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Hypothesis Testing

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1. Multiple Choice Edit 30 seconds 1 pt What is definition of null hypothesis? The independent variable has no effect on the dependent variable for the population The independent variable does have an effect on the dependent variable The dependent variable has no effect on the independent variable The dependent variable does have effec on the independent variable
2. Multiple Choice Edit 30 seconds 1 pt If the alpha level is increased from 0.01 to 0.05, then the boundaries for the critical region move farther away from the center of the distribution. True False
3. Multiple Choice Edit 30 seconds 1 pt To check the normality test using Shapiro-Wilk, if the p-value is more than 0.05? The data is significant The data is not normal The data is normal Reject null hypothesis
4. Multiple Choice Edit 30 seconds 1 pt To check the normality test using Shapiro-Wilk, if the p-value is below 0.05? Accept null hypothesis Reject null hypothesis Failed to reject null hypothesis Reject alternative hypothesis
5. Multiple Choice Edit 30 seconds 1 pt Define a Type I error? The failure to reject a false null hypothesis Rejecting a true null hypothesis The acceptance to reject a null hypothesis Accepting a true null hypothesis
6. Multiple Choice Edit 30 seconds 1 pt If a sample mean is in the critical region with alpha level 0.05, it would still (always) be in the critical region if alpha were changed to 0.01? False True
7. Multiple Choice Edit 30 seconds 1 pt If a sample mean is in the critical region with alpha level 0.01, it would still(always) be in the critical region if alpha were changed to 0.05? False True
8. Multiple Choice Edit 30 seconds 1 pt In a research report, the term "significant" is used when the null hypothesis is rejected. True False
9. Multiple Choice Edit 30 seconds 1 pt In a research report, the results of a hypothesis test include the phrase " z=3.15, p<0.01". This means that the test failed to reject the null hypothesis. True False
10. Multiple Choice Edit 30 seconds 1 pt A z-score value in critical region means that you should reject the null hypothesis. True False

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9.1: Null and Alternative Hypotheses

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The actual test begins by considering two hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints.

$H_0$: The null hypothesis: It is a statement of no difference between the variables—they are not related. This can often be considered the status quo and as a result if you cannot accept the null it requires some action.

$H_a$: The alternative hypothesis: It is a claim about the population that is contradictory to $H_0$ and what we conclude when we reject $H_0$. This is usually what the researcher is trying to prove.

Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.

After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are "reject $H_0$" if the sample information favors the alternative hypothesis or "do not reject $H_0$" or "decline to reject $H_0$" if the sample information is insufficient to reject the null hypothesis.

$H_{0}$ always has a symbol with an equal in it. $H_{a}$ never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers (including one of the co-authors in research work) use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.

Example $\PageIndex{1}$

$H_{0}$: No more than 30% of the registered voters in Santa Clara County voted in the primary election. $p \leq 30$
$H_{a}$: More than 30% of the registered voters in Santa Clara County voted in the primary election. $p > 30$

Exercise $\PageIndex{1}$

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypotheses.

$H_{0}$: The drug reduces cholesterol by 25%. $p = 0.25$
$H_{a}$: The drug does not reduce cholesterol by 25%. $p \neq 0.25$

Example $\PageIndex{2}$

We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are:

$H_{0}: \mu = 2.0$
$H_{a}: \mu \neq 2.0$

Exercise $\PageIndex{2}$

We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol $(=, \neq, \geq, <, \leq, >)$ for the null and alternative hypotheses.

$H_{0}: \mu \_ 66$
$H_{a}: \mu \_ 66$
$H_{0}: \mu = 66$
$H_{a}: \mu \neq 66$

Example $\PageIndex{3}$

We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are:

$H_{0}: \mu \geq 5$
$H_{a}: \mu < 5$

Exercise $\PageIndex{3}$

We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

$H_{0}: \mu \_ 45$
$H_{a}: \mu \_ 45$
$H_{0}: \mu \geq 45$
$H_{a}: \mu < 45$

Example $\PageIndex{4}$

In an issue of U. S. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass. The same article stated that 6.6% of U.S. students take advanced placement exams and 4.4% pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6%. State the null and alternative hypotheses.

$H_{0}: p \leq 0.066$
$H_{a}: p > 0.066$

Exercise $\PageIndex{4}$

On a state driver’s test, about 40% pass the test on the first try. We want to test if more than 40% pass on the first try. Fill in the correct symbol ($=, \neq, \geq, <, \leq, >$) for the null and alternative hypotheses.

$H_{0}: p \_ 0.40$
$H_{a}: p \_ 0.40$
$H_{0}: p = 0.40$
$H_{a}: p > 0.40$

COLLABORATIVE EXERCISE

Bring to class a newspaper, some news magazines, and some Internet articles . In groups, find articles from which your group can write null and alternative hypotheses. Discuss your hypotheses with the rest of the class.

In a hypothesis test , sample data is evaluated in order to arrive at a decision about some type of claim. If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we:

Evaluate the null hypothesis , typically denoted with $H_{0}$. The null is not rejected unless the hypothesis test shows otherwise. The null statement must always contain some form of equality $(=, \leq \text{or} \geq)$
Always write the alternative hypothesis , typically denoted with $H_{a}$ or $H_{1}$, using less than, greater than, or not equals symbols, i.e., $(\neq, >, \text{or} <)$.
If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis.
Never state that a claim is proven true or false. Keep in mind the underlying fact that hypothesis testing is based on probability laws; therefore, we can talk only in terms of non-absolute certainties.

Formula Review

$H_{0}$ and $H_{a}$ are contradictory.

If $\alpha \leq p$-value, then do not reject $H_{0}$.
If$\alpha > p$-value, then reject $H_{0}$.

$\alpha$ is preconceived. Its value is set before the hypothesis test starts. The $p$-value is calculated from the data.References

Data from the National Institute of Mental Health. Available online at http://www.nimh.nih.gov/publicat/depression.cfm .

Null Hypothesis Definition and Examples

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Ph.D., Biomedical Sciences, University of Tennessee at Knoxville
B.A., Physics and Mathematics, Hastings College

In a scientific experiment, the null hypothesis is the proposition that there is no effect or no relationship between phenomena or populations. If the null hypothesis is true, any observed difference in phenomena or populations would be due to sampling error (random chance) or experimental error. The null hypothesis is useful because it can be tested and found to be false, which then implies that there is a relationship between the observed data. It may be easier to think of it as a nullifiable hypothesis or one that the researcher seeks to nullify. The null hypothesis is also known as the H 0, or no-difference hypothesis.

The alternate hypothesis, H A or H 1 , proposes that observations are influenced by a non-random factor. In an experiment, the alternate hypothesis suggests that the experimental or independent variable has an effect on the dependent variable .

How to State a Null Hypothesis

There are two ways to state a null hypothesis. One is to state it as a declarative sentence, and the other is to present it as a mathematical statement.

For example, say a researcher suspects that exercise is correlated to weight loss, assuming diet remains unchanged. The average length of time to achieve a certain amount of weight loss is six weeks when a person works out five times a week. The researcher wants to test whether weight loss takes longer to occur if the number of workouts is reduced to three times a week.

The first step to writing the null hypothesis is to find the (alternate) hypothesis. In a word problem like this, you're looking for what you expect to be the outcome of the experiment. In this case, the hypothesis is "I expect weight loss to take longer than six weeks."

This can be written mathematically as: H 1 : μ > 6

In this example, μ is the average.

Now, the null hypothesis is what you expect if this hypothesis does not happen. In this case, if weight loss isn't achieved in greater than six weeks, then it must occur at a time equal to or less than six weeks. This can be written mathematically as:

H 0 : μ ≤ 6

The other way to state the null hypothesis is to make no assumption about the outcome of the experiment. In this case, the null hypothesis is simply that the treatment or change will have no effect on the outcome of the experiment. For this example, it would be that reducing the number of workouts would not affect the time needed to achieve weight loss:

H 0 : μ = 6

Null Hypothesis Examples

"Hyperactivity is unrelated to eating sugar " is an example of a null hypothesis. If the hypothesis is tested and found to be false, using statistics, then a connection between hyperactivity and sugar ingestion may be indicated. A significance test is the most common statistical test used to establish confidence in a null hypothesis.

Another example of a null hypothesis is "Plant growth rate is unaffected by the presence of cadmium in the soil ." A researcher could test the hypothesis by measuring the growth rate of plants grown in a medium lacking cadmium, compared with the growth rate of plants grown in mediums containing different amounts of cadmium. Disproving the null hypothesis would set the groundwork for further research into the effects of different concentrations of the element in soil.

