research test null hypothesis

Want to create or adapt books like this? Learn more about how Pressbooks supports open publishing practices.

Chapter 13: Inferential Statistics

Understanding Null Hypothesis Testing

Learning Objectives

Explain the purpose of null hypothesis testing, including the role of sampling error.
Describe the basic logic of null hypothesis testing.
Describe the role of relationship strength and sample size in determining statistical significance and make reasonable judgments about statistical significance based on these two factors.

The Purpose of Null Hypothesis Testing

As we have seen, psychological research typically involves measuring one or more variables for a sample and computing descriptive statistics for that sample. In general, however, the researcher’s goal is not to draw conclusions about that sample but to draw conclusions about the population that the sample was selected from. Thus researchers must use sample statistics to draw conclusions about the corresponding values in the population. These corresponding values in the population are called parameters . Imagine, for example, that a researcher measures the number of depressive symptoms exhibited by each of 50 clinically depressed adults and computes the mean number of symptoms. The researcher probably wants to use this sample statistic (the mean number of symptoms for the sample) to draw conclusions about the corresponding population parameter (the mean number of symptoms for clinically depressed adults).

Unfortunately, sample statistics are not perfect estimates of their corresponding population parameters. This is because there is a certain amount of random variability in any statistic from sample to sample. The mean number of depressive symptoms might be 8.73 in one sample of clinically depressed adults, 6.45 in a second sample, and 9.44 in a third—even though these samples are selected randomly from the same population. Similarly, the correlation (Pearson’s r ) between two variables might be +.24 in one sample, −.04 in a second sample, and +.15 in a third—again, even though these samples are selected randomly from the same population. This random variability in a statistic from sample to sample is called sampling error . (Note that the term error here refers to random variability and does not imply that anyone has made a mistake. No one “commits a sampling error.”)

One implication of this is that when there is a statistical relationship in a sample, it is not always clear that there is a statistical relationship in the population. A small difference between two group means in a sample might indicate that there is a small difference between the two group means in the population. But it could also be that there is no difference between the means in the population and that the difference in the sample is just a matter of sampling error. Similarly, a Pearson’s r value of −.29 in a sample might mean that there is a negative relationship in the population. But it could also be that there is no relationship in the population and that the relationship in the sample is just a matter of sampling error.

In fact, any statistical relationship in a sample can be interpreted in two ways:

There is a relationship in the population, and the relationship in the sample reflects this.
There is no relationship in the population, and the relationship in the sample reflects only sampling error.

The purpose of null hypothesis testing is simply to help researchers decide between these two interpretations.

The Logic of Null Hypothesis Testing

Null hypothesis testing is a formal approach to deciding between two interpretations of a statistical relationship in a sample. One interpretation is called the null hypothesis (often symbolized H 0 and read as “H-naught”). This is the idea that there is no relationship in the population and that the relationship in the sample reflects only sampling error. Informally, the null hypothesis is that the sample relationship “occurred by chance.” The other interpretation is called the alternative hypothesis (often symbolized as H 1 ). This is the idea that there is a relationship in the population and that the relationship in the sample reflects this relationship in the population.

Again, every statistical relationship in a sample can be interpreted in either of these two ways: It might have occurred by chance, or it might reflect a relationship in the population. So researchers need a way to decide between them. Although there are many specific null hypothesis testing techniques, they are all based on the same general logic. The steps are as follows:

Assume for the moment that the null hypothesis is true. There is no relationship between the variables in the population.
Determine how likely the sample relationship would be if the null hypothesis were true.
If the sample relationship would be extremely unlikely, then reject the null hypothesis in favour of the alternative hypothesis. If it would not be extremely unlikely, then retain the null hypothesis .

Following this logic, we can begin to understand why Mehl and his colleagues concluded that there is no difference in talkativeness between women and men in the population. In essence, they asked the following question: “If there were no difference in the population, how likely is it that we would find a small difference of d = 0.06 in our sample?” Their answer to this question was that this sample relationship would be fairly likely if the null hypothesis were true. Therefore, they retained the null hypothesis—concluding that there is no evidence of a sex difference in the population. We can also see why Kanner and his colleagues concluded that there is a correlation between hassles and symptoms in the population. They asked, “If the null hypothesis were true, how likely is it that we would find a strong correlation of +.60 in our sample?” Their answer to this question was that this sample relationship would be fairly unlikely if the null hypothesis were true. Therefore, they rejected the null hypothesis in favour of the alternative hypothesis—concluding that there is a positive correlation between these variables in the population.

A crucial step in null hypothesis testing is finding the likelihood of the sample result if the null hypothesis were true. This probability is called the p value . A low p value means that the sample result would be unlikely if the null hypothesis were true and leads to the rejection of the null hypothesis. A high p value means that the sample result would be likely if the null hypothesis were true and leads to the retention of the null hypothesis. But how low must the p value be before the sample result is considered unlikely enough to reject the null hypothesis? In null hypothesis testing, this criterion is called α (alpha) and is almost always set to .05. If there is less than a 5% chance of a result as extreme as the sample result if the null hypothesis were true, then the null hypothesis is rejected. When this happens, the result is said to be statistically significant . If there is greater than a 5% chance of a result as extreme as the sample result when the null hypothesis is true, then the null hypothesis is retained. This does not necessarily mean that the researcher accepts the null hypothesis as true—only that there is not currently enough evidence to conclude that it is true. Researchers often use the expression “fail to reject the null hypothesis” rather than “retain the null hypothesis,” but they never use the expression “accept the null hypothesis.”

The Misunderstood p Value

The p value is one of the most misunderstood quantities in psychological research (Cohen, 1994) [1] . Even professional researchers misinterpret it, and it is not unusual for such misinterpretations to appear in statistics textbooks!

The most common misinterpretation is that the p value is the probability that the null hypothesis is true—that the sample result occurred by chance. For example, a misguided researcher might say that because the p value is .02, there is only a 2% chance that the result is due to chance and a 98% chance that it reflects a real relationship in the population. But this is incorrect . The p value is really the probability of a result at least as extreme as the sample result if the null hypothesis were true. So a p value of .02 means that if the null hypothesis were true, a sample result this extreme would occur only 2% of the time.

You can avoid this misunderstanding by remembering that the p value is not the probability that any particular hypothesis is true or false. Instead, it is the probability of obtaining the sample result if the null hypothesis were true.

Role of Sample Size and Relationship Strength

Recall that null hypothesis testing involves answering the question, “If the null hypothesis were true, what is the probability of a sample result as extreme as this one?” In other words, “What is the p value?” It can be helpful to see that the answer to this question depends on just two considerations: the strength of the relationship and the size of the sample. Specifically, the stronger the sample relationship and the larger the sample, the less likely the result would be if the null hypothesis were true. That is, the lower the p value. This should make sense. Imagine a study in which a sample of 500 women is compared with a sample of 500 men in terms of some psychological characteristic, and Cohen’s d is a strong 0.50. If there were really no sex difference in the population, then a result this strong based on such a large sample should seem highly unlikely. Now imagine a similar study in which a sample of three women is compared with a sample of three men, and Cohen’s d is a weak 0.10. If there were no sex difference in the population, then a relationship this weak based on such a small sample should seem likely. And this is precisely why the null hypothesis would be rejected in the first example and retained in the second.

Of course, sometimes the result can be weak and the sample large, or the result can be strong and the sample small. In these cases, the two considerations trade off against each other so that a weak result can be statistically significant if the sample is large enough and a strong relationship can be statistically significant even if the sample is small. Table 13.1 shows roughly how relationship strength and sample size combine to determine whether a sample result is statistically significant. The columns of the table represent the three levels of relationship strength: weak, medium, and strong. The rows represent four sample sizes that can be considered small, medium, large, and extra large in the context of psychological research. Thus each cell in the table represents a combination of relationship strength and sample size. If a cell contains the word Yes , then this combination would be statistically significant for both Cohen’s d and Pearson’s r . If it contains the word No , then it would not be statistically significant for either. There is one cell where the decision for d and r would be different and another where it might be different depending on some additional considerations, which are discussed in Section 13.2 “Some Basic Null Hypothesis Tests”

Although Table 13.1 provides only a rough guideline, it shows very clearly that weak relationships based on medium or small samples are never statistically significant and that strong relationships based on medium or larger samples are always statistically significant. If you keep this lesson in mind, you will often know whether a result is statistically significant based on the descriptive statistics alone. It is extremely useful to be able to develop this kind of intuitive judgment. One reason is that it allows you to develop expectations about how your formal null hypothesis tests are going to come out, which in turn allows you to detect problems in your analyses. For example, if your sample relationship is strong and your sample is medium, then you would expect to reject the null hypothesis. If for some reason your formal null hypothesis test indicates otherwise, then you need to double-check your computations and interpretations. A second reason is that the ability to make this kind of intuitive judgment is an indication that you understand the basic logic of this approach in addition to being able to do the computations.

Statistical Significance Versus Practical Significance

Table 13.1 illustrates another extremely important point. A statistically significant result is not necessarily a strong one. Even a very weak result can be statistically significant if it is based on a large enough sample. This is closely related to Janet Shibley Hyde’s argument about sex differences (Hyde, 2007) [2] . The differences between women and men in mathematical problem solving and leadership ability are statistically significant. But the word significant can cause people to interpret these differences as strong and important—perhaps even important enough to influence the college courses they take or even who they vote for. As we have seen, however, these statistically significant differences are actually quite weak—perhaps even “trivial.”

This is why it is important to distinguish between the statistical significance of a result and the practical significance of that result. Practical significance refers to the importance or usefulness of the result in some real-world context. Many sex differences are statistically significant—and may even be interesting for purely scientific reasons—but they are not practically significant. In clinical practice, this same concept is often referred to as “clinical significance.” For example, a study on a new treatment for social phobia might show that it produces a statistically significant positive effect. Yet this effect still might not be strong enough to justify the time, effort, and other costs of putting it into practice—especially if easier and cheaper treatments that work almost as well already exist. Although statistically significant, this result would be said to lack practical or clinical significance.

