in Central and South America reporting AI adoption. Looking by industry, the biggest increase in adoption can be found in professional services. 2 Includes respondents working for organizations focused on human resources, legal services, management consulting, market research, R&D, tax preparation, and training.

Also, responses suggest that companies are now using AI in more parts of the business. Half of respondents say their organizations have adopted AI in two or more business functions, up from less than a third of respondents in 2023 (Exhibit 2).

Gen AI adoption is most common in the functions where it can create the most value

Most respondents now report that their organizations—and they as individuals—are using gen AI. Sixty-five percent of respondents say their organizations are regularly using gen AI in at least one business function, up from one-third last year. The average organization using gen AI is doing so in two functions, most often in marketing and sales and in product and service development—two functions in which previous research  determined that gen AI adoption could generate the most value 3 “ The economic potential of generative AI: The next productivity frontier ,” McKinsey, June 14, 2023. —as well as in IT (Exhibit 3). The biggest increase from 2023 is found in marketing and sales, where reported adoption has more than doubled. Yet across functions, only two use cases, both within marketing and sales, are reported by 15 percent or more of respondents.

Gen AI also is weaving its way into respondents’ personal lives. Compared with 2023, respondents are much more likely to be using gen AI at work and even more likely to be using gen AI both at work and in their personal lives (Exhibit 4). The survey finds upticks in gen AI use across all regions, with the largest increases in Asia–Pacific and Greater China. Respondents at the highest seniority levels, meanwhile, show larger jumps in the use of gen Al tools for work and outside of work compared with their midlevel-management peers. Looking at specific industries, respondents working in energy and materials and in professional services report the largest increase in gen AI use.

Investments in gen AI and analytical AI are beginning to create value

The latest survey also shows how different industries are budgeting for gen AI. Responses suggest that, in many industries, organizations are about equally as likely to be investing more than 5 percent of their digital budgets in gen AI as they are in nongenerative, analytical-AI solutions (Exhibit 5). Yet in most industries, larger shares of respondents report that their organizations spend more than 20 percent on analytical AI than on gen AI. Looking ahead, most respondents—67 percent—expect their organizations to invest more in AI over the next three years.

Where are those investments paying off? For the first time, our latest survey explored the value created by gen AI use by business function. The function in which the largest share of respondents report seeing cost decreases is human resources. Respondents most commonly report meaningful revenue increases (of more than 5 percent) in supply chain and inventory management (Exhibit 6). For analytical AI, respondents most often report seeing cost benefits in service operations—in line with what we found last year —as well as meaningful revenue increases from AI use in marketing and sales.

Inaccuracy: The most recognized and experienced risk of gen AI use

As businesses begin to see the benefits of gen AI, they’re also recognizing the diverse risks associated with the technology. These can range from data management risks such as data privacy, bias, or intellectual property (IP) infringement to model management risks, which tend to focus on inaccurate output or lack of explainability. A third big risk category is security and incorrect use.

Respondents to the latest survey are more likely than they were last year to say their organizations consider inaccuracy and IP infringement to be relevant to their use of gen AI, and about half continue to view cybersecurity as a risk (Exhibit 7).

Conversely, respondents are less likely than they were last year to say their organizations consider workforce and labor displacement to be relevant risks and are not increasing efforts to mitigate them.

In fact, inaccuracy— which can affect use cases across the gen AI value chain , ranging from customer journeys and summarization to coding and creative content—is the only risk that respondents are significantly more likely than last year to say their organizations are actively working to mitigate.

Some organizations have already experienced negative consequences from the use of gen AI, with 44 percent of respondents saying their organizations have experienced at least one consequence (Exhibit 8). Respondents most often report inaccuracy as a risk that has affected their organizations, followed by cybersecurity and explainability.

Our previous research has found that there are several elements of governance that can help in scaling gen AI use responsibly, yet few respondents report having these risk-related practices in place. 4 “ Implementing generative AI with speed and safety ,” McKinsey Quarterly , March 13, 2024. For example, just 18 percent say their organizations have an enterprise-wide council or board with the authority to make decisions involving responsible AI governance, and only one-third say gen AI risk awareness and risk mitigation controls are required skill sets for technical talent.