Why Test a Null Hypothesis?

You may be wondering why you would want to test a hypothesis just to find it false. Why not just test an alternate hypothesis and find it true? The short answer is that it is part of the scientific method. In science, propositions are not explicitly "proven." Rather, science uses math to determine the probability that a statement is true or false. It turns out it's much easier to disprove a hypothesis than to positively prove one. Also, while the null hypothesis may be simply stated, there's a good chance the alternate hypothesis is incorrect.

For example, if your null hypothesis is that plant growth is unaffected by duration of sunlight, you could state the alternate hypothesis in several different ways. Some of these statements might be incorrect. You could say plants are harmed by more than 12 hours of sunlight or that plants need at least three hours of sunlight, etc. There are clear exceptions to those alternate hypotheses, so if you test the wrong plants, you could reach the wrong conclusion. The null hypothesis is a general statement that can be used to develop an alternate hypothesis, which may or may not be correct.

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Examples of Independent and Dependent Variables
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What Is a Hypothesis? (Science)
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Scientific Hypothesis Examples
What Is a Control Group?
Understanding Simple vs Controlled Experiments
Six Steps of the Scientific Method
Scientific Method Vocabulary Terms
Definition of a Hypothesis
How to Conduct a Hypothesis Test
Type I and Type II Errors in Statistics

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Null Hypothesis , often denoted as H 0, is a foundational concept in statistical hypothesis testing. It represents an assumption that no significant difference, effect, or relationship exists between variables within a population. It serves as a baseline assumption, positing no observed change or effect occurring. The null is t he truth or falsity of an idea in analysis.

In this article, we will discuss the null hypothesis in detail, along with some solved examples and questions on the null hypothesis.

Table of Content

What is Null Hypothesis?

Null hypothesis symbol, formula of null hypothesis, types of null hypothesis, null hypothesis examples, principle of null hypothesis, how do you find null hypothesis, null hypothesis in statistics, null hypothesis and alternative hypothesis, null hypothesis and alternative hypothesis examples, null hypothesis – practice problems.

Null Hypothesis in statistical analysis suggests the absence of statistical significance within a specific set of observed data. Hypothesis testing, using sample data, evaluates the validity of this hypothesis. Commonly denoted as H 0 or simply “null,” it plays an important role in quantitative analysis, examining theories related to markets, investment strategies, or economies to determine their validity.

Null Hypothesis Meaning

Null Hypothesis represents a default position, often suggesting no effect or difference, against which researchers compare their experimental results. The Null Hypothesis, often denoted as H 0 asserts a default assumption in statistical analysis. It posits no significant difference or effect, serving as a baseline for comparison in hypothesis testing.

The null Hypothesis is represented as H 0 , the Null Hypothesis symbolizes the absence of a measurable effect or difference in the variables under examination.

Certainly, a simple example would be asserting that the mean score of a group is equal to a specified value like stating that the average IQ of a population is 100.

The Null Hypothesis is typically formulated as a statement of equality or absence of a specific parameter in the population being studied. It provides a clear and testable prediction for comparison with the alternative hypothesis. The formulation of the Null Hypothesis typically follows a concise structure, stating the equality or absence of a specific parameter in the population.

Mean Comparison (Two-sample t-test)

H 0 : μ 1 = μ 2

This asserts that there is no significant difference between the means of two populations or groups.

Proportion Comparison

H 0 : p 1 − p 2 = 0

This suggests no significant difference in proportions between two populations or conditions.

Equality in Variance (F-test in ANOVA)

H 0 : σ 1 = σ 2

This states that there’s no significant difference in variances between groups or populations.

Independence (Chi-square Test of Independence):

H 0 : Variables are independent

This asserts that there’s no association or relationship between categorical variables.

Null Hypotheses vary including simple and composite forms, each tailored to the complexity of the research question. Understanding these types is pivotal for effective hypothesis testing.

Equality Null Hypothesis (Simple Null Hypothesis)

The Equality Null Hypothesis, also known as the Simple Null Hypothesis, is a fundamental concept in statistical hypothesis testing that assumes no difference, effect or relationship between groups, conditions or populations being compared.

Non-Inferiority Null Hypothesis

In some studies, the focus might be on demonstrating that a new treatment or method is not significantly worse than the standard or existing one.

Superiority Null Hypothesis

The concept of a superiority null hypothesis comes into play when a study aims to demonstrate that a new treatment, method, or intervention is significantly better than an existing or standard one.

Independence Null Hypothesis

In certain statistical tests, such as chi-square tests for independence, the null hypothesis assumes no association or independence between categorical variables.

Homogeneity Null Hypothesis

In tests like ANOVA (Analysis of Variance), the null hypothesis suggests that there’s no difference in population means across different groups.

Medicine: Null Hypothesis: “No significant difference exists in blood pressure levels between patients given the experimental drug versus those given a placebo.”
Education: Null Hypothesis: “There’s no significant variation in test scores between students using a new teaching method and those using traditional teaching.”
Economics: Null Hypothesis: “There’s no significant change in consumer spending pre- and post-implementation of a new taxation policy.”
Environmental Science: Null Hypothesis: “There’s no substantial difference in pollution levels before and after a water treatment plant’s establishment.”

The principle of the null hypothesis is a fundamental concept in statistical hypothesis testing. It involves making an assumption about the population parameter or the absence of an effect or relationship between variables.

In essence, the null hypothesis (H 0 ) proposes that there is no significant difference, effect, or relationship between variables. It serves as a starting point or a default assumption that there is no real change, no effect or no difference between groups or conditions.

The null hypothesis is usually formulated to be tested against an alternative hypothesis (H 1 or H [Tex]\alpha [/Tex] ) which suggests that there is an effect, difference or relationship present in the population.

Null Hypothesis Rejection

Rejecting the Null Hypothesis occurs when statistical evidence suggests a significant departure from the assumed baseline. It implies that there is enough evidence to support the alternative hypothesis, indicating a meaningful effect or difference. Null Hypothesis rejection occurs when statistical evidence suggests a deviation from the assumed baseline, prompting a reconsideration of the initial hypothesis.

Identifying the Null Hypothesis involves defining the status quotient, asserting no effect and formulating a statement suitable for statistical analysis.

When is Null Hypothesis Rejected?

The Null Hypothesis is rejected when statistical tests indicate a significant departure from the expected outcome, leading to the consideration of alternative hypotheses. It occurs when statistical evidence suggests a deviation from the assumed baseline, prompting a reconsideration of the initial hypothesis.

In statistical hypothesis testing, researchers begin by stating the null hypothesis, often based on theoretical considerations or previous research. The null hypothesis is then tested against an alternative hypothesis (Ha), which represents the researcher’s claim or the hypothesis they seek to support.

The process of hypothesis testing involves collecting sample data and using statistical methods to assess the likelihood of observing the data if the null hypothesis were true. This assessment is typically done by calculating a test statistic, which measures the difference between the observed data and what would be expected under the null hypothesis.

In the realm of hypothesis testing, the null hypothesis (H 0 ) and alternative hypothesis (H₁ or Ha) play critical roles. The null hypothesis generally assumes no difference, effect, or relationship between variables, suggesting that any observed change or effect is due to random chance. Its counterpart, the alternative hypothesis, asserts the presence of a significant difference, effect, or relationship between variables, challenging the null hypothesis. These hypotheses are formulated based on the research question and guide statistical analyses.

Difference Between Null Hypothesis and Alternative Hypothesis

The null hypothesis (H 0 ) serves as the baseline assumption in statistical testing, suggesting no significant effect, relationship, or difference within the data. It often proposes that any observed change or correlation is merely due to chance or random variation. Conversely, the alternative hypothesis (H 1 or Ha) contradicts the null hypothesis, positing the existence of a genuine effect, relationship or difference in the data. It represents the researcher’s intended focus, seeking to provide evidence against the null hypothesis and support for a specific outcome or theory. These hypotheses form the crux of hypothesis testing, guiding the assessment of data to draw conclusions about the population being studied.

Let’s envision a scenario where a researcher aims to examine the impact of a new medication on reducing blood pressure among patients. In this context:

Null Hypothesis (H 0 ): “The new medication does not produce a significant effect in reducing blood pressure levels among patients.”

Alternative Hypothesis (H 1 or Ha): “The new medication yields a significant effect in reducing blood pressure levels among patients.”

The null hypothesis implies that any observed alterations in blood pressure subsequent to the medication’s administration are a result of random fluctuations rather than a consequence of the medication itself. Conversely, the alternative hypothesis contends that the medication does indeed generate a meaningful alteration in blood pressure levels, distinct from what might naturally occur or by random chance.