Key Takeaways

Null hypothesis testing is a formal approach to deciding whether a statistical relationship in a sample reflects a real relationship in the population or is just due to chance.
The logic of null hypothesis testing involves assuming that the null hypothesis is true, finding how likely the sample result would be if this assumption were correct, and then making a decision. If the sample result would be unlikely if the null hypothesis were true, then it is rejected in favour of the alternative hypothesis. If it would not be unlikely, then the null hypothesis is retained.
The probability of obtaining the sample result if the null hypothesis were true (the p value) is based on two considerations: relationship strength and sample size. Reasonable judgments about whether a sample relationship is statistically significant can often be made by quickly considering these two factors.
Statistical significance is not the same as relationship strength or importance. Even weak relationships can be statistically significant if the sample size is large enough. It is important to consider relationship strength and the practical significance of a result in addition to its statistical significance.
Discussion: Imagine a study showing that people who eat more broccoli tend to be happier. Explain for someone who knows nothing about statistics why the researchers would conduct a null hypothesis test.
The correlation between two variables is r = −.78 based on a sample size of 137.
The mean score on a psychological characteristic for women is 25 ( SD = 5) and the mean score for men is 24 ( SD = 5). There were 12 women and 10 men in this study.
In a memory experiment, the mean number of items recalled by the 40 participants in Condition A was 0.50 standard deviations greater than the mean number recalled by the 40 participants in Condition B.
In another memory experiment, the mean scores for participants in Condition A and Condition B came out exactly the same!
A student finds a correlation of r = .04 between the number of units the students in his research methods class are taking and the students’ level of stress.

Long Descriptions

“Null Hypothesis” long description: A comic depicting a man and a woman talking in the foreground. In the background is a child working at a desk. The man says to the woman, “I can’t believe schools are still teaching kids about the null hypothesis. I remember reading a big study that conclusively disproved it years ago.” [Return to “Null Hypothesis”]

“Conditional Risk” long description: A comic depicting two hikers beside a tree during a thunderstorm. A bolt of lightning goes “crack” in the dark sky as thunder booms. One of the hikers says, “Whoa! We should get inside!” The other hiker says, “It’s okay! Lightning only kills about 45 Americans a year, so the chances of dying are only one in 7,000,000. Let’s go on!” The comic’s caption says, “The annual death rate among people who know that statistic is one in six.” [Return to “Conditional Risk”]

Media Attributions

Null Hypothesis by XKCD CC BY-NC (Attribution NonCommercial)
Conditional Risk by XKCD CC BY-NC (Attribution NonCommercial)
Cohen, J. (1994). The world is round: p < .05. American Psychologist, 49 , 997–1003. ↵
Hyde, J. S. (2007). New directions in the study of gender similarities and differences. Current Directions in Psychological Science, 16 , 259–263. ↵

Values in a population that correspond to variables measured in a study.

The random variability in a statistic from sample to sample.

A formal approach to deciding between two interpretations of a statistical relationship in a sample.

The idea that there is no relationship in the population and that the relationship in the sample reflects only sampling error.

The idea that there is a relationship in the population and that the relationship in the sample reflects this relationship in the population.

When the relationship found in the sample would be extremely unlikely, the idea that the relationship occurred “by chance” is rejected.

When the relationship found in the sample is likely to have occurred by chance, the null hypothesis is not rejected.

The probability that, if the null hypothesis were true, the result found in the sample would occur.

How low the p value must be before the sample result is considered unlikely in null hypothesis testing.

When there is less than a 5% chance of a result as extreme as the sample result occurring and the null hypothesis is rejected.

Research Methods in Psychology - 2nd Canadian Edition Copyright © 2015 by Paul C. Price, Rajiv Jhangiani, & I-Chant A. Chiang is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

Share This Book

9.1 Null and Alternative Hypotheses

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: a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0.

H a —, the alternative hypothesis: a claim about the population that is contradictory to H 0 and what we conclude when we reject H 0 .

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.

Mathematical Symbols Used in H 0 and H a :

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 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 9.1

H 0 : No more than 30 percent of the registered voters in Santa Clara County voted in the primary election. p ≤ 30 H a : More than 30 percent of the registered voters in Santa Clara County voted in the primary election. p > 30

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

Example 9.2

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 the following: H 0 : μ = 2.0 H a : μ ≠ 2.0

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 (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

H 0 : μ __ 66
H a : μ __ 66

Example 9.3

We want to test if college students take fewer than five years to graduate from college, on the average. The null and alternative hypotheses are the following: H 0 : μ ≥ 5 H a : μ < 5

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 : μ __ 45
H a : μ __ 45

Example 9.4

An article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third of the students pass. The same article stated that 6.6 percent of U.S. students take advanced placement exams and 4.4 percent pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6 percent. State the null and alternative hypotheses. H 0 : p ≤ 0.066 H a : p > 0.066

On a state driver’s test, about 40 percent pass the test on the first try. We want to test if more than 40 percent pass on the first try. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

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.

As an Amazon Associate we earn from qualifying purchases.

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute Texas Education Agency (TEA). The original material is available at: https://www.texasgateway.org/book/tea-statistics . Changes were made to the original material, including updates to art, structure, and other content updates.

Access for free at https://openstax.org/books/statistics/pages/1-introduction

Authors: Barbara Illowsky, Susan Dean
Publisher/website: OpenStax
Book title: Statistics
Publication date: Mar 27, 2020
Location: Houston, Texas
Book URL: https://openstax.org/books/statistics/pages/1-introduction
Section URL: https://openstax.org/books/statistics/pages/9-1-null-and-alternative-hypotheses

© Jan 23, 2024 Texas Education Agency (TEA). The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

13.1 Understanding Null Hypothesis Testing

Learning objectives.

Explain the purpose of null hypothesis testing, including the role of sampling error.
Describe the basic logic of null hypothesis testing.
Describe the role of relationship strength and sample size in determining statistical significance and make reasonable judgments about statistical significance based on these two factors.

The Purpose of Null Hypothesis Testing

As we have seen, psychological research typically involves measuring one or more variables in a sample and computing descriptive statistics for that sample. In general, however, the researcher’s goal is not to draw conclusions about that sample but to draw conclusions about the population that the sample was selected from. Thus researchers must use sample statistics to draw conclusions about the corresponding values in the population. These corresponding values in the population are called parameters . Imagine, for example, that a researcher measures the number of depressive symptoms exhibited by each of 50 adults with clinical depression and computes the mean number of symptoms. The researcher probably wants to use this sample statistic (the mean number of symptoms for the sample) to draw conclusions about the corresponding population parameter (the mean number of symptoms for adults with clinical depression).

Unfortunately, sample statistics are not perfect estimates of their corresponding population parameters. This is because there is a certain amount of random variability in any statistic from sample to sample. The mean number of depressive symptoms might be 8.73 in one sample of adults with clinical depression, 6.45 in a second sample, and 9.44 in a third—even though these samples are selected randomly from the same population. Similarly, the correlation (Pearson’s r ) between two variables might be +.24 in one sample, −.04 in a second sample, and +.15 in a third—again, even though these samples are selected randomly from the same population. This random variability in a statistic from sample to sample is called sampling error . (Note that the term error here refers to random variability and does not imply that anyone has made a mistake. No one “commits a sampling error.”)

In fact, any statistical relationship in a sample can be interpreted in two ways:

There is a relationship in the population, and the relationship in the sample reflects this.
There is no relationship in the population, and the relationship in the sample reflects only sampling error.

The purpose of null hypothesis testing is simply to help researchers decide between these two interpretations.

The Logic of Null Hypothesis Testing

Assume for the moment that the null hypothesis is true. There is no relationship between the variables in the population.
Determine how likely the sample relationship would be if the null hypothesis were true.
If the sample relationship would be extremely unlikely, then reject the null hypothesis in favor of the alternative hypothesis. If it would not be extremely unlikely, then retain the null hypothesis .

Following this logic, we can begin to understand why Mehl and his colleagues concluded that there is no difference in talkativeness between women and men in the population. In essence, they asked the following question: “If there were no difference in the population, how likely is it that we would find a small difference of d = 0.06 in our sample?” Their answer to this question was that this sample relationship would be fairly likely if the null hypothesis were true. Therefore, they retained the null hypothesis—concluding that there is no evidence of a sex difference in the population. We can also see why Kanner and his colleagues concluded that there is a correlation between hassles and symptoms in the population. They asked, “If the null hypothesis were true, how likely is it that we would find a strong correlation of +.60 in our sample?” Their answer to this question was that this sample relationship would be fairly unlikely if the null hypothesis were true. Therefore, they rejected the null hypothesis in favor of the alternative hypothesis—concluding that there is a positive correlation between these variables in the population.

A crucial step in null hypothesis testing is finding the likelihood of the sample result if the null hypothesis were true. This probability is called the p value . A low p value means that the sample result would be unlikely if the null hypothesis were true and leads to the rejection of the null hypothesis. A p value that is not low means that the sample result would be likely if the null hypothesis were true and leads to the retention of the null hypothesis. But how low must the p value be before the sample result is considered unlikely enough to reject the null hypothesis? In null hypothesis testing, this criterion is called α (alpha) and is almost always set to .05. If there is a 5% chance or less of a result as extreme as the sample result if the null hypothesis were true, then the null hypothesis is rejected. When this happens, the result is said to be statistically significant . If there is greater than a 5% chance of a result as extreme as the sample result when the null hypothesis is true, then the null hypothesis is retained. This does not necessarily mean that the researcher accepts the null hypothesis as true—only that there is not currently enough evidence to reject it. Researchers often use the expression “fail to reject the null hypothesis” rather than “retain the null hypothesis,” but they never use the expression “accept the null hypothesis.”

The Misunderstood p Value

“Null Hypothesis” retrieved from http://imgs.xkcd.com/comics/null_hypothesis.png (CC-BY-NC 2.5)

Role of Sample Size and Relationship Strength

Statistical Significance Versus Practical Significance

“Conditional Risk” retrieved from http://imgs.xkcd.com/comics/conditional_risk.png (CC-BY-NC 2.5)

Key Takeaways

Null hypothesis testing is a formal approach to deciding whether a statistical relationship in a sample reflects a real relationship in the population or is just due to chance.
The logic of null hypothesis testing involves assuming that the null hypothesis is true, finding how likely the sample result would be if this assumption were correct, and then making a decision. If the sample result would be unlikely if the null hypothesis were true, then it is rejected in favor of the alternative hypothesis. If it would not be unlikely, then the null hypothesis is retained.
The probability of obtaining the sample result if the null hypothesis were true (the p value) is based on two considerations: relationship strength and sample size. Reasonable judgments about whether a sample relationship is statistically significant can often be made by quickly considering these two factors.
Statistical significance is not the same as relationship strength or importance. Even weak relationships can be statistically significant if the sample size is large enough. It is important to consider relationship strength and the practical significance of a result in addition to its statistical significance.
Discussion: Imagine a study showing that people who eat more broccoli tend to be happier. Explain for someone who knows nothing about statistics why the researchers would conduct a null hypothesis test.
The correlation between two variables is r = −.78 based on a sample size of 137.
The mean score on a psychological characteristic for women is 25 ( SD = 5) and the mean score for men is 24 ( SD = 5). There were 12 women and 10 men in this study.
In a memory experiment, the mean number of items recalled by the 40 participants in Condition A was 0.50 standard deviations greater than the mean number recalled by the 40 participants in Condition B.
In another memory experiment, the mean scores for participants in Condition A and Condition B came out exactly the same!
A student finds a correlation of r = .04 between the number of units the students in his research methods class are taking and the students’ level of stress.
Cohen, J. (1994). The world is round: p < .05. American Psychologist, 49 , 997–1003. ↵
Hyde, J. S. (2007). New directions in the study of gender similarities and differences. Current Directions in Psychological Science, 16 , 259–263. ↵

Share This Book

Increase Font Size

Hypothesis Testing

When you conduct a piece of quantitative research, you are inevitably attempting to answer a research question or hypothesis that you have set. One method of evaluating this research question is via a process called hypothesis testing , which is sometimes also referred to as significance testing . Since there are many facets to hypothesis testing, we start with the example we refer to throughout this guide.