Bringing gen AI capabilities to bear

The latest survey also sought to understand how, and how quickly, organizations are deploying these new gen AI tools. We have found three archetypes for implementing gen AI solutions : takers use off-the-shelf, publicly available solutions; shapers customize those tools with proprietary data and systems; and makers develop their own foundation models from scratch. 5 “ Technology’s generational moment with generative AI: A CIO and CTO guide ,” McKinsey, July 11, 2023. Across most industries, the survey results suggest that organizations are finding off-the-shelf offerings applicable to their business needs—though many are pursuing opportunities to customize models or even develop their own (Exhibit 9). About half of reported gen AI uses within respondents’ business functions are utilizing off-the-shelf, publicly available models or tools, with little or no customization. Respondents in energy and materials, technology, and media and telecommunications are more likely to report significant customization or tuning of publicly available models or developing their own proprietary models to address specific business needs.

Respondents most often report that their organizations required one to four months from the start of a project to put gen AI into production, though the time it takes varies by business function (Exhibit 10). It also depends upon the approach for acquiring those capabilities. Not surprisingly, reported uses of highly customized or proprietary models are 1.5 times more likely than off-the-shelf, publicly available models to take five months or more to implement.

Gen AI high performers are excelling despite facing challenges

Gen AI is a new technology, and organizations are still early in the journey of pursuing its opportunities and scaling it across functions. So it’s little surprise that only a small subset of respondents (46 out of 876) report that a meaningful share of their organizations’ EBIT can be attributed to their deployment of gen AI. Still, these gen AI leaders are worth examining closely. These, after all, are the early movers, who already attribute more than 10 percent of their organizations’ EBIT to their use of gen AI. Forty-two percent of these high performers say more than 20 percent of their EBIT is attributable to their use of nongenerative, analytical AI, and they span industries and regions—though most are at organizations with less than $1 billion in annual revenue. The AI-related practices at these organizations can offer guidance to those looking to create value from gen AI adoption at their own organizations.

To start, gen AI high performers are using gen AI in more business functions—an average of three functions, while others average two. They, like other organizations, are most likely to use gen AI in marketing and sales and product or service development, but they’re much more likely than others to use gen AI solutions in risk, legal, and compliance; in strategy and corporate finance; and in supply chain and inventory management. They’re more than three times as likely as others to be using gen AI in activities ranging from processing of accounting documents and risk assessment to R&D testing and pricing and promotions. While, overall, about half of reported gen AI applications within business functions are utilizing publicly available models or tools, gen AI high performers are less likely to use those off-the-shelf options than to either implement significantly customized versions of those tools or to develop their own proprietary foundation models.

What else are these high performers doing differently? For one thing, they are paying more attention to gen-AI-related risks. Perhaps because they are further along on their journeys, they are more likely than others to say their organizations have experienced every negative consequence from gen AI we asked about, from cybersecurity and personal privacy to explainability and IP infringement. Given that, they are more likely than others to report that their organizations consider those risks, as well as regulatory compliance, environmental impacts, and political stability, to be relevant to their gen AI use, and they say they take steps to mitigate more risks than others do.

Gen AI high performers are also much more likely to say their organizations follow a set of risk-related best practices (Exhibit 11). For example, they are nearly twice as likely as others to involve the legal function and embed risk reviews early on in the development of gen AI solutions—that is, to “ shift left .” They’re also much more likely than others to employ a wide range of other best practices, from strategy-related practices to those related to scaling.

In addition to experiencing the risks of gen AI adoption, high performers have encountered other challenges that can serve as warnings to others (Exhibit 12). Seventy percent say they have experienced difficulties with data, including defining processes for data governance, developing the ability to quickly integrate data into AI models, and an insufficient amount of training data, highlighting the essential role that data play in capturing value. High performers are also more likely than others to report experiencing challenges with their operating models, such as implementing agile ways of working and effective sprint performance management.

About the research

The online survey was in the field from February 22 to March 5, 2024, and garnered responses from 1,363 participants representing the full range of regions, industries, company sizes, functional specialties, and tenures. Of those respondents, 981 said their organizations had adopted AI in at least one business function, and 878 said their organizations were regularly using gen AI in at least one function. To adjust for differences in response rates, the data are weighted by the contribution of each respondent’s nation to global GDP.

Alex Singla and Alexander Sukharevsky  are global coleaders of QuantumBlack, AI by McKinsey, and senior partners in McKinsey’s Chicago and London offices, respectively; Lareina Yee  is a senior partner in the Bay Area office, where Michael Chui , a McKinsey Global Institute partner, is a partner; and Bryce Hall  is an associate partner in the Washington, DC, office.

They wish to thank Kaitlin Noe, Larry Kanter, Mallika Jhamb, and Shinjini Srivastava for their contributions to this work.

This article was edited by Heather Hanselman, a senior editor in McKinsey’s Atlanta office.

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