Summary – Null Hypothesis and Alternative Hypothesis

The null hypothesis (H 0 ) and alternative hypothesis (H a ) are fundamental concepts in statistical hypothesis testing. The null hypothesis represents the default assumption, stating that there is no significant effect, difference, or relationship between variables. It serves as the baseline against which the alternative hypothesis is tested. In contrast, the alternative hypothesis represents the researcher’s hypothesis or the claim to be tested, suggesting that there is a significant effect, difference, or relationship between variables. The relationship between the null and alternative hypotheses is such that they are complementary, and statistical tests are conducted to determine whether the evidence from the data is strong enough to reject the null hypothesis in favor of the alternative hypothesis. This decision is based on the strength of the evidence and the chosen level of significance. Ultimately, the choice between the null and alternative hypotheses depends on the specific research question and the direction of the effect being investigated.

FAQs on Null Hypothesis

What does null hypothesis stands for.

The null hypothesis, denoted as H 0 , is a fundamental concept in statistics used for hypothesis testing. It represents the statement that there is no effect or no difference, and it is the hypothesis that the researcher typically aims to provide evidence against.

How to Form a Null Hypothesis?

A null hypothesis is formed based on the assumption that there is no significant difference or effect between the groups being compared or no association between variables being tested. It often involves stating that there is no relationship, no change, or no effect in the population being studied.

When Do we reject the Null Hypothesis?

In statistical hypothesis testing, if the p-value (the probability of obtaining the observed results) is lower than the chosen significance level (commonly 0.05), we reject the null hypothesis. This suggests that the data provides enough evidence to refute the assumption made in the null hypothesis.

What is a Null Hypothesis in Research?

In research, the null hypothesis represents the default assumption or position that there is no significant difference or effect. Researchers often try to test this hypothesis by collecting data and performing statistical analyses to see if the observed results contradict the assumption.

What Are Alternative and Null Hypotheses?

The null hypothesis (H0) is the default assumption that there is no significant difference or effect. The alternative hypothesis (H1 or Ha) is the opposite, suggesting there is a significant difference, effect or relationship.

What Does it Mean to Reject the Null Hypothesis?

Rejecting the null hypothesis implies that there is enough evidence in the data to support the alternative hypothesis. In simpler terms, it suggests that there might be a significant difference, effect or relationship between the groups or variables being studied.

How to Find Null Hypothesis?

Formulating a null hypothesis often involves considering the research question and assuming that no difference or effect exists. It should be a statement that can be tested through data collection and statistical analysis, typically stating no relationship or no change between variables or groups.

How is Null Hypothesis denoted?

The null hypothesis is commonly symbolized as H 0 in statistical notation.

What is the Purpose of the Null hypothesis in Statistical Analysis?

The null hypothesis serves as a starting point for hypothesis testing, enabling researchers to assess if there’s enough evidence to reject it in favor of an alternative hypothesis.

What happens if we Reject the Null hypothesis?

Rejecting the null hypothesis implies that there is sufficient evidence to support an alternative hypothesis, suggesting a significant effect or relationship between variables.

What are Test for Null Hypothesis?

Various statistical tests, such as t-tests or chi-square tests, are employed to evaluate the validity of the Null Hypothesis in different scenarios.

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Null hypothesis

Null hypothesis n., plural: null hypotheses [nʌl haɪˈpɒθɪsɪs] Definition: a hypothesis that is valid or presumed true until invalidated by a statistical test

Table of Contents

Null Hypothesis Definition

Null hypothesis is defined as “the commonly accepted fact (such as the sky is blue) and researcher aim to reject or nullify this fact”.

More formally, we can define a null hypothesis as “a statistical theory suggesting that no statistical relationship exists between given observed variables” .

In biology , the null hypothesis is used to nullify or reject a common belief. The researcher carries out the research which is aimed at rejecting the commonly accepted belief.

What Is a Null Hypothesis?

A hypothesis is defined as a theory or an assumption that is based on inadequate evidence. It needs and requires more experiments and testing for confirmation. There are two possibilities that by doing more experiments and testing, a hypothesis can be false or true. It means it can either prove wrong or true (Blackwelder, 1982).

For example, Susie assumes that mineral water helps in the better growth and nourishment of plants over distilled water. To prove this hypothesis, she performs this experiment for almost a month. She watered some plants with mineral water and some with distilled water.

In a hypothesis when there are no statistically significant relationships among the two variables, the hypothesis is said to be a null hypothesis. The investigator is trying to disprove such a hypothesis. In the above example of plants, the null hypothesis is:

There are no statistical relationships among the forms of water that are given to plants for growth and nourishment.

Usually, an investigator tries to prove the null hypothesis wrong and tries to explain a relation and association between the two variables.

An opposite and reverse of the null hypothesis are known as the alternate hypothesis . In the example of plants the alternate hypothesis is:

There are statistical relationships among the forms of water that are given to plants for growth and nourishment.

The example below shows the difference between null vs alternative hypotheses:

Alternate Hypothesis: The world is round Null Hypothesis: The world is not round.

Copernicus and many other scientists try to prove the null hypothesis wrong and false. By their experiments and testing, they make people believe that alternate hypotheses are correct and true. If they do not prove the null hypothesis experimentally wrong then people will not believe them and never consider the alternative hypothesis true and correct.

The alternative and null hypothesis for Susie’s assumption is:

Null Hypothesis: If one plant is watered with distilled water and the other with mineral water, then there is no difference in the growth and nourishment of these two plants.
Alternative Hypothesis: If one plant is watered with distilled water and the other with mineral water, then the plant with mineral water shows better growth and nourishment.

The null hypothesis suggests that there is no significant or statistical relationship. The relation can either be in a single set of variables or among two sets of variables.

Most people consider the null hypothesis true and correct. Scientists work and perform different experiments and do a variety of research so that they can prove the null hypothesis wrong or nullify it. For this purpose, they design an alternate hypothesis that they think is correct or true. The null hypothesis symbol is H 0 (it is read as H null or H zero ).

Why is it named the “Null”?

The name null is given to this hypothesis to clarify and explain that the scientists are working to prove it false i.e. to nullify the hypothesis. Sometimes it confuses the readers; they might misunderstand it and think that statement has nothing. It is blank but, actually, it is not. It is more appropriate and suitable to call it a nullifiable hypothesis instead of the null hypothesis.

Why do we need to assess it? Why not just verify an alternate one?

In science, the scientific method is used. It involves a series of different steps. Scientists perform these steps so that a hypothesis can be proved false or true. Scientists do this to confirm that there will be any limitation or inadequacy in the new hypothesis. Experiments are done by considering both alternative and null hypotheses, which makes the research safe. It gives a negative as well as a bad impact on research if a null hypothesis is not included or a part of the study. It seems like you are not taking your research seriously and not concerned about it and just want to impose your results as correct and true if the null hypothesis is not a part of the study.

Development of the Null

In statistics, firstly it is necessary to design alternate and null hypotheses from the given problem. Splitting the problem into small steps makes the pathway towards the solution easier and less challenging. how to write a null hypothesis?

Writing a null hypothesis consists of two steps:

Firstly, initiate by asking a question.
Secondly, restate the question in such a way that it seems there are no relationships among the variables.

In other words, assume in such a way that the treatment does not have any effect.

The usual recovery duration after knee surgery is considered almost 8 weeks.

A researcher thinks that the recovery period may get elongated if patients go to a physiotherapist for rehabilitation twice per week, instead of thrice per week, i.e. recovery duration reduces if the patient goes three times for rehabilitation instead of two times.

Step 1: Look for the problem in the hypothesis. The hypothesis either be a word or can be a statement. In the above example the hypothesis is:

“The expected recovery period in knee rehabilitation is more than 8 weeks”

Step 2: Make a mathematical statement from the hypothesis. Averages can also be represented as μ, thus the null hypothesis formula will be.

In the above equation, the hypothesis is equivalent to H1, the average is denoted by μ and > that the average is greater than eight.

Step 3: Explain what will come up if the hypothesis does not come right i.e., the rehabilitation period may not proceed more than 08 weeks.

There are two options: either the recovery will be less than or equal to 8 weeks.

H 0 : μ ≤ 8

In the above equation, the null hypothesis is equivalent to H 0 , the average is denoted by μ and ≤ represents that the average is less than or equal to eight.

What will happen if the scientist does not have any knowledge about the outcome?