An example of a lecturer's dilemma

Two statistics lecturers, Sarah and Mike, think that they use the best method to teach their students. Each lecturer has 50 statistics students who are studying a graduate degree in management. In Sarah's class, students have to attend one lecture and one seminar class every week, whilst in Mike's class students only have to attend one lecture. Sarah thinks that seminars, in addition to lectures, are an important teaching method in statistics, whilst Mike believes that lectures are sufficient by themselves and thinks that students are better off solving problems by themselves in their own time. This is the first year that Sarah has given seminars, but since they take up a lot of her time, she wants to make sure that she is not wasting her time and that seminars improve her students' performance.

The research hypothesis

The first step in hypothesis testing is to set a research hypothesis. In Sarah and Mike's study, the aim is to examine the effect that two different teaching methods – providing both lectures and seminar classes (Sarah), and providing lectures by themselves (Mike) – had on the performance of Sarah's 50 students and Mike's 50 students. More specifically, they want to determine whether performance is different between the two different teaching methods. Whilst Mike is skeptical about the effectiveness of seminars, Sarah clearly believes that giving seminars in addition to lectures helps her students do better than those in Mike's class. This leads to the following research hypothesis:

Before moving onto the second step of the hypothesis testing process, we need to take you on a brief detour to explain why you need to run hypothesis testing at all. This is explained next.

Sample to population

If you have measured individuals (or any other type of "object") in a study and want to understand differences (or any other type of effect), you can simply summarize the data you have collected. For example, if Sarah and Mike wanted to know which teaching method was the best, they could simply compare the performance achieved by the two groups of students – the group of students that took lectures and seminar classes, and the group of students that took lectures by themselves – and conclude that the best method was the teaching method which resulted in the highest performance. However, this is generally of only limited appeal because the conclusions could only apply to students in this study. However, if those students were representative of all statistics students on a graduate management degree, the study would have wider appeal.

In statistics terminology, the students in the study are the sample and the larger group they represent (i.e., all statistics students on a graduate management degree) is called the population . Given that the sample of statistics students in the study are representative of a larger population of statistics students, you can use hypothesis testing to understand whether any differences or effects discovered in the study exist in the population. In layman's terms, hypothesis testing is used to establish whether a research hypothesis extends beyond those individuals examined in a single study.

Another example could be taking a sample of 200 breast cancer sufferers in order to test a new drug that is designed to eradicate this type of cancer. As much as you are interested in helping these specific 200 cancer sufferers, your real goal is to establish that the drug works in the population (i.e., all breast cancer sufferers).

As such, by taking a hypothesis testing approach, Sarah and Mike want to generalize their results to a population rather than just the students in their sample. However, in order to use hypothesis testing, you need to re-state your research hypothesis as a null and alternative hypothesis. Before you can do this, it is best to consider the process/structure involved in hypothesis testing and what you are measuring. This structure is presented on the next page .

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

Julia Simkus

Editor at Simply Psychology

BA (Hons) Psychology, Princeton University

Julia Simkus is a graduate of Princeton University with a Bachelor of Arts in Psychology. She is currently studying for a Master's Degree in Counseling for Mental Health and Wellness in September 2023. Julia's research has been published in peer reviewed journals.

Learn about our Editorial Process

Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul Mcleod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

On This Page:

A null hypothesis is a statistical concept suggesting no significant difference or relationship between measured variables. It’s the default assumption unless empirical evidence proves otherwise.

The null hypothesis states no relationship exists between the two variables being studied (i.e., one variable does not affect the other).

The null hypothesis is the statement that a researcher or an investigator wants to disprove.

Testing the null hypothesis can tell you whether your results are due to the effects of manipulating the dependent variable or due to random chance.

How to Write a Null Hypothesis

Null hypotheses (H0) start as research questions that the investigator rephrases as statements indicating no effect or relationship between the independent and dependent variables.

It is a default position that your research aims to challenge or confirm.

For example, if studying the impact of exercise on weight loss, your null hypothesis might be:

There is no significant difference in weight loss between individuals who exercise daily and those who do not.

Examples of Null Hypotheses

When do we reject the null hypothesis .

We reject the null hypothesis when the data provide strong enough evidence to conclude that it is likely incorrect. This often occurs when the p-value (probability of observing the data given the null hypothesis is true) is below a predetermined significance level.

If the collected data does not meet the expectation of the null hypothesis, a researcher can conclude that the data lacks sufficient evidence to back up the null hypothesis, and thus the null hypothesis is rejected.

Rejecting the null hypothesis means that a relationship does exist between a set of variables and the effect is statistically significant ( p > 0.05).

If the data collected from the random sample is not statistically significance , then the null hypothesis will be accepted, and the researchers can conclude that there is no relationship between the variables.

You need to perform a statistical test on your data in order to evaluate how consistent it is with the null hypothesis. A p-value is one statistical measurement used to validate a hypothesis against observed data.

Calculating the p-value is a critical part of null-hypothesis significance testing because it quantifies how strongly the sample data contradicts the null hypothesis.

The level of statistical significance is often expressed as a p -value between 0 and 1. The smaller the p-value, the stronger the evidence that you should reject the null hypothesis.

Probability and statistical significance in ab testing. Statistical significance in a b experiments

Usually, a researcher uses a confidence level of 95% or 99% (p-value of 0.05 or 0.01) as general guidelines to decide if you should reject or keep the null.

When your p-value is less than or equal to your significance level, you reject the null hypothesis.

In other words, smaller p-values are taken as stronger evidence against the null hypothesis. Conversely, when the p-value is greater than your significance level, you fail to reject the null hypothesis.

In this case, the sample data provides insufficient data to conclude that the effect exists in the population.

Because you can never know with complete certainty whether there is an effect in the population, your inferences about a population will sometimes be incorrect.

When you incorrectly reject the null hypothesis, it’s called a type I error. When you incorrectly fail to reject it, it’s called a type II error.

Why Do We Never Accept The Null Hypothesis?

The reason we do not say “accept the null” is because we are always assuming the null hypothesis is true and then conducting a study to see if there is evidence against it. And, even if we don’t find evidence against it, a null hypothesis is not accepted.

A lack of evidence only means that you haven’t proven that something exists. It does not prove that something doesn’t exist.

It is risky to conclude that the null hypothesis is true merely because we did not find evidence to reject it. It is always possible that researchers elsewhere have disproved the null hypothesis, so we cannot accept it as true, but instead, we state that we failed to reject the null.

One can either reject the null hypothesis, or fail to reject it, but can never accept it.

Why Do We Use The Null Hypothesis?

We can never prove with 100% certainty that a hypothesis is true; We can only collect evidence that supports a theory. However, testing a hypothesis can set the stage for rejecting or accepting this hypothesis within a certain confidence level.

The null hypothesis is useful because it can tell us whether the results of our study are due to random chance or the manipulation of a variable (with a certain level of confidence).

A null hypothesis is rejected if the measured data is significantly unlikely to have occurred and a null hypothesis is accepted if the observed outcome is consistent with the position held by the null hypothesis.

Rejecting the null hypothesis sets the stage for further experimentation to see if a relationship between two variables exists.

Hypothesis testing is a critical part of the scientific method as it helps decide whether the results of a research study support a particular theory about a given population. Hypothesis testing is a systematic way of backing up researchers’ predictions with statistical analysis.

It helps provide sufficient statistical evidence that either favors or rejects a certain hypothesis about the population parameter.

Purpose of a Null Hypothesis

The primary purpose of the null hypothesis is to disprove an assumption.
Whether rejected or accepted, the null hypothesis can help further progress a theory in many scientific cases.
A null hypothesis can be used to ascertain how consistent the outcomes of multiple studies are.

Do you always need both a Null Hypothesis and an Alternative Hypothesis?

The null (H0) and alternative (Ha or H1) hypotheses are two competing claims that describe the effect of the independent variable on the dependent variable. They are mutually exclusive, which means that only one of the two hypotheses can be true.

While the null hypothesis states that there is no effect in the population, an alternative hypothesis states that there is statistical significance between two variables.

The goal of hypothesis testing is to make inferences about a population based on a sample. In order to undertake hypothesis testing, you must express your research hypothesis as a null and alternative hypothesis. Both hypotheses are required to cover every possible outcome of the study.

What is the difference between a null hypothesis and an alternative hypothesis?

The alternative hypothesis is the complement to the null hypothesis. The null hypothesis states that there is no effect or no relationship between variables, while the alternative hypothesis claims that there is an effect or relationship in the population.

It is the claim that you expect or hope will be true. The null hypothesis and the alternative hypothesis are always mutually exclusive, meaning that only one can be true at a time.

What are some problems with the null hypothesis?

One major problem with the null hypothesis is that researchers typically will assume that accepting the null is a failure of the experiment. However, accepting or rejecting any hypothesis is a positive result. Even if the null is not refuted, the researchers will still learn something new.

Why can a null hypothesis not be accepted?

We can either reject or fail to reject a null hypothesis, but never accept it. If your test fails to detect an effect, this is not proof that the effect doesn’t exist. It just means that your sample did not have enough evidence to conclude that it exists.

We can’t accept a null hypothesis because a lack of evidence does not prove something that does not exist. Instead, we fail to reject it.

Failing to reject the null indicates that the sample did not provide sufficient enough evidence to conclude that an effect exists.

If the p-value is greater than the significance level, then you fail to reject the null hypothesis.

Is a null hypothesis directional or non-directional?

A hypothesis test can either contain an alternative directional hypothesis or a non-directional alternative hypothesis. A directional hypothesis is one that contains the less than (“<“) or greater than (“>”) sign.

A nondirectional hypothesis contains the not equal sign (“≠”). However, a null hypothesis is neither directional nor non-directional.

A null hypothesis is a prediction that there will be no change, relationship, or difference between two variables.

The directional hypothesis or nondirectional hypothesis would then be considered alternative hypotheses to the null hypothesis.

Gill, J. (1999). The insignificance of null hypothesis significance testing. Political research quarterly , 52 (3), 647-674.

Krueger, J. (2001). Null hypothesis significance testing: On the survival of a flawed method. American Psychologist , 56 (1), 16.

Masson, M. E. (2011). A tutorial on a practical Bayesian alternative to null-hypothesis significance testing. Behavior research methods , 43 , 679-690.

Nickerson, R. S. (2000). Null hypothesis significance testing: a review of an old and continuing controversy. Psychological methods , 5 (2), 241.

Rozeboom, W. W. (1960). The fallacy of the null-hypothesis significance test. Psychological bulletin , 57 (5), 416.

Statistics Made Easy

How to Write a Null Hypothesis (5 Examples)

A hypothesis test uses sample data to determine whether or not some claim about a population parameter is true.

Whenever we perform a hypothesis test, we always write a null hypothesis and an alternative hypothesis, which take the following forms:

H 0 (Null Hypothesis): Population parameter =, ≤, ≥ some value

H A (Alternative Hypothesis): Population parameter <, >, ≠ some value

Note that the null hypothesis always contains the equal sign .

We interpret the hypotheses as follows:

Null hypothesis: The sample data provides no evidence to support some claim being made by an individual.

Alternative hypothesis: The sample data does provide sufficient evidence to support the claim being made by an individual.

For example, suppose it’s assumed that the average height of a certain species of plant is 20 inches tall. However, one botanist claims the true average height is greater than 20 inches.

To test this claim, she may go out and collect a random sample of plants. She can then use this sample data to perform a hypothesis test using the following two hypotheses:

H 0 : μ ≤ 20 (the true mean height of plants is equal to or even less than 20 inches)

H A : μ > 20 (the true mean height of plants is greater than 20 inches)

If the sample data gathered by the botanist shows that the mean height of this species of plants is significantly greater than 20 inches, she can reject the null hypothesis and conclude that the mean height is greater than 20 inches.

Read through the following examples to gain a better understanding of how to write a null hypothesis in different situations.

Example 1: Weight of Turtles

A biologist wants to test whether or not the true mean weight of a certain species of turtles is 300 pounds. To test this, he goes out and measures the weight of a random sample of 40 turtles.

Here is how to write the null and alternative hypotheses for this scenario:

H 0 : μ = 300 (the true mean weight is equal to 300 pounds)

H A : μ ≠ 300 (the true mean weight is not equal to 300 pounds)

Example 2: Height of Males

It’s assumed that the mean height of males in a certain city is 68 inches. However, an independent researcher believes the true mean height is greater than 68 inches. To test this, he goes out and collects the height of 50 males in the city.

H 0 : μ ≤ 68 (the true mean height is equal to or even less than 68 inches)

H A : μ > 68 (the true mean height is greater than 68 inches)

Example 3: Graduation Rates

A university states that 80% of all students graduate on time. However, an independent researcher believes that less than 80% of all students graduate on time. To test this, she collects data on the proportion of students who graduated on time last year at the university.

H 0 : p ≥ 0.80 (the true proportion of students who graduate on time is 80% or higher)

H A : μ < 0.80 (the true proportion of students who graduate on time is less than 80%)

Example 4: Burger Weights

A food researcher wants to test whether or not the true mean weight of a burger at a certain restaurant is 7 ounces. To test this, he goes out and measures the weight of a random sample of 20 burgers from this restaurant.

H 0 : μ = 7 (the true mean weight is equal to 7 ounces)

H A : μ ≠ 7 (the true mean weight is not equal to 7 ounces)

Example 5: Citizen Support

A politician claims that less than 30% of citizens in a certain town support a certain law. To test this, he goes out and surveys 200 citizens on whether or not they support the law.

H 0 : p ≥ .30 (the true proportion of citizens who support the law is greater than or equal to 30%)

H A : μ < 0.30 (the true proportion of citizens who support the law is less than 30%)

Additional Resources

Introduction to Hypothesis Testing Introduction to Confidence Intervals An Explanation of P-Values and Statistical Significance

Published by Zach

Understanding Null Hypothesis Testing

Rajiv S. Jhangiani; I-Chant A. Chiang; Carrie Cuttler; and Dana C. Leighton

Learning Objectives

Explain the purpose of null hypothesis testing, including the role of sampling error.
Describe the basic logic of null hypothesis testing.
Describe the role of relationship strength and sample size in determining statistical significance and make reasonable judgments about statistical significance based on these two factors.

The Purpose of Null Hypothesis Testing

As we have seen, psychological research typically involves measuring one or more variables in a sample and computing descriptive summary data (e.g., means, correlation coefficients) for those variables. These descriptive data for the sample are called statistics . In general, however, the researcher’s goal is not to draw conclusions about that sample but to draw conclusions about the population that the sample was selected from. Thus researchers must use sample statistics to draw conclusions about the corresponding values in the population. These corresponding values in the population are called parameters . Imagine, for example, that a researcher measures the number of depressive symptoms exhibited by each of 50 adults with clinical depression and computes the mean number of symptoms. The researcher probably wants to use this sample statistic (the mean number of symptoms for the sample) to draw conclusions about the corresponding population parameter (the mean number of symptoms for adults with clinical depression).

Unfortunately, sample statistics are not perfect estimates of their corresponding population parameters. This is because there is a certain amount of random variability in any statistic from sample to sample. The mean number of depressive symptoms might be 8.73 in one sample of adults with clinical depression, 6.45 in a second sample, and 9.44 in a third—even though these samples are selected randomly from the same population. Similarly, the correlation (Pearson’s r ) between two variables might be +.24 in one sample, −.04 in a second sample, and +.15 in a third—again, even though these samples are selected randomly from the same population. This random variability in a statistic from sample to sample is called sampling error . (Note that the term error here refers to random variability and does not imply that anyone has made a mistake. No one “commits a sampling error.”)

In fact, any statistical relationship in a sample can be interpreted in two ways:

There is a relationship in the population, and the relationship in the sample reflects this.
There is no relationship in the population, and the relationship in the sample reflects only sampling error.

The purpose of null hypothesis testing is simply to help researchers decide between these two interpretations.

The Logic of Null Hypothesis Testing

Null hypothesis testing (often called null hypothesis significance testing or NHST) is a formal approach to deciding between two interpretations of a statistical relationship in a sample. One interpretation is called the null hypothesis (often symbolized H 0 and read as “H-zero”). This is the idea that there is no relationship in the population and that the relationship in the sample reflects only sampling error. Informally, the null hypothesis is that the sample relationship “occurred by chance.” The other interpretation is called the alternative hypothesis (often symbolized as H 1 ). This is the idea that there is a relationship in the population and that the relationship in the sample reflects this relationship in the population.

Assume for the moment that the null hypothesis is true. There is no relationship between the variables in the population.
Determine how likely the sample relationship would be if the null hypothesis were true.
If the sample relationship would be extremely unlikely, then reject the null hypothesis in favor of the alternative hypothesis. If it would not be extremely unlikely, then retain the null hypothesis .

Following this logic, we can begin to understand why Mehl and his colleagues concluded that there is no difference in talkativeness between women and men in the population. In essence, they asked the following question: “If there were no difference in the population, how likely is it that we would find a small difference of d = 0.06 in our sample?” Their answer to this question was that this sample relationship would be fairly likely if the null hypothesis were true. Therefore, they retained the null hypothesis—concluding that there is no evidence of a sex difference in the population. We can also see why Kanner and his colleagues concluded that there is a correlation between hassles and symptoms in the population. They asked, “If the null hypothesis were true, how likely is it that we would find a strong correlation of +.60 in our sample?” Their answer to this question was that this sample relationship would be fairly unlikely if the null hypothesis were true. Therefore, they rejected the null hypothesis in favor of the alternative hypothesis—concluding that there is a positive correlation between these variables in the population.

A crucial step in null hypothesis testing is finding the probability of the sample result or a more extreme result if the null hypothesis were true (Lakens, 2017). [1] This probability is called the p value . A low p value means that the sample or more extreme result would be unlikely if the null hypothesis were true and leads to the rejection of the null hypothesis. A p value that is not low means that the sample or more extreme result would be likely if the null hypothesis were true and leads to the retention of the null hypothesis. But how low must the p value criterion be before the sample result is considered unlikely enough to reject the null hypothesis? In null hypothesis testing, this criterion is called α (alpha) and is almost always set to .05. If there is a 5% chance or less of a result at least as extreme as the sample result if the null hypothesis were true, then the null hypothesis is rejected. When this happens, the result is said to be statistically significant . If there is greater than a 5% chance of a result as extreme as the sample result when the null hypothesis is true, then the null hypothesis is retained. This does not necessarily mean that the researcher accepts the null hypothesis as true—only that there is not currently enough evidence to reject it. Researchers often use the expression “fail to reject the null hypothesis” rather than “retain the null hypothesis,” but they never use the expression “accept the null hypothesis.”

The Misunderstood p Value

The p value is one of the most misunderstood quantities in psychological research (Cohen, 1994) [2] . Even professional researchers misinterpret it, and it is not unusual for such misinterpretations to appear in statistics textbooks!

Null Hypothesis. Image description available.

Role of Sample Size and Relationship Strength

Statistical Significance Versus Practical Significance

Table 13.1 illustrates another extremely important point. A statistically significant result is not necessarily a strong one. Even a very weak result can be statistically significant if it is based on a large enough sample. This is closely related to Janet Shibley Hyde’s argument about sex differences (Hyde, 2007) [3] . The differences between women and men in mathematical problem solving and leadership ability are statistically significant. But the word significant can cause people to interpret these differences as strong and important—perhaps even important enough to influence the college courses they take or even who they vote for. As we have seen, however, these statistically significant differences are actually quite weak—perhaps even “trivial.”

Image Description

Media Attributions

Null Hypothesis by XKCD CC BY-NC (Attribution NonCommercial)
Conditional Risk by XKCD CC BY-NC (Attribution NonCommercial)
Lakens, D. (2017, December 25). About p -values: Understanding common misconceptions. [Blog post] Retrieved from https://correlaid.org/en/blog/understand-p-values/ ↵
Cohen, J. (1994). The world is round: p < .05. American Psychologist, 49 , 997–1003. ↵
Hyde, J. S. (2007). New directions in the study of gender similarities and differences. Current Directions in Psychological Science, 16 , 259–263. ↵

Descriptive data that involves measuring one or more variables in a sample and computing descriptive summary data (e.g., means, correlation coefficients) for those variables.