Problem: An investigator investigates the post-operative impact and influence of radical exercise on patients who have operative procedures of the knee. The chances are either the exercise will improve the recovery or will make it worse. The usual time for recovery is 8 weeks.

Step 1: Make a null hypothesis i.e. the exercise does not show any effect and the recovery time remains almost 8 weeks.

H 0 : μ = 8

In the above equation, the null hypothesis is equivalent to H 0 , the average is denoted by μ, and the equal sign (=) shows that the average is equal to eight.

Step 2: Make the alternate hypothesis which is the reverse of the null hypothesis. Particularly what will happen if treatment (exercise) makes an impact?

In the above equation, the alternate hypothesis is equivalent to H1, the average is denoted by μ and not equal sign (≠) represents that the average is not equal to eight.

Significance Tests

To get a reasonable and probable clarification of statistics (data), a significance test is performed. The null hypothesis does not have data. It is a piece of information or statement which contains numerical figures about the population. The data can be in different forms like in means or proportions. It can either be the difference of proportions and means or any odd ratio.

The following table will explain the symbols:

P-value is the chief statistical final result of the significance test of the null hypothesis.

P-value = Pr(data or data more extreme | H 0 true)
| = “given”
Pr = probability
H 0 = the null hypothesis

The first stage of Null Hypothesis Significance Testing (NHST) is to form an alternate and null hypothesis. By this, the research question can be briefly explained.

Null Hypothesis = no effect of treatment, no difference, no association Alternative Hypothesis = effective treatment, difference, association

When to reject the null hypothesis?

Researchers will reject the null hypothesis if it is proven wrong after experimentation. Researchers accept null hypothesis to be true and correct until it is proven wrong or false. On the other hand, the researchers try to strengthen the alternate hypothesis. The binomial test is performed on a sample and after that, a series of tests were performed (Frick, 1995).

Step 1: Evaluate and read the research question carefully and consciously and make a null hypothesis. Verify the sample that supports the binomial proportion. If there is no difference then find out the value of the binomial parameter.

Show the null hypothesis as:

H 0 :p= the value of p if H 0 is true

To find out how much it varies from the proposed data and the value of the null hypothesis, calculate the sample proportion.

Step 2: In test statistics, find the binomial test that comes under the null hypothesis. The test must be based on precise and thorough probabilities. Also make a list of pmf that apply, when the null hypothesis proves true and correct.

When H 0 is true, X~b(n, p)

N = size of the sample

P = assume value if H 0 proves true.

Step 3: Find out the value of P. P-value is the probability of data that is under observation.

Rise or increase in the P value = Pr(X ≥ x)

X = observed number of successes

P value = Pr(X ≤ x).

Step 4: Demonstrate the findings or outcomes in a descriptive detailed way.

Sample proportion
The direction of difference (either increases or decreases)

Perceived Problems With the Null Hypothesis

Variable or model selection and less information in some cases are the chief important issues that affect the testing of the null hypothesis. Statistical tests of the null hypothesis are reasonably not strong. There is randomization about significance. (Gill, 1999) The main issue with the testing of the null hypothesis is that they all are wrong or false on a ground basis.

There is another problem with the a-level . This is an ignored but also a well-known problem. The value of a-level is without a theoretical basis and thus there is randomization in conventional values, most commonly 0.q, 0.5, or 0.01. If a fixed value of a is used, it will result in the formation of two categories (significant and non-significant) The issue of a randomized rejection or non-rejection is also present when there is a practical matter which is the strong point of the evidence related to a scientific matter.

The P-value has the foremost importance in the testing of null hypothesis but as an inferential tool and for interpretation, it has a problem. The P-value is the probability of getting a test statistic at least as extreme as the observed one.

The main point about the definition is: Observed results are not based on a-value

Moreover, the evidence against the null hypothesis was overstated due to unobserved results. A-value has importance more than just being a statement. It is a precise statement about the evidence from the observed results or data. Similarly, researchers found that P-values are objectionable. They do not prefer null hypotheses in testing. It is also clear that the P-value is strictly dependent on the null hypothesis. It is computer-based statistics. In some precise experiments, the null hypothesis statistics and actual sampling distribution are closely related but this does not become possible in observational studies.

Some researchers pointed out that the P-value is depending on the sample size. If the true and exact difference is small, a null hypothesis even of a large sample may get rejected. This shows the difference between biological importance and statistical significance. (Killeen, 2005)

Another issue is the fix a-level, i.e., 0.1. On the basis, if a-level a null hypothesis of a large sample may get accepted or rejected. If the size of simple is infinity and the null hypothesis is proved true there are still chances of Type I error. That is the reason this approach or method is not considered consistent and reliable. There is also another problem that the exact information about the precision and size of the estimated effect cannot be known. The only solution is to state the size of the effect and its precision.

Null Hypothesis Examples

Here are some examples:

Example 1: Hypotheses with One Sample of One Categorical Variable

Among all the population of humans, almost 10% of people prefer to do their task with their left hand i.e. left-handed. Let suppose, a researcher in the Penn States says that the population of students at the College of Arts and Architecture is mostly left-handed as compared to the general population of humans in general public society. In this case, there is only a sample and there is a comparison among the known population values to the population proportion of sample value.

Research Question: Do artists more expected to be left-handed as compared to the common population persons in society?
Response Variable: Sorting the student into two categories. One category has left-handed persons and the other category have right-handed persons.
Form Null Hypothesis: Arts and Architecture college students are no more predicted to be lefty as compared to the common population persons in society (Lefty students of Arts and Architecture college population is 10% or p= 0.10)

Example 2: Hypotheses with One Sample of One Measurement Variable

A generic brand of antihistamine Diphenhydramine making medicine in the form of a capsule, having a 50mg dose. The maker of the medicines is concerned that the machine has come out of calibration and is not making more capsules with the suitable and appropriate dose.

Research Question: Does the statistical data recommended about the mean and average dosage of the population differ from 50mg?
Response Variable: Chemical assay used to find the appropriate dosage of the active ingredient.
Null Hypothesis: Usually, the 50mg dosage of capsules of this trade name (population average and means dosage =50 mg).

Example 3: Hypotheses with Two Samples of One Categorical Variable

Several people choose vegetarian meals on a daily basis. Typically, the researcher thought that females like vegetarian meals more than males.

Research Question: Does the data recommend that females (women) prefer vegetarian meals more than males (men) regularly?
Response Variable: Cataloguing the persons into vegetarian and non-vegetarian categories. Grouping Variable: Gender
Null Hypothesis: Gender is not linked to those who like vegetarian meals. (Population percent of women who eat vegetarian meals regularly = population percent of men who eat vegetarian meals regularly or p women = p men).

Example 4: Hypotheses with Two Samples of One Measurement Variable

Nowadays obesity and being overweight is one of the major and dangerous health issues. Research is performed to confirm that a low carbohydrates diet leads to faster weight loss than a low-fat diet.

Research Question: Does the given data recommend that usually, a low-carbohydrate diet helps in losing weight faster as compared to a low-fat diet?
Response Variable: Weight loss (pounds)
Explanatory Variable: Form of diet either low carbohydrate or low fat
Null Hypothesis: There is no significant difference when comparing the mean loss of weight of people using a low carbohydrate diet to people using a diet having low fat. (population means loss of weight on a low carbohydrate diet = population means loss of weight on a diet containing low fat).

Example 5: Hypotheses about the relationship between Two Categorical Variables

A case-control study was performed. The study contains nonsmokers, stroke patients, and controls. The subjects are of the same occupation and age and the question was asked if someone at their home or close surrounding smokes?

Research Question: Did second-hand smoke enhance the chances of stroke?
Variables: There are 02 diverse categories of variables. (Controls and stroke patients) (whether the smoker lives in the same house). The chances of having a stroke will be increased if a person is living with a smoker.
Null Hypothesis: There is no significant relationship between a passive smoker and stroke or brain attack. (odds ratio between stroke and the passive smoker is equal to 1).

Example 6: Hypotheses about the relationship between Two Measurement Variables

A financial expert observes that there is somehow a positive and effective relationship between the variation in stock rate price and the quantity of stock bought by non-management employees

Response variable- Regular alteration in price
Explanatory Variable- Stock bought by non-management employees
Null Hypothesis: The association and relationship between the regular stock price alteration ($) and the daily stock-buying by non-management employees ($) = 0.

Example 7: Hypotheses about comparing the relationship between Two Measurement Variables in Two Samples

Research Question: Is the relation between the bill paid in a restaurant and the tip given to the waiter, is linear? Is this relation different for dining and family restaurants?
Explanatory Variable- total bill amount
Response Variable- the amount of tip
Null Hypothesis: The relationship and association between the total bill quantity at a family or dining restaurant and the tip, is the same.