Corresponding values in the population.

The random variability in a statistic from sample to sample.

A formal approach to deciding between two interpretations of a statistical relationship in a sample.

The idea that there is no relationship in the population and that the relationship in the sample reflects only sampling error (often symbolized H0 and read as “H-zero”).

An alternative to the null hypothesis (often symbolized as H1), this hypothesis proposes that there is a relationship in the population and that the relationship in the sample reflects this relationship in the population.

A decision made by researchers using null hypothesis testing which occurs when the sample relationship would be extremely unlikely.

A decision made by researchers in null hypothesis testing which occurs when the sample relationship would not be extremely unlikely.

The probability of obtaining the sample result or a more extreme result if the null hypothesis were true.

The criterion that shows how low a p-value should be before the sample result is considered unlikely enough to reject the null hypothesis (Usually set to .05).

An effect that is unlikely due to random chance and therefore likely represents a real effect in the population.

Refers to the importance or usefulness of the result in some real-world context.

Understanding Null Hypothesis Testing Copyright © 2022 by Rajiv S. Jhangiani; I-Chant A. Chiang; Carrie Cuttler; and Dana C. Leighton is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

Share This Book

Have a language expert improve your writing

Run a free plagiarism check in 10 minutes, generate accurate citations for free.

Knowledge Base

Methodology

How to Write a Strong Hypothesis | Steps & Examples

How to Write a Strong Hypothesis | Steps & Examples

Published on May 6, 2022 by Shona McCombes . Revised on November 20, 2023.

A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection .

Example: Hypothesis

Daily apple consumption leads to fewer doctor’s visits.

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, other interesting articles, frequently asked questions about writing hypotheses.

A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.

A hypothesis is not just a guess – it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Variables in hypotheses

Hypotheses propose a relationship between two or more types of variables .

An independent variable is something the researcher changes or controls.
A dependent variable is something the researcher observes and measures.

If there are any control variables , extraneous variables , or confounding variables , be sure to jot those down as you go to minimize the chances that research bias will affect your results.

In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .

Receive feedback on language, structure, and formatting

Professional editors proofread and edit your paper by focusing on:

Academic style
Vague sentences
Style consistency

See an example

Step 1. Ask a question

Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.

Step 2. Do some preliminary research

Your initial answer to the question should be based on what is already known about the topic. Look for theories and previous studies to help you form educated assumptions about what your research will find.

At this stage, you might construct a conceptual framework to ensure that you’re embarking on a relevant topic . This can also help you identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalize more complex constructs.

Step 3. Formulate your hypothesis

Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.

4. Refine your hypothesis

You need to make sure your hypothesis is specific and testable. There are various ways of phrasing a hypothesis, but all the terms you use should have clear definitions, and the hypothesis should contain:

The relevant variables
The specific group being studied
The predicted outcome of the experiment or analysis

5. Phrase your hypothesis in three ways

To identify the variables, you can write a simple prediction in if…then form. The first part of the sentence states the independent variable and the second part states the dependent variable.

In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.

If you are comparing two groups, the hypothesis can state what difference you expect to find between them.

6. Write a null hypothesis

If your research involves statistical hypothesis testing , you will also have to write a null hypothesis . The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a .

H 0 : The number of lectures attended by first-year students has no effect on their final exam scores.
H 1 : The number of lectures attended by first-year students has a positive effect on their final exam scores.

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

Sampling methods
Simple random sampling
Stratified sampling
Cluster sampling
Likert scales
Reproducibility

Statistics

Null hypothesis
Statistical power
Probability distribution
Effect size
Poisson distribution

Research bias

Optimism bias
Cognitive bias
Implicit bias
Hawthorne effect
Anchoring bias
Explicit bias

Here's why students love Scribbr's proofreading services

Discover proofreading & editing

A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).

Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.

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

Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the “Cite this Scribbr article” button to automatically add the citation to our free Citation Generator.

McCombes, S. (2023, November 20). How to Write a Strong Hypothesis | Steps & Examples. Scribbr. Retrieved April 17, 2024, from https://www.scribbr.com/methodology/hypothesis/

Is this article helpful?

Shona McCombes

Other students also liked, construct validity | definition, types, & examples, what is a conceptual framework | tips & examples, operationalization | a guide with examples, pros & cons, unlimited academic ai-proofreading.

✔ Document error-free in 5minutes ✔ Unlimited document corrections ✔ Specialized in correcting academic texts

Want to create or adapt books like this? Learn more about how Pressbooks supports open publishing practices.

Inferential Statistics

58 Some Basic Null Hypothesis Tests

Learning objectives.

Conduct and interpret one-sample, dependent-samples, and independent-samples t- tests.
Interpret the results of one-way, repeated measures, and factorial ANOVAs.
Conduct and interpret null hypothesis tests of Pearson’s r .

In this section, we look at several common null hypothesis testing procedures. The emphasis here is on providing enough information to allow you to conduct and interpret the most basic versions. In most cases, the online statistical analysis tools mentioned in Chapter 12 will handle the computations—as will programs such as Microsoft Excel and SPSS.

The t- Test

As we have seen throughout this book, many studies in psychology focus on the difference between two means. The most common null hypothesis test for this type of statistical relationship is the t- test . In this section, we look at three types of t tests that are used for slightly different research designs: the one-sample t- test, the dependent-samples t- test, and the independent-samples t- test. You may have already taken a course in statistics, but we will refresh your statistical

One-Sample t- Test

The one-sample t- test is used to compare a sample mean ( M ) with a hypothetical population mean (μ 0 ) that provides some interesting standard of comparison. The null hypothesis is that the mean for the population (µ) is equal to the hypothetical population mean: μ = μ 0 . The alternative hypothesis is that the mean for the population is different from the hypothetical population mean: μ ≠ μ 0 . To decide between these two hypotheses, we need to find the probability of obtaining the sample mean (or one more extreme) if the null hypothesis were true. But finding this p value requires first computing a test statistic called t . (A test statistic is a statistic that is computed only to help find the p value.) The formula for t is as follows:

[latex]t=\dfrac{{M -µ{_0}}}{\left(\dfrac{SD}{\sqrt N}\right)}[/latex]

Again, M is the sample mean and µ 0 is the hypothetical population mean of interest. SD is the sample standard deviation and N is the sample size.

The reason the t statistic (or any test statistic) is useful is that we know how it is distributed when the null hypothesis is true. As shown in Figure 13.1, this distribution is unimodal and symmetrical, and it has a mean of 0. Its precise shape depends on a statistical concept called the degrees of freedom, which for a one-sample t -test is N − 1. (There are 24 degrees of freedom for the distribution shown in Figure 13.1.) The important point is that knowing this distribution makes it possible to find the p value for any t score. Consider, for example, a t score of 1.50 based on a sample of 25. The probability of a t score at least this extreme is given by the proportion of t scores in the distribution that are at least this extreme. For now, let us define extreme as being far from zero in either direction. Thus the p value is the proportion of t scores that are 1.50 or above or that are −1.50 or below—a value that turns out to be .14.

Fortunately, we do not have to deal directly with the distribution of t scores. If we were to enter our sample data and hypothetical mean of interest into one of the online statistical tools in Chapter 12 or into a program like SPSS (Excel does not have a one-sample t- test function), the output would include both the t score and the p value. At this point, the rest of the procedure is simple. If p is equal to or less than .05, we reject the null hypothesis and conclude that the population mean differs from the hypothetical mean of interest. If p is greater than .05, we retain the null hypothesis and conclude that there is not enough evidence to say that the population mean differs from the hypothetical mean of interest. (Again, technically, we conclude only that we do not have enough evidence to conclude that it does differ.)

If we were to compute the t score by hand, we could use a table like Table 13.2 to make the decision. This table does not provide actual p values. Instead, it provides the critical values of t for different degrees of freedom ( df) when α is .05. For now, let us focus on the two-tailed critical values in the last column of the table. Each of these values should be interpreted as a pair of values: one positive and one negative. For example, the two-tailed critical values when there are 24 degrees of freedom are 2.064 and −2.064. These are represented by the red vertical lines in Figure 13.1. The idea is that any t score below the lower critical value (the left-hand red line in Figure 13.1) is in the lowest 2.5% of the distribution, while any t score above the upper critical value (the right-hand red line) is in the highest 2.5% of the distribution. Therefore any t score beyond the critical value in either direction is in the most extreme 5% of t scores when the null hypothesis is true and has a p value less than .05. Thus if the t score we compute is beyond the critical value in either direction, then we reject the null hypothesis. If the t score we compute is between the upper and lower critical values, then we retain the null hypothesis.

Thus far, we have considered what is called a two-tailed test , where we reject the null hypothesis if the t score for the sample is extreme in either direction. This test makes sense when we believe that the sample mean might differ from the hypothetical population mean but we do not have good reason to expect the difference to go in a particular direction. But it is also possible to do a one-tailed test , where we reject the null hypothesis only if the t score for the sample is extreme in one direction that we specify before collecting the data. This test makes sense when we have good reason to expect the sample mean will differ from the hypothetical population mean in a particular direction.

Here is how it works. Each one-tailed critical value in Table 13.2 can again be interpreted as a pair of values: one positive and one negative. A t score below the lower critical value is in the lowest 5% of the distribution, and a t score above the upper critical value is in the highest 5% of the distribution. For 24 degrees of freedom, these values are −1.711 and 1.711. (These are represented by the green vertical lines in Figure 13.1.) However, for a one-tailed test, we must decide before collecting data whether we expect the sample mean to be lower than the hypothetical population mean, in which case we would use only the lower critical value, or we expect the sample mean to be greater than the hypothetical population mean, in which case we would use only the upper critical value. Notice that we still reject the null hypothesis when the t score for our sample is in the most extreme 5% of the t scores we would expect if the null hypothesis were true—so α remains at .05. We have simply redefined extreme to refer only to one tail of the distribution. The advantage of the one-tailed test is that critical values are less extreme. If the sample mean differs from the hypothetical population mean in the expected direction, then we have a better chance of rejecting the null hypothesis. The disadvantage is that if the sample mean differs from the hypothetical population mean in the unexpected direction, then there is no chance at all of rejecting the null hypothesis.

Example One-Sample t – Test

Imagine that a health psychologist is interested in the accuracy of university students’ estimates of the number of calories in a chocolate chip cookie. He shows the cookie to a sample of 10 students and asks each one to estimate the number of calories in it. Because the actual number of calories in the cookie is 250, this is the hypothetical population mean of interest (µ 0 ). The null hypothesis is that the mean estimate for the population (μ) is 250. Because he has no real sense of whether the students will underestimate or overestimate the number of calories, he decides to do a two-tailed test. Now imagine further that the participants’ actual estimates are as follows:

250, 280, 200, 150, 175, 200, 200, 220, 180, 250.

The mean estimate for the sample ( M ) is 212.00 calories and the standard deviation ( SD ) is 39.17. The health psychologist can now compute the t score for his sample:

[latex]t=\dfrac{{212-250}}{\left(\dfrac{39.17}{\sqrt10}\right)}=-3.07[/latex]

If he enters the data into one of the online analysis tools or uses SPSS, it would also tell him that the two-tailed p value for this t score (with 10 − 1 = 9 degrees of freedom) is .013. Because this is less than .05, the health psychologist would reject the null hypothesis and conclude that university students tend to underestimate the number of calories in a chocolate chip cookie. If he computes the t score by hand, he could look at Table 13.2 and see that the critical value of t for a two-tailed test with 9 degrees of freedom is ±2.262. The fact that his t score was more extreme than this critical value would tell him that his p value is less than .05 and that he should reject the null hypothesis. Using APA style, these results would be reported as follows: t (9) = -3.07, p = .01. Note that the t and p are italicized, the degrees of freedom appear in brackets with no decimal remainder, and the values of t and p are rounded to two decimal places.

Finally, if this researcher had gone into this study with good reason to expect that university students underestimate the number of calories, then he could have done a one-tailed test instead of a two-tailed test. The only thing this decision would change is the critical value, which would be −1.833. This slightly less extreme value would make it a bit easier to reject the null hypothesis. However, if it turned out that university students overestimate the number of calories—no matter how much they overestimate it—the researcher would not have been able to reject the null hypothesis.

The Dependent-Samples t – Test

The dependent-samples t -test (sometimes called the paired-samples t- test) is used to compare two means for the same sample tested at two different times or under two different conditions. This comparison is appropriate for pretest-posttest designs or within-subjects experiments. The null hypothesis is that the means at the two times or under the two conditions are the same in the population. The alternative hypothesis is that they are not the same. This test can also be one-tailed if the researcher has good reason to expect the difference goes in a particular direction.

It helps to think of the dependent-samples t- test as a special case of the one-sample t- test. However, the first step in the dependent-samples t- test is to reduce the two scores for each participant to a single difference score by taking the difference between them. At this point, the dependent-samples t- test becomes a one-sample t- test on the difference scores. The hypothetical population mean (µ 0 ) of interest is 0 because this is what the mean difference score would be if there were no difference on average between the two times or two conditions. We can now think of the null hypothesis as being that the mean difference score in the population is 0 (µ 0 = 0) and the alternative hypothesis as being that the mean difference score in the population is not 0 (µ 0 ≠ 0).

Example Dependent-Samples t – Test

Imagine that the health psychologist now knows that people tend to underestimate the number of calories in junk food and has developed a short training program to improve their estimates. To test the effectiveness of this program, he conducts a pretest-posttest study in which 10 participants estimate the number of calories in a chocolate chip cookie before the training program and then again afterward. Because he expects the program to increase the participants’ estimates, he decides to do a one-tailed test. Now imagine further that the pretest estimates are

230, 250, 280, 175, 150, 200, 180, 210, 220, 190

and that the posttest estimates (for the same participants in the same order) are

250, 260, 250, 200, 160, 200, 200, 180, 230, 240.

The difference scores, then, are as follows:

20, 10, −30, 25, 10, 0, 20, −30, 10, 50.

Note that it does not matter whether the first set of scores is subtracted from the second or the second from the first as long as it is done the same way for all participants. In this example, it makes sense to subtract the pretest estimates from the posttest estimates so that positive difference scores mean that the estimates went up after the training and negative difference scores mean the estimates went down.

The mean of the difference scores is 8.50 with a standard deviation of 27.27. The health psychologist can now compute the t score for his sample as follows:

[latex]t=\dfrac{{8.5-0}}{\left(\dfrac{27.27}{\sqrt10}\right)}=1.11[/latex]

If he enters the data into one of the online analysis tools or uses Excel or SPSS, it would tell him that the one-tailed p value for this t score (again with 10 − 1 = 9 degrees of freedom) is .148. Because this is greater than .05, he would retain the null hypothesis and conclude that the training program does not significantly increase people’s calorie estimates. If he were to compute the t score by hand, he could look at Table 13.2 and see that the critical value of t for a one-tailed test with 9 degrees of freedom is 1.833. (It is positive this time because he was expecting a positive mean difference score.) The fact that his t score was less extreme than this critical value would tell him that his p value is greater than .05 and that he should fail to reject the null hypothesis.

The Independent-Samples t- Test

The independent-samples t- test is used to compare the means of two separate samples ( M 1 and M 2 ). The two samples might have been tested under different conditions in a between-subjects experiment, or they could be pre-existing groups in a cross-sectional design (e.g., women and men, extraverts and introverts). The null hypothesis is that the means of the two populations are the same: µ 1 = µ 2 . The alternative hypothesis is that they are not the same: µ 1 ≠ µ 2 . Again, the test can be one-tailed if the researcher has good reason to expect the difference goes in a particular direction.

The t statistic here is a bit more complicated because it must take into account two sample means, two standard deviations, and two sample sizes. The formula is as follows:

[latex]t=\dfrac{{M{_1}-M{_2}}}{\sqrt{\dfrac{SD{^2}{_1}}{n{_1}}+\dfrac{SD{^2}{_2}}{n{_2}}}}[/latex]

Notice that this formula includes squared standard deviations (the variances) that appear inside the square root symbol. Also, lowercase n 1 and n 2 refer to the sample sizes in the two groups or condition (as opposed to capital N , which generally refers to the total sample size). The only additional thing to know here is that there are N − 2 degrees of freedom for the independent-samples t- test.

Example Independent-Samples t – Test

Now the health psychologist wants to compare the calorie estimates of people who regularly eat junk food with the estimates of people who rarely eat junk food. He believes the difference could come out in either direction so he decides to conduct a two-tailed test. He collects data from a sample of eight participants who eat junk food regularly and seven participants who rarely eat junk food. The data are as follows:

Junk food eaters: 180, 220, 150, 85, 200, 170, 150, 190

Non–junk food eaters: 200, 240, 190, 175, 200, 300, 240

The mean for the non-junk food eaters is 220.71 with a standard deviation of 41.23. The mean for the junk food eaters is 168.12 with a standard deviation of 42.66. He can now compute his t score as follows:

[latex]t=\dfrac{{220.71-168.12}}{\sqrt{\dfrac{41.23{^2}}{8}+\dfrac{42.66{^2}}{7}}}= 2.42[/latex]

If he enters the data into one of the online analysis tools or uses Excel or SPSS, it would tell him that the two-tailed p value for this t score (with 15 − 2 = 13 degrees of freedom) is .015. Because this p value is less than .05, the health psychologist would reject the null hypothesis and conclude that people who eat junk food regularly make lower calorie estimates than people who eat it rarely. If he were to compute the t score by hand, he could look at Table 13.2 and see that the critical value of t for a two-tailed test with 13 degrees of freedom is ±2.160. The fact that his t score was more extreme than this critical value would tell him that his p value is less than .05 and that he should reject the null hypothesis.

The Analysis of Variance

T -tests are used to compare two means (a sample mean with a population mean, the means of two conditions or two groups). When there are more than two groups or condition means to be compared, the most common null hypothesis test is the analysis of variance (ANOVA) . In this section, we look primarily at the one-way ANOVA , which is used for between-subjects designs with a single independent variable. We then briefly consider some other versions of the ANOVA that are used for within-subjects and factorial research designs.

One-Way ANOVA

The one-way ANOVA is used to compare the means of more than two samples ( M 1 , M 2 … M G ) in a between-subjects design. The null hypothesis is that all the means are equal in the population: µ 1 = µ 2 =…= µ G . The alternative hypothesis is that not all the means in the population are equal.

The test statistic for the ANOVA is called F . It is a ratio of two estimates of the population variance based on the sample data. One estimate of the population variance is called the mean squares between groups (MS B ) and is based on the differences among the sample means. The other is called the mean squares within groups (MS W ) and is based on the differences among the scores within each group. The F statistic is the ratio of the MS B to the MS W and can, therefore, be expressed as follows:

F = MS B / MS W

Again, the reason that F is useful is that we know how it is distributed when the null hypothesis is true. As shown in Figure 13.2, this distribution is unimodal and positively skewed with values that cluster around 1. The precise shape of the distribution depends on both the number of groups and the sample size, and there are degrees of freedom values associated with each of these. The between-groups degrees of freedom is the number of groups minus one: df B = ( G − 1). The within-groups degrees of freedom is the total sample size minus the number of groups: df W = N − G . Again, knowing the distribution of F when the null hypothesis is true allows us to find the p value.

The online tools in Chapter 12 and statistical software such as Excel and SPSS will compute F and find the p value. If p is equal to or less than .05, then we reject the null hypothesis and conclude that there are differences among the group means in the population. If p is greater than .05, then we retain the null hypothesis and conclude that there is not enough evidence to say that there are differences. In the unlikely event that we would compute F by hand, we can use a table of critical values like Table 13.3 “Table of Critical Values of ” to make the decision. The idea is that any F ratio greater than the critical value has a p value of less than .05. Thus if the F ratio we compute is beyond the critical value, then we reject the null hypothesis. If the F ratio we compute is less than the critical value, then we retain the null hypothesis.

Example One-Way ANOVA

Imagine that the health psychologist wants to compare the calorie estimates of psychology majors, nutrition majors, and professional dieticians. He collects the following data:

Psych majors: 200, 180, 220, 160, 150, 200, 190, 200

Nutrition majors: 190, 220, 200, 230, 160, 150, 200, 210, 195

Dieticians: 220, 250, 240, 275, 250, 230, 200, 240

The means are 187.50 ( SD = 23.14), 195.00 ( SD = 27.77), and 238.13 ( SD = 22.35), respectively. So it appears that dieticians made substantially more accurate estimates on average. The researcher would almost certainly enter these data into a program such as Excel or SPSS, which would compute F for him or her and find the p value. Table 13.4 shows the output of the one-way ANOVA function in Excel for these data. This table is referred to as an ANOVA table. It shows that MS B is 5,971.88, MS W is 602.23, and their ratio, F , is 9.92. The p value is .0009. Because this value is below .05, the researcher would reject the null hypothesis and conclude that the mean calorie estimates for the three groups are not the same in the population. Notice that the ANOVA table also includes the “sum of squares” ( SS ) for between groups and for within groups. These values are computed on the way to finding MS B and MS W but are not typically reported by the researcher. Finally, if the researcher were to compute the F ratio by hand, he could look at Table 13.3 and see that the critical value of F with 2 and 21 degrees of freedom is 3.467 (the same value in Table 13.4 under F crit ). The fact that his F score was more extreme than this critical value would tell him that his p value is less than .05 and that he should reject the null hypothesis.