Try to answer the quiz below to check what you have learned so far about the null hypothesis.

Choose the best answer.

Send Your Results (Optional)

Blackwelder, W. C. (1982). “Proving the null hypothesis” in clinical trials. Controlled Clinical Trials , 3(4), 345–353.
Frick, R. W. (1995). Accepting the null hypothesis. Memory & Cognition, 23(1), 132–138.
Gill, J. (1999). The insignificance of null hypothesis significance testing. Political Research Quarterly , 52(3), 647–674.
Killeen, P. R. (2005). An alternative to null-hypothesis significance tests. Psychological Science, 16(5), 345–353.

Last updated on June 16th, 2022

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Null Hypothesis

In mathematics, Statistics deals with the study of research and surveys on the numerical data. For taking surveys, we have to define the hypothesis. Generally, there are two types of hypothesis. One is a null hypothesis, and another is an alternative hypothesis .

In probability and statistics, the null hypothesis is a comprehensive statement or default status that there is zero happening or nothing happening. For example, there is no connection among groups or no association between two measured events. It is generally assumed here that the hypothesis is true until any other proof has been brought into the light to deny the hypothesis. Let us learn more here with definition, symbol, principle, types and example, in this article.

Table of contents:

Comparison with Alternative Hypothesis

Null Hypothesis Definition

The null hypothesis is a kind of hypothesis which explains the population parameter whose purpose is to test the validity of the given experimental data. This hypothesis is either rejected or not rejected based on the viability of the given population or sample . In other words, the null hypothesis is a hypothesis in which the sample observations results from the chance. It is said to be a statement in which the surveyors wants to examine the data. It is denoted by H 0 .

Null Hypothesis Symbol

In statistics, the null hypothesis is usually denoted by letter H with subscript ‘0’ (zero), such that H 0 . It is pronounced as H-null or H-zero or H-nought. At the same time, the alternative hypothesis expresses the observations determined by the non-random cause. It is represented by H 1 or H a .

Null Hypothesis Principle

The principle followed for null hypothesis testing is, collecting the data and determining the chances of a given set of data during the study on some random sample, assuming that the null hypothesis is true. In case if the given data does not face the expected null hypothesis, then the outcome will be quite weaker, and they conclude by saying that the given set of data does not provide strong evidence against the null hypothesis because of insufficient evidence. Finally, the researchers tend to reject that.

Null Hypothesis Formula

Here, the hypothesis test formulas are given below for reference.

The formula for the null hypothesis is:

H 0 : p = p 0

The formula for the alternative hypothesis is:

H a = p >p 0 , < p 0 ≠ p 0

The formula for the test static is:

Remember that, p 0 is the null hypothesis and p – hat is the sample proportion.

Also, read:

Types of Null Hypothesis

There are different types of hypothesis. They are:

Simple Hypothesis

It completely specifies the population distribution. In this method, the sampling distribution is the function of the sample size.

Composite Hypothesis

The composite hypothesis is one that does not completely specify the population distribution.

Exact Hypothesis

Exact hypothesis defines the exact value of the parameter. For example μ= 50

Inexact Hypothesis

This type of hypothesis does not define the exact value of the parameter. But it denotes a specific range or interval. For example 45< μ <60

Null Hypothesis Rejection

Sometimes the null hypothesis is rejected too. If this hypothesis is rejected means, that research could be invalid. Many researchers will neglect this hypothesis as it is merely opposite to the alternate hypothesis. It is a better practice to create a hypothesis and test it. The goal of researchers is not to reject the hypothesis. But it is evident that a perfect statistical model is always associated with the failure to reject the null hypothesis.

How do you Find the Null Hypothesis?

The null hypothesis says there is no correlation between the measured event (the dependent variable) and the independent variable. We don’t have to believe that the null hypothesis is true to test it. On the contrast, you will possibly assume that there is a connection between a set of variables ( dependent and independent).

When is Null Hypothesis Rejected?

The null hypothesis is rejected using the P-value approach. If the P-value is less than or equal to the α, there should be a rejection of the null hypothesis in favour of the alternate hypothesis. In case, if P-value is greater than α, the null hypothesis is not rejected.

Null Hypothesis and Alternative Hypothesis

Now, let us discuss the difference between the null hypothesis and the alternative hypothesis.

Null Hypothesis Examples

Here, some of the examples of the null hypothesis are given below. Go through the below ones to understand the concept of the null hypothesis in a better way.

If a medicine reduces the risk of cardiac stroke, then the null hypothesis should be “the medicine does not reduce the chance of cardiac stroke”. This testing can be performed by the administration of a drug to a certain group of people in a controlled way. If the survey shows that there is a significant change in the people, then the hypothesis is rejected.

Few more examples are:

1). Are there is 100% chance of getting affected by dengue?

Ans: There could be chances of getting affected by dengue but not 100%.

2). Do teenagers are using mobile phones more than grown-ups to access the internet?

Ans: Age has no limit on using mobile phones to access the internet.

3). Does having apple daily will not cause fever?

Ans: Having apple daily does not assure of not having fever, but increases the immunity to fight against such diseases.

4). Do the children more good in doing mathematical calculations than grown-ups?

Ans: Age has no effect on Mathematical skills.

In many common applications, the choice of the null hypothesis is not automated, but the testing and calculations may be automated. Also, the choice of the null hypothesis is completely based on previous experiences and inconsistent advice. The choice can be more complicated and based on the variety of applications and the diversity of the objectives.

The main limitation for the choice of the null hypothesis is that the hypothesis suggested by the data is based on the reasoning which proves nothing. It means that if some hypothesis provides a summary of the data set, then there would be no value in the testing of the hypothesis on the particular set of data.

Frequently Asked Questions on Null Hypothesis

What is meant by the null hypothesis.

In Statistics, a null hypothesis is a type of hypothesis which explains the population parameter whose purpose is to test the validity of the given experimental data.

What are the benefits of hypothesis testing?

Hypothesis testing is defined as a form of inferential statistics, which allows making conclusions from the entire population based on the sample representative.

When a null hypothesis is accepted and rejected?

The null hypothesis is either accepted or rejected in terms of the given data. If P-value is less than α, then the null hypothesis is rejected in favor of the alternative hypothesis, and if the P-value is greater than α, then the null hypothesis is accepted in favor of the alternative hypothesis.

Why is the null hypothesis important?

The importance of the null hypothesis is that it provides an approximate description of the phenomena of the given data. It allows the investigators to directly test the relational statement in a research study.

How to accept or reject the null hypothesis in the chi-square test?

If the result of the chi-square test is bigger than the critical value in the table, then the data does not fit the model, which represents the rejection of the null hypothesis.

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This glossary is intended to assist you in understanding commonly used terms and concepts when reading, interpreting, and evaluating scholarly research. Also included are common words and phrases defined within the context of how they apply to research in the social and behavioral sciences.