ANOVA Elaborations

Post hoc comparisons.

When we reject the null hypothesis in a one-way ANOVA, we conclude that the group means are not all the same in the population. But this can indicate different things. With three groups, it can indicate that all three means are significantly different from each other. Or it can indicate that one of the means is significantly different from the other two, but the other two are not significantly different from each other. It could be, for example, that the mean calorie estimates of psychology majors, nutrition majors, and dieticians are all significantly different from each other. Or it could be that the mean for dieticians is significantly different from the means for psychology and nutrition majors, but the means for psychology and nutrition majors are not significantly different from each other. For this reason, statistically significant one-way ANOVA results are typically followed up with a series of post hoc comparisons of selected pairs of group means to determine which are different from which others.

One approach to post hoc comparisons would be to conduct a series of independent-samples t- tests comparing each group mean to each of the other group means. But there is a problem with this approach. In general, if we conduct a t -test when the null hypothesis is true, we have a 5% chance of mistakenly rejecting the null hypothesis (see Section 13.3 “Additional Considerations” for more on such Type I errors). If we conduct several t- tests when the null hypothesis is true, the chance of mistakenly rejecting at least one null hypothesis increases with each test we conduct. Thus researchers do not usually make post hoc comparisons using standard t- tests because there is too great a chance that they will mistakenly reject at least one null hypothesis. Instead, they use one of several modified t -test procedures—among them the Bonferonni procedure, Fisher’s least significant difference (LSD) test, and Tukey’s honestly significant difference (HSD) test. The details of these approaches are beyond the scope of this book, but it is important to understand their purpose. It is to keep the risk of mistakenly rejecting a true null hypothesis to an acceptable level (close to 5%).

Repeated-Measures ANOVA

Recall that the one-way ANOVA is appropriate for between-subjects designs in which the means being compared come from separate groups of participants. It is not appropriate for within-subjects designs in which the means being compared come from the same participants tested under different conditions or at different times. This requires a slightly different approach, called the repeated-measures ANOVA . The basics of the repeated-measures ANOVA are the same as for the one-way ANOVA. The main difference is that measuring the dependent variable multiple times for each participant allows for a more refined measure of MS W . Imagine, for example, that the dependent variable in a study is a measure of reaction time. Some participants will be faster or slower than others because of stable individual differences in their nervous systems, muscles, and other factors. In a between-subjects design, these stable individual differences would simply add to the variability within the groups and increase the value of MS W (which would, in turn, decrease the value of F). In a within-subjects design, however, these stable individual differences can be measured and subtracted from the value of MS W . This lower value of MS W means a higher value of F and a more sensitive test.

Factorial ANOVA

When more than one independent variable is included in a factorial design, the appropriate approach is the factorial ANOVA . Again, the basics of the factorial ANOVA are the same as for the one-way and repeated-measures ANOVAs. The main difference is that it produces an F ratio and p value for each main effect and for each interaction. Returning to our calorie estimation example, imagine that the health psychologist tests the effect of participant major (psychology vs. nutrition) and food type (cookie vs. hamburger) in a factorial design. A factorial ANOVA would produce separate F ratios and p values for the main effect of major, the main effect of food type, and the interaction between major and food. Appropriate modifications must be made depending on whether the design is between-subjects, within-subjects, or mixed.

Testing Correlation Coefficients

For relationships between quantitative variables, where Pearson’s r (the correlation coefficient) is used to describe the strength of those relationships, the appropriate null hypothesis test is a test of the correlation coefficient. The basic logic is exactly the same as for other null hypothesis tests. In this case, the null hypothesis is that there is no relationship in the population. We can use the Greek lowercase rho (ρ) to represent the relevant parameter: ρ = 0. The alternative hypothesis is that there is a relationship in the population: ρ ≠ 0. As with the t- test, this test can be two-tailed if the researcher has no expectation about the direction of the relationship or one-tailed if the researcher expects the relationship to go in a particular direction.

It is possible to use the correlation coefficient for the sample to compute a t score with N − 2 degrees of freedom and then to proceed as for a t- test. However, because of the way it is computed, the correlation coefficient can also be treated as its own test statistic. The online statistical tools and statistical software such as Excel and SPSS generally compute the correlation coefficient and provide the p value associated with that value. As always, if the p value is equal to or less than .05, we reject the null hypothesis and conclude that there is a relationship between the variables in the population. If the p value is greater than .05, we retain the null hypothesis and conclude that there is not enough evidence to say there is a relationship in the population. If we compute the correlation coefficient by hand, we can use a table like Table 13.5, which shows the critical values of r for various samples sizes when α is .05. A sample value of the correlation coefficient that is more extreme than the critical value is statistically significant.

Example Test of a Correlation Coefficient

Imagine that the health psychologist is interested in the correlation between people’s calorie estimates and their weight. She has no expectation about the direction of the relationship, so she decides to conduct a two-tailed test. She computes the correlation coefficient for a sample of 22 university students and finds that Pearson’s r is −.21. The statistical software she uses tells her that the p value is .348. It is greater than .05, so she retains the null hypothesis and concludes that there is no relationship between people’s calorie estimates and their weight. If she were to compute the correlation coefficient by hand, she could look at Table 13.5 and see that the critical value for 22 − 2 = 20 degrees of freedom is .444. The fact that the correlation coefficient for her sample is less extreme than this critical value tells her that the p value is greater than .05 and that she should retain the null hypothesis.

A test that involves looking at the difference between two means.

Used to compare a sample mean (M) with a hypothetical population mean (μ0) that provides some interesting standard of comparison.

A statistic (e.g., F , t , etc.) that is computed to compare against what is expected in the null hypothesis, and thus helps find the p value.

The absolute value that a test statistic (e.g., F , t , etc.) must exceed to be considered statistically significant.

Where we reject the null hypothesis if the test statistic for the sample is extreme in either direction (+/-).

Where we reject the null hypothesis only if the t score for the sample is extreme in one direction that we specify before collecting the data.

Used to compare two means for the same sample tested at two different times or under two different conditions (sometimes called the paired-samples t -test).

A method to reduce pairs of scores (e.g., pre- and post-test) to a single score by calculating the difference between them.

Used to compare the means of two separate samples (M1 and M2).

A statistical test used when there are more than two groups or condition means to be compared.

Used for between-subjects designs with a single independent variable.

An estimate of the population variance and is based on the differences among the sample means.

An estimate of the population variance and is based on the differences among the scores within each group.

An unplanned (not hypothesized) test of which pairs of group mean scores are different from which others.

Compares the means from the same participants tested under different conditions or at different times in which the dependent variable is measured multiple times for each participant.

A statistical method to detect differences in the means between conditions when there are two or more independent variables in a factorial design. It allows the detection of main effects and interaction effects.

Research Methods in Psychology Copyright © 2023 by William L. Kelemen, Rajiv S. Jhangiani, I-Chant A. Chiang, Carrie Cuttler, & Dana C. Leighton is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

Share This Book

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

AP®︎/College Statistics

Course: ap®︎/college statistics > unit 10.

Idea behind hypothesis testing

Examples of null and alternative hypotheses

Writing null and alternative hypotheses
P-values and significance tests
Comparing P-values to different significance levels
Estimating a P-value from a simulation
Estimating P-values from simulations
Using P-values to make conclusions

Want to join the conversation?

Upvote Button navigates to signup page
Downvote Button navigates to signup page
Flag Button navigates to signup page

Video transcript

school Campus Bookshelves
menu_book Bookshelves
perm_media Learning Objects
login Login
how_to_reg Request Instructor Account
hub Instructor Commons
Download Page (PDF)
Download Full Book (PDF)
Periodic Table
Physics Constants
Scientific Calculator
Reference & Cite
Tools expand_more
Readability

selected template will load here

This action is not available.

7.3: The Research Hypothesis and the Null Hypothesis

Last updated
Save as PDF
Page ID 18038

Michelle Oja
Taft College

Hypotheses are predictions of expected findings.

The Research Hypothesis

A research hypothesis is a mathematical way of stating a research question. A research hypothesis names the groups (we'll start with a sample and a population), what was measured, and which we think will have a higher mean. The last one gives the research hypothesis a direction. In other words, a research hypothesis should include:

The name of the groups being compared. This is sometimes considered the IV.
What was measured. This is the DV.
Which group are we predicting will have the higher mean.

There are two types of research hypotheses related to sample means and population means: Directional Research Hypotheses and Non-Directional Research Hypotheses

Directional Research Hypothesis

If we expect our obtained sample mean to be above or below the other group's mean (the population mean, for example), we have a directional hypothesis. There are two options:

Symbol: $ \displaystyle \bar{X} > \mu $
(The mean of the sample is greater than than the mean of the population.)
Symbol: $ \displaystyle \bar{X} < \mu $
(The mean of the sample is less than than mean of the population.)

Example $\PageIndex{1}$

A study by Blackwell, Trzesniewski, and Dweck (2007) measured growth mindset and how long the junior high student participants spent on their math homework. What’s a directional hypothesis for how scoring higher on growth mindset (compared to the population of junior high students) would be related to how long students spent on their homework? Write this out in words and symbols.

Answer in Words: Students who scored high on growth mindset would spend more time on their homework than the population of junior high students.

Answer in Symbols: $ \displaystyle \bar{X} > \mu $

Non-Directional Research Hypothesis

A non-directional hypothesis states that the means will be different, but does not specify which will be higher. In reality, there is rarely a situation in which we actually don't want one group to be higher than the other, so we will focus on directional research hypotheses. There is only one option for a non-directional research hypothesis: "The sample mean differs from the population mean." These types of research hypotheses don’t give a direction, the hypothesis doesn’t say which will be higher or lower.

A non-directional research hypothesis in symbols should look like this: $ \displaystyle \bar{X} \neq \mu $ (The mean of the sample is not equal to the mean of the population).

Exercise $\PageIndex{1}$

What’s a non-directional hypothesis for how scoring higher on growth mindset higher on growth mindset (compared to the population of junior high students) would be related to how long students spent on their homework (Blackwell, Trzesniewski, & Dweck, 2007)? Write this out in words and symbols.

Answer in Words: Students who scored high on growth mindset would spend a different amount of time on their homework than the population of junior high students.

Answer in Symbols: $ \displaystyle \bar{X} \neq \mu $

See how a non-directional research hypothesis doesn't really make sense? The big issue is not if the two groups differ, but if one group seems to improve what was measured (if having a growth mindset leads to more time spent on math homework). This textbook will only use directional research hypotheses because researchers almost always have a predicted direction (meaning that we almost always know which group we think will score higher).

The Null Hypothesis

The hypothesis that an apparent effect is due to chance is called the null hypothesis, written $H_0$ (“H-naught”). We usually test this through comparing an experimental group to a comparison (control) group. This null hypothesis can be written as:

\[\mathrm{H}_{0}: \bar{X} = \mu \nonumber \]

For most of this textbook, the null hypothesis is that the means of the two groups are similar. Much later, the null hypothesis will be that there is no relationship between the two groups. Either way, remember that a null hypothesis is always saying that nothing is different.

This is where descriptive statistics diverge from inferential statistics. We know what the value of $\overline{\mathrm{X}}$ is – it’s not a mystery or a question, it is what we observed from the sample. What we are using inferential statistics to do is infer whether this sample's descriptive statistics probably represents the population's descriptive statistics. This is the null hypothesis, that the two groups are similar.

Keep in mind that the null hypothesis is typically the opposite of the research hypothesis. A research hypothesis for the ESP example is that those in my sample who say that they have ESP would get more correct answers than the population would get correct, while the null hypothesis is that the average number correct for the two groups will be similar.

In general, the null hypothesis is the idea that nothing is going on: there is no effect of our treatment, no relation between our variables, and no difference in our sample mean from what we expected about the population mean. This is always our baseline starting assumption, and it is what we seek to reject. If we are trying to treat depression, we want to find a difference in average symptoms between our treatment and control groups. If we are trying to predict job performance, we want to find a relation between conscientiousness and evaluation scores. However, until we have evidence against it, we must use the null hypothesis as our starting point.

In sum, the null hypothesis is always : There is no difference between the groups’ means OR There is no relationship between the variables .

In the next chapter, the null hypothesis is that there’s no difference between the sample mean and population mean. In other words:

There is no mean difference between the sample and population.
The mean of the sample is the same as the mean of a specific population.
$\mathrm{H}_{0}: \bar{X} = \mu \nonumber $
We expect our sample’s mean to be same as the population mean.

Exercise $\PageIndex{2}$

A study by Blackwell, Trzesniewski, and Dweck (2007) measured growth mindset and how long the junior high student participants spent on their math homework. What’s the null hypothesis for scoring higher on growth mindset (compared to the population of junior high students) and how long students spent on their homework? Write this out in words and symbols.

Answer in Words: Students who scored high on growth mindset would spend a similar amount of time on their homework as the population of junior high students.

Answer in Symbols: $ \bar{X} = \mu $

Contributors and Attributions

Foster et al. (University of Missouri-St. Louis, Rice University, & University of Houston, Downtown Campus)

Dr. MO ( Taft College )

An official website of the United States government

The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Publications
Account settings

Preview improvements coming to the PMC website in October 2024. Learn More or Try it out now .

Advanced Search
Journal List

Why we habitually engage in null-hypothesis significance testing: A qualitative study

Jonah stunt.

1 Department of Health Sciences, Section of Methodology and Applied Statistics, Vrije Universiteit, Amsterdam, The Netherlands

2 Department of Radiation Oncology, Erasmus Medical Center, Rotterdam, The Netherlands

Leonie van Grootel

3 Rathenau Institute, The Hague, The Netherlands

4 Department of Philosophy, Vrije Universiteit, Amsterdam, The Netherlands

5 Department of Epidemiology and Data Science, Amsterdam University Medical Centers, Amsterdam, The Netherlands

David Trafimow

6 Psychology Department, New Mexico State University, Las Cruces, New Mexico, United States of America

Trynke Hoekstra

Michiel de boer.

7 Department of General Practice and Elderly Care, University Medical Center Groningen, Groningen, The Netherlands

Associated Data

A full study protocol, including a detailed data analysis plan, was preregistered ( https://osf.io/4qg38/ ). At the start of this study, preregistration forms for qualitative studies were not developed yet. Therefore, preregistration for this study is based on an outdated form. Presently, there is a preregistration form available for qualitative studies. Information about data collection, data management, data sharing and data storage is described in a Data Management Plan. Sensitive data is stored in Darkstor, an offline archive for storing sensitive information or data (information that involves i.e., privacy or copyright). As the recordings and transcripts of the interviews and focus groups contain privacy-sensitive data, these files are archived in Darkstor and can be accessed only on request by authorized individuals (i.e., the original researcher or a research coordinator)1. Non-sensitive data is stored in DANS ( https://doi.org/10.17026/dans-2at-nzfs ) (Data Archiving and Networked Services; the Netherlands institute for permanent access to digital research resources). 1. Data requests can be send to ln.uv@mdr .

Null Hypothesis Significance Testing (NHST) is the most familiar statistical procedure for making inferences about population effects. Important problems associated with this method have been addressed and various alternatives that overcome these problems have been developed. Despite its many well-documented drawbacks, NHST remains the prevailing method for drawing conclusions from data. Reasons for this have been insufficiently investigated. Therefore, the aim of our study was to explore the perceived barriers and facilitators related to the use of NHST and alternative statistical procedures among relevant stakeholders in the scientific system.

Individual semi-structured interviews and focus groups were conducted with junior and senior researchers, lecturers in statistics, editors of scientific journals and program leaders of funding agencies. During the focus groups, important themes that emerged from the interviews were discussed. Data analysis was performed using the constant comparison method, allowing emerging (sub)themes to be fully explored. A theory substantiating the prevailing use of NHST was developed based on the main themes and subthemes we identified.

Twenty-nine interviews and six focus groups were conducted. Several interrelated facilitators and barriers associated with the use of NHST and alternative statistical procedures were identified. These factors were subsumed under three main themes: the scientific climate, scientific duty, and reactivity. As a result of the factors, most participants feel dependent in their actions upon others, have become reactive, and await action and initiatives from others. This may explain why NHST is still the standard and ubiquitously used by almost everyone involved.

Our findings demonstrate how perceived barriers to shift away from NHST set a high threshold for actual behavioral change and create a circle of interdependency between stakeholders. By taking small steps it should be possible to decrease the scientific community’s strong dependence on NHST and p-values.

Introduction

Empirical studies often start from the idea that there might be an association between a specific factor and a certain outcome within a population. This idea is referred to as the alternative hypothesis (H1). Its complement, the null hypothesis (H0), typically assumes no association or effect (although it is possible to test other effect sizes than no effect with the null hypothesis). At the stage of data-analysis, the probability of obtaining the observed, or a more extreme, association is calculated under the assumption of no effect in the population (H0) and a number of inferential assumptions [ 1 ]. The probability of obtaining the observed, or more extreme, data is known as ‘the p-value’. The p-value demonstrates the compatibility between the observed data and the expected data under the null hypothesis, where 0 is complete incompatibility and 1 is perfect compatibility [ 2 ]. When the p-value is smaller than a prespecified value (labelled as alpha, usually set at 5% (0.05)), results are generally declared to be statistically significant. At this point, researchers commonly reject the null hypothesis and accept the alternative hypothesis [ 2 ]. Assessing statistical significance by means of contrasting the data with the null hypothesis is called Null Hypothesis Significance Testing (NHST). NHST is the best known and most widely used statistical procedure for making inferences about population effects. The procedure has become the prevailing paradigm in empirical science [ 3 ], and reaching and being able to report statistically significant results has become the ultimate goal for many researchers.

Despite its widespread use, NHST and the p-value have been criticized since its inception. Numerous publications have addressed problems associated with NHST and p-values. Arguably the most important drawback is the fact that NHST is a form of indirect or inverse inference: researchers usually want to know if the null or alternative hypothesis can be accepted and use NHST to conclude either way. But with NHST, the probability of a finding, or more extreme findings, given the null hypothesis is calculated [ 4 ]. Ergo, NHST doesn’t tell us what we want to know. In fact, p-values were never meant to serve as a basis to draw conclusions, but as a continuous measure of incompatibility between empirical findings and a statistical model [ 2 ]. Moreover, the procedure promotes a dichotomous way of thinking, by using the outcome of a significance test as a dichotomous indicator for an effect (p<0.05: effect, p>0.05: no effect). Reducing empirical findings to two categories also results in a great loss of information. Further, a significant outcome is often unjustly interpreted as relevant, but a p-value does not convey any information about the strength or importance of the association. Worse yet, the p-values on which NHST is based confound effect size and sample size. A trivial effect size may nevertheless result in statistical significance provided a sufficiently large sample size. Or an important effect size may fail to result in statistical significance if the sample size is too small. P-values do not validly index the size, relevance, or precision of an effect [ 5 ]. Furthermore, statistical models include not only null hypotheses, but additional assumptions, some of which are wrong, such as the ubiquitous assumption of random and independent sampling from a defined population [ 1 ]. Therefore, although p-values validly index the incompatibility of data with models, p-values do not validly index incompatibility of data with hypotheses that are embedded in wrong models. These are important drawbacks rendering NHST unsuitable as the default procedure for drawing conclusions from empirical data [ 2 , 3 , 5 – 13 ].

A number of alternatives have been developed that overcome these pitfalls, such as Bayesian inference methods [ 7 , 11 , 14 , 15 ], informative hypothesis testing [ 9 , 16 ] and a priori inferential statistics [ 4 , 17 ]. These alternatives build on the idea that research usually starts with a more informed research-question than one merely assuming the null hypothesis of no effect. These methods overcome the problem of inverse inference, although the first two might still lead to dichotomous thinking with the use of thresholds. Despite the availability of alternatives, statistical behavior in the research community has hardly changed. Researchers have been slow to adopt alternative methods and NHST is still the prevailing paradigm for making inferences about population effects [ 3 ].

Until now, reasons for the continuous and ubiquitous use of NHST and the p-value have scarcely been investigated. One explanation is that NHST provides a very simple means for drawing conclusions from empirical data, usually based on the 5% cut-off. Secondly, most researchers are unaware of the pitfalls of NHST; it has been shown that NHST and the p-value are often misunderstood and misinterpreted [ 2 , 3 , 8 , 11 , 18 , 19 ]. Thirdly, NHST has a central role in most methods and statistics courses in higher education. Courses on alternative methods are increasingly being offered but are usually not mandatory. To our knowledge, there is a lack of in depth, empirical research, aimed at elucidating why NHST nevertheless remains the dominant approach, or what actions can be taken to shift the sciences away from NHST. Therefore, the aim of our study was to explore the perceived barriers and facilitators, as well as behavioral intentions related to the use of NHST and alternatives statistical procedures, among all relevant stakeholders