Acculturation -- refers to the process of adapting to another culture, particularly in reference to blending in with the majority population [e.g., an immigrant adopting American customs]. However, acculturation also implies that both cultures add something to one another, but still remain distinct groups unto themselves.
Accuracy -- a term used in survey research to refer to the match between the target population and the sample.
Affective Measures -- procedures or devices used to obtain quantified descriptions of an individual's feelings, emotional states, or dispositions.
Aggregate -- a total created from smaller units. For instance, the population of a county is an aggregate of the populations of the cities, rural areas, etc. that comprise the county. As a verb, it refers to total data from smaller units into a large unit.
Anonymity -- a research condition in which no one, including the researcher, knows the identities of research participants.
Baseline -- a control measurement carried out before an experimental treatment.
Behaviorism -- school of psychological thought concerned with the observable, tangible, objective facts of behavior, rather than with subjective phenomena such as thoughts, emotions, or impulses. Contemporary behaviorism also emphasizes the study of mental states such as feelings and fantasies to the extent that they can be directly observed and measured.
Beliefs -- ideas, doctrines, tenets, etc. that are accepted as true on grounds which are not immediately susceptible to rigorous proof.
Benchmarking -- systematically measuring and comparing the operations and outcomes of organizations, systems, processes, etc., against agreed upon "best-in-class" frames of reference.
Bias -- a loss of balance and accuracy in the use of research methods. It can appear in research via the sampling frame, random sampling, or non-response. It can also occur at other stages in research, such as while interviewing, in the design of questions, or in the way data are analyzed and presented. Bias means that the research findings will not be representative of, or generalizable to, a wider population.
Case Study -- the collection and presentation of detailed information about a particular participant or small group, frequently including data derived from the subjects themselves.
Causal Hypothesis -- a statement hypothesizing that the independent variable affects the dependent variable in some way.
Causal Relationship -- the relationship established that shows that an independent variable, and nothing else, causes a change in a dependent variable. It also establishes how much of a change is shown in the dependent variable.
Causality -- the relation between cause and effect.
Central Tendency -- any way of describing or characterizing typical, average, or common values in some distribution.
Chi-square Analysis -- a common non-parametric statistical test which compares an expected proportion or ratio to an actual proportion or ratio.
Claim -- a statement, similar to a hypothesis, which is made in response to the research question and that is affirmed with evidence based on research.
Classification -- ordering of related phenomena into categories, groups, or systems according to characteristics or attributes.
Cluster Analysis -- a method of statistical analysis where data that share a common trait are grouped together. The data is collected in a way that allows the data collector to group data according to certain characteristics.
Cohort Analysis -- group by group analytic treatment of individuals having a statistical factor in common to each group. Group members share a particular characteristic [e.g., born in a given year] or a common experience [e.g., entering a college at a given time].
Confidentiality -- a research condition in which no one except the researcher(s) knows the identities of the participants in a study. It refers to the treatment of information that a participant has disclosed to the researcher in a relationship of trust and with the expectation that it will not be revealed to others in ways that violate the original consent agreement, unless permission is granted by the participant.
Confirmability Objectivity -- the findings of the study could be confirmed by another person conducting the same study.
Construct -- refers to any of the following: something that exists theoretically but is not directly observable; a concept developed [constructed] for describing relations among phenomena or for other research purposes; or, a theoretical definition in which concepts are defined in terms of other concepts. For example, intelligence cannot be directly observed or measured; it is a construct.
Construct Validity -- seeks an agreement between a theoretical concept and a specific measuring device, such as observation.
Constructivism -- the idea that reality is socially constructed. It is the view that reality cannot be understood outside of the way humans interact and that the idea that knowledge is constructed, not discovered. Constructivists believe that learning is more active and self-directed than either behaviorism or cognitive theory would postulate.
Content Analysis -- the systematic, objective, and quantitative description of the manifest or latent content of print or nonprint communications.
Context Sensitivity -- awareness by a qualitative researcher of factors such as values and beliefs that influence cultural behaviors.
Control Group -- the group in an experimental design that receives either no treatment or a different treatment from the experimental group. This group can thus be compared to the experimental group.
Controlled Experiment -- an experimental design with two or more randomly selected groups [an experimental group and control group] in which the researcher controls or introduces the independent variable and measures the dependent variable at least two times [pre- and post-test measurements].
Correlation -- a common statistical analysis, usually abbreviated as r, that measures the degree of relationship between pairs of interval variables in a sample. The range of correlation is from -1.00 to zero to +1.00. Also, a non-cause and effect relationship between two variables.
Covariate -- a product of the correlation of two related variables times their standard deviations. Used in true experiments to measure the difference of treatment between them.
Credibility -- a researcher's ability to demonstrate that the object of a study is accurately identified and described based on the way in which the study was conducted.
Critical Theory -- an evaluative approach to social science research, associated with Germany's neo-Marxist “Frankfurt School,” that aims to criticize as well as analyze society, opposing the political orthodoxy of modern communism. Its goal is to promote human emancipatory forces and to expose ideas and systems that impede them.
Data -- factual information [as measurements or statistics] used as a basis for reasoning, discussion, or calculation.
Data Mining -- the process of analyzing data from different perspectives and summarizing it into useful information, often to discover patterns and/or systematic relationships among variables.
Data Quality -- this is the degree to which the collected data [results of measurement or observation] meet the standards of quality to be considered valid [trustworthy] and reliable [dependable].
Deductive -- a form of reasoning in which conclusions are formulated about particulars from general or universal premises.
Dependability -- being able to account for changes in the design of the study and the changing conditions surrounding what was studied.
Dependent Variable -- a variable that varies due, at least in part, to the impact of the independent variable. In other words, its value “depends” on the value of the independent variable. For example, in the variables “gender” and “academic major,” academic major is the dependent variable, meaning that your major cannot determine whether you are male or female, but your gender might indirectly lead you to favor one major over another.
Deviation -- the distance between the mean and a particular data point in a given distribution.
Discourse Community -- a community of scholars and researchers in a given field who respond to and communicate to each other through published articles in the community's journals and presentations at conventions. All members of the discourse community adhere to certain conventions for the presentation of their theories and research.
Discrete Variable -- a variable that is measured solely in whole units, such as, gender and number of siblings.
Distribution -- the range of values of a particular variable.
Effect Size -- the amount of change in a dependent variable that can be attributed to manipulations of the independent variable. A large effect size exists when the value of the dependent variable is strongly influenced by the independent variable. It is the mean difference on a variable between experimental and control groups divided by the standard deviation on that variable of the pooled groups or of the control group alone.
Emancipatory Research -- research is conducted on and with people from marginalized groups or communities. It is led by a researcher or research team who is either an indigenous or external insider; is interpreted within intellectual frameworks of that group; and, is conducted largely for the purpose of empowering members of that community and improving services for them. It also engages members of the community as co-constructors or validators of knowledge.
Empirical Research -- the process of developing systematized knowledge gained from observations that are formulated to support insights and generalizations about the phenomena being researched.
Epistemology -- concerns knowledge construction; asks what constitutes knowledge and how knowledge is validated.
Ethnography -- method to study groups and/or cultures over a period of time. The goal of this type of research is to comprehend the particular group/culture through immersion into the culture or group. Research is completed through various methods but, since the researcher is immersed within the group for an extended period of time, more detailed information is usually collected during the research.
Expectancy Effect -- any unconscious or conscious cues that convey to the participant in a study how the researcher wants them to respond. Expecting someone to behave in a particular way has been shown to promote the expected behavior. Expectancy effects can be minimized by using standardized interactions with subjects, automated data-gathering methods, and double blind protocols.
External Validity -- the extent to which the results of a study are generalizable or transferable.
Factor Analysis -- a statistical test that explores relationships among data. The test explores which variables in a data set are most related to each other. In a carefully constructed survey, for example, factor analysis can yield information on patterns of responses, not simply data on a single response. Larger tendencies may then be interpreted, indicating behavior trends rather than simply responses to specific questions.
Field Studies -- academic or other investigative studies undertaken in a natural setting, rather than in laboratories, classrooms, or other structured environments.
Focus Groups -- small, roundtable discussion groups charged with examining specific topics or problems, including possible options or solutions. Focus groups usually consist of 4-12 participants, guided by moderators to keep the discussion flowing and to collect and report the results.
Framework -- the structure and support that may be used as both the launching point and the on-going guidelines for investigating a research problem.
Generalizability -- the extent to which research findings and conclusions conducted on a specific study to groups or situations can be applied to the population at large.
Grey Literature -- research produced by organizations outside of commercial and academic publishing that publish materials, such as, working papers, research reports, and briefing papers.
Grounded Theory -- practice of developing other theories that emerge from observing a group. Theories are grounded in the group's observable experiences, but researchers add their own insight into why those experiences exist.
Group Behavior -- behaviors of a group as a whole, as well as the behavior of an individual as influenced by his or her membership in a group.
Hypothesis -- a tentative explanation based on theory to predict a causal relationship between variables.
Independent Variable -- the conditions of an experiment that are systematically manipulated by the researcher. A variable that is not impacted by the dependent variable, and that itself impacts the dependent variable. In the earlier example of "gender" and "academic major," (see Dependent Variable) gender is the independent variable.
Individualism -- a theory or policy having primary regard for the liberty, rights, or independent actions of individuals.
Inductive -- a form of reasoning in which a generalized conclusion is formulated from particular instances.
Inductive Analysis -- a form of analysis based on inductive reasoning; a researcher using inductive analysis starts with answers, but formulates questions throughout the research process.
Insiderness -- a concept in qualitative research that refers to the degree to which a researcher has access to and an understanding of persons, places, or things within a group or community based on being a member of that group or community.
Internal Consistency -- the extent to which all questions or items assess the same characteristic, skill, or quality.
Internal Validity -- the rigor with which the study was conducted [e.g., the study's design, the care taken to conduct measurements, and decisions concerning what was and was not measured]. It is also the extent to which the designers of a study have taken into account alternative explanations for any causal relationships they explore. In studies that do not explore causal relationships, only the first of these definitions should be considered when assessing internal validity.
Life History -- a record of an event/events in a respondent's life told [written down, but increasingly audio or video recorded] by the respondent from his/her own perspective in his/her own words. A life history is different from a "research story" in that it covers a longer time span, perhaps a complete life, or a significant period in a life.
Margin of Error -- the permittable or acceptable deviation from the target or a specific value. The allowance for slight error or miscalculation or changing circumstances in a study.
Measurement -- process of obtaining a numerical description of the extent to which persons, organizations, or things possess specified characteristics.
Meta-Analysis -- an analysis combining the results of several studies that address a set of related hypotheses.
Methodology -- a theory or analysis of how research does and should proceed.
Methods -- systematic approaches to the conduct of an operation or process. It includes steps of procedure, application of techniques, systems of reasoning or analysis, and the modes of inquiry employed by a discipline.
Mixed-Methods -- a research approach that uses two or more methods from both the quantitative and qualitative research categories. It is also referred to as blended methods, combined methods, or methodological triangulation.
Modeling -- the creation of a physical or computer analogy to understand a particular phenomenon. Modeling helps in estimating the relative magnitude of various factors involved in a phenomenon. A successful model can be shown to account for unexpected behavior that has been observed, to predict certain behaviors, which can then be tested experimentally, and to demonstrate that a given theory cannot account for certain phenomenon.
Models -- representations of objects, principles, processes, or ideas often used for imitation or emulation.
Naturalistic Observation -- observation of behaviors and events in natural settings without experimental manipulation or other forms of interference.
Norm -- the norm in statistics is the average or usual performance. For example, students usually complete their high school graduation requirements when they are 18 years old. Even though some students graduate when they are younger or older, the norm is that any given student will graduate when he or she is 18 years old.
Null Hypothesis -- the proposition, to be tested statistically, that the experimental intervention has "no effect," meaning that the treatment and control groups will not differ as a result of the intervention. Investigators usually hope that the data will demonstrate some effect from the intervention, thus allowing the investigator to reject the null hypothesis.
Ontology -- a discipline of philosophy that explores the science of what is, the kinds and structures of objects, properties, events, processes, and relations in every area of reality.
Panel Study -- a longitudinal study in which a group of individuals is interviewed at intervals over a period of time.
Participant -- individuals whose physiological and/or behavioral characteristics and responses are the object of study in a research project.
Peer-Review -- the process in which the author of a book, article, or other type of publication submits his or her work to experts in the field for critical evaluation, usually prior to publication. This is standard procedure in publishing scholarly research.
Phenomenology -- a qualitative research approach concerned with understanding certain group behaviors from that group's point of view.
Philosophy -- critical examination of the grounds for fundamental beliefs and analysis of the basic concepts, doctrines, or practices that express such beliefs.
Phonology -- the study of the ways in which speech sounds form systems and patterns in language.
Policy -- governing principles that serve as guidelines or rules for decision making and action in a given area.
Policy Analysis -- systematic study of the nature, rationale, cost, impact, effectiveness, implications, etc., of existing or alternative policies, using the theories and methodologies of relevant social science disciplines.
Population -- the target group under investigation. The population is the entire set under consideration. Samples are drawn from populations.
Position Papers -- statements of official or organizational viewpoints, often recommending a particular course of action or response to a situation.
Positivism -- a doctrine in the philosophy of science, positivism argues that science can only deal with observable entities known directly to experience. The positivist aims to construct general laws, or theories, which express relationships between phenomena. Observation and experiment is used to show whether the phenomena fit the theory.
Predictive Measurement -- use of tests, inventories, or other measures to determine or estimate future events, conditions, outcomes, or trends.
Principal Investigator -- the scientist or scholar with primary responsibility for the design and conduct of a research project.
Probability -- the chance that a phenomenon will occur randomly. As a statistical measure, it is shown as p [the "p" factor].
Questionnaire -- structured sets of questions on specified subjects that are used to gather information, attitudes, or opinions.
Random Sampling -- a process used in research to draw a sample of a population strictly by chance, yielding no discernible pattern beyond chance. Random sampling can be accomplished by first numbering the population, then selecting the sample according to a table of random numbers or using a random-number computer generator. The sample is said to be random because there is no regular or discernible pattern or order. Random sample selection is used under the assumption that sufficiently large samples assigned randomly will exhibit a distribution comparable to that of the population from which the sample is drawn. The random assignment of participants increases the probability that differences observed between participant groups are the result of the experimental intervention.
Reliability -- the degree to which a measure yields consistent results. If the measuring instrument [e.g., survey] is reliable, then administering it to similar groups would yield similar results. Reliability is a prerequisite for validity. An unreliable indicator cannot produce trustworthy results.
Representative Sample -- sample in which the participants closely match the characteristics of the population, and thus, all segments of the population are represented in the sample. A representative sample allows results to be generalized from the sample to the population.
Rigor -- degree to which research methods are scrupulously and meticulously carried out in order to recognize important influences occurring in an experimental study.
Sample -- the population researched in a particular study. Usually, attempts are made to select a "sample population" that is considered representative of groups of people to whom results will be generalized or transferred. In studies that use inferential statistics to analyze results or which are designed to be generalizable, sample size is critical, generally the larger the number in the sample, the higher the likelihood of a representative distribution of the population.
Sampling Error -- the degree to which the results from the sample deviate from those that would be obtained from the entire population, because of random error in the selection of respondent and the corresponding reduction in reliability.
Saturation -- a situation in which data analysis begins to reveal repetition and redundancy and when new data tend to confirm existing findings rather than expand upon them.
Semantics -- the relationship between symbols and meaning in a linguistic system. Also, the cuing system that connects what is written in the text to what is stored in the reader's prior knowledge.
Social Theories -- theories about the structure, organization, and functioning of human societies.
Sociolinguistics -- the study of language in society and, more specifically, the study of language varieties, their functions, and their speakers.
Standard Deviation -- a measure of variation that indicates the typical distance between the scores of a distribution and the mean; it is determined by taking the square root of the average of the squared deviations in a given distribution. It can be used to indicate the proportion of data within certain ranges of scale values when the distribution conforms closely to the normal curve.
Statistical Analysis -- application of statistical processes and theory to the compilation, presentation, discussion, and interpretation of numerical data.
Statistical Bias -- characteristics of an experimental or sampling design, or the mathematical treatment of data, that systematically affects the results of a study so as to produce incorrect, unjustified, or inappropriate inferences or conclusions.
Statistical Significance -- the probability that the difference between the outcomes of the control and experimental group are great enough that it is unlikely due solely to chance. The probability that the null hypothesis can be rejected at a predetermined significance level [0.05 or 0.01].
Statistical Tests -- researchers use statistical tests to make quantitative decisions about whether a study's data indicate a significant effect from the intervention and allow the researcher to reject the null hypothesis. That is, statistical tests show whether the differences between the outcomes of the control and experimental groups are great enough to be statistically significant. If differences are found to be statistically significant, it means that the probability [likelihood] that these differences occurred solely due to chance is relatively low. Most researchers agree that a significance value of .05 or less [i.e., there is a 95% probability that the differences are real] sufficiently determines significance.
Subcultures -- ethnic, regional, economic, or social groups exhibiting characteristic patterns of behavior sufficient to distinguish them from the larger society to which they belong.
Testing -- the act of gathering and processing information about individuals' ability, skill, understanding, or knowledge under controlled conditions.
Theory -- a general explanation about a specific behavior or set of events that is based on known principles and serves to organize related events in a meaningful way. A theory is not as specific as a hypothesis.
Treatment -- the stimulus given to a dependent variable.
Trend Samples -- method of sampling different groups of people at different points in time from the same population.
Triangulation -- a multi-method or pluralistic approach, using different methods in order to focus on the research topic from different viewpoints and to produce a multi-faceted set of data. Also used to check the validity of findings from any one method.
Unit of Analysis -- the basic observable entity or phenomenon being analyzed by a study and for which data are collected in the form of variables.
Validity -- the degree to which a study accurately reflects or assesses the specific concept that the researcher is attempting to measure. A method can be reliable, consistently measuring the same thing, but not valid.
Variable -- any characteristic or trait that can vary from one person to another [race, gender, academic major] or for one person over time [age, political beliefs].
Weighted Scores -- scores in which the components are modified by different multipliers to reflect their relative importance.
White Paper -- an authoritative report that often states the position or philosophy about a social, political, or other subject, or a general explanation of an architecture, framework, or product technology written by a group of researchers. A white paper seeks to contain unbiased information and analysis regarding a business or policy problem that the researchers may be facing.

Elliot, Mark, Fairweather, Ian, Olsen, Wendy Kay, and Pampaka, Maria. A Dictionary of Social Research Methods. Oxford, UK: Oxford University Press, 2016; Free Social Science Dictionary. Socialsciencedictionary.com [2008]. Glossary. Institutional Review Board. Colorado College; Glossary of Key Terms. Writing@CSU. Colorado State University; Glossary A-Z. Education.com; Glossary of Research Terms. Research Mindedness Virtual Learning Resource. Centre for Human Servive Technology. University of Southampton; Miller, Robert L. and Brewer, John D. The A-Z of Social Research: A Dictionary of Key Social Science Research Concepts London: SAGE, 2003; Jupp, Victor. The SAGE Dictionary of Social and Cultural Research Methods . London: Sage, 2006.

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Last Updated: May 22, 2024 12:03 PM
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1.1 Etymology
1.2 Pronunciation
1.3.1 Synonyms
1.3.2 Derived terms
1.3.3 Translations
2.1 Etymology
2.2 Pronunciation
2.3.1 Declension

English [ edit ]

Etymology [ edit ].

Recorded since 1596, from Middle French hypothese , from Late Latin hypothesis , from Ancient Greek ὑπόθεσις ( hupóthesis , “ base, basis of an argument, supposition ” , literally “ a placing under ” ) , itself from ὑποτίθημι ( hupotíthēmi , “ I set before, suggest ” ) , from ὑπό ( hupó , “ below ” ) + τίθημι ( títhēmi , “ I put, place ” ) .

Pronunciation [ edit ]

( UK ) IPA ( key ) : /haɪˈpɒθɪsɪs/ , /hɪˈpɒθɪsɪs/ , /həˈpɒθɪsɪs/ , /-əsəs/ , /-əsɪs/
( US ) IPA ( key ) : /haɪˈpɑː.θə.sɪs/

Noun [ edit ]

hypothesis ( plural hypotheses )

2001 September 27, Terrie E. Moffitt, Avshalom Caspi, Michael Rutter, Phil A. Silva, Sex Differences in Antisocial Behaviour: Conduct Disorder, Delinquency, and Violence in the Dunedin Longitudinal Study ‎ [1] , Cambridge University Press , →ISBN , page 151 : This hypothesis goes by many names, including group resistence, the threshold effect, and the gender paradox. Because the hypothesis holds such wide appeal, it is worth revisiting the logic behind it. The hypothesis is built on the factual observation that fewer females than males act antisocially.
2005 , Ronald H. Pine, http://www.csicop.org/specialarticles/show/intelligent_design_or_no_model_creationism , 15 October 2005: Far too many of us have been taught in school that a scientist, in the course of trying to figure something out, will first come up with a " hypothesis " (a guess or surmise—not necessarily even an "educated" guess). ... [But t]he word " hypothesis " should be used, in science, exclusively for a reasoned, sensible, knowledge-informed explanation for why some phenomenon exists or occurs. An hypothesis can be as yet untested; can have already been tested; may have been falsified; may have not yet been falsified, although tested; or may have been tested in a myriad of ways countless times without being falsified; and it may come to be universally accepted by the scientific community. An understanding of the word " hypothesis ," as used in science, requires a grasp of the principles underlying Occam's Razor and Karl Popper's thought in regard to " falsifiability "—including the notion that any respectable scientific hypothesis must, in principle, be "capable of" being proven wrong (if it should, in fact, just happen to be wrong), but none can ever be proved to be true. One aspect of a proper understanding of the word " hypothesis ," as used in science, is that only a vanishingly small percentage of hypotheses could ever potentially become a theory.
( general ) An assumption taken to be true for the purpose of argument or investigation .
( grammar ) The antecedent of a conditional statement .

Synonyms [ edit ]

supposition
educated guess
See also Thesaurus:supposition

Derived terms [ edit ]

alternative hypothesis
aquatic ape hypothesis
Avogadro's hypothesis
conspiracy hypothesis
continuum hypothesis
cosmic censorship hypothesis
documentary hypothesis
efficient market hypothesis
ergodic hypothesis
expectations hypothesis
Fisher hypothesis
Gaia hypothesis
generalized continuum hypothesis
God hypothesis
Griesbach hypothesis
hypothesize
hypothetical
hypothetically
interface hypothesis
just-world hypothesis
level-ordering hypothesis
mafia hypothesis
Medea hypothesis
Monro-Kellie hypothesis
null hypothesis
Omphalos hypothesis
Out of India hypothesis
ovulatory shift hypothesis
permanent income hypothesis
Prout's hypothesis
Rare Earth hypothesis
Red Queen hypothesis
Riemann hypothesis
Sapir-Whorf hypothesis
Schinzel's hypothesis H
sexy son hypothesis
simulation hypothesis
swoon hypothesis
trickle-down hypothesis
trickle down hypothesis
Wellhausen's hypothesis
working hypothesis
zombie hypothesis

Translations [ edit ]

Latin [ edit ].

Borrowed from Ancient Greek ὑπόθεσις ( hupóthesis , “ hypothesis ” , noun ) .

( Classical ) IPA ( key ) : /hyˈpo.tʰe.sis/ , [hʏˈpɔt̪ʰɛs̠ɪs̠]
( modern Italianate Ecclesiastical ) IPA ( key ) : /iˈpo.te.sis/ , [iˈpɔːt̪es̬is]

hypothesis f ( genitive hypothesis or hypotheseōs or hypothesios ) ; third declension

Declension [ edit ]

1 Found sometimes in Medieval and New Latin.

There is also genitive plural hypotheseōn .
The genitive singular is also spelled hypotheseωs and the genitive plural hypotheseωn .

English terms derived from Proto-Indo-European
English terms derived from the Proto-Indo-European root *dʰeh₁-
English terms borrowed from Middle French
English terms derived from Middle French
English terms derived from Late Latin
English terms derived from Ancient Greek
English 4-syllable words
English terms with IPA pronunciation
English terms with audio links
English lemmas
English nouns
English countable nouns
English nouns with irregular plurals
en:Sciences
English terms with quotations
Latin terms borrowed from Ancient Greek
Latin terms derived from Ancient Greek
Latin 4-syllable words
Latin terms with IPA pronunciation
Latin lemmas
Latin nouns
Latin third declension nouns
Latin feminine nouns in the third declension
Latin terms spelled with Y
Latin feminine nouns
English entries with language name categories using raw markup
Requests for translations into Burmese
Urdu terms with non-redundant manual transliterations
Requests for translations into Russian
Requests for review of French translations
Requests for review of Icelandic translations
Requests for review of Persian translations
Requests for review of Romanian translations
Requests for review of Swedish translations
Requests for review of Turkish translations
Latin nouns with red links in their inflection tables

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Hypothesis Testing

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9.1: Null and Alternative Hypotheses

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COLLABORATIVE EXERCISE

Formula Review

Null Hypothesis Definition and Examples

How to State a Null Hypothesis

Why Test a Null Hypothesis?

Null Hypothesis

What is Null Hypothesis?

Null Hypothesis Meaning

Mean Comparison (Two-sample t-test)

Proportion Comparison

Equality in Variance (F-test in ANOVA)

Independence (Chi-square Test of Independence):

Equality Null Hypothesis (Simple Null Hypothesis)

Non-Inferiority Null Hypothesis

Superiority Null Hypothesis

Independence Null Hypothesis

Homogeneity Null Hypothesis

Null Hypothesis Rejection

When is Null Hypothesis Rejected?

Difference Between Null Hypothesis and Alternative Hypothesis

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What is a Null Hypothesis in Research?

What Are Alternative and Null Hypotheses?

What Does it Mean to Reject the Null Hypothesis?

How to Find Null Hypothesis?

How is Null Hypothesis denoted?

What is the Purpose of the Null hypothesis in Statistical Analysis?

What happens if we Reject the Null hypothesis?

What are Test for Null Hypothesis?

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Null Hypothesis Definition

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Null Hypothesis Examples

Example 1: Hypotheses with One Sample of One Categorical Variable

Example 2: Hypotheses with One Sample of One Measurement Variable

Example 3: Hypotheses with Two Samples of One Categorical Variable

Example 4: Hypotheses with Two Samples of One Measurement Variable

Example 5: Hypotheses about the relationship between Two Categorical Variables

Example 6: Hypotheses about the relationship between Two Measurement Variables

Example 7: Hypotheses about comparing the relationship between Two Measurement Variables in Two Samples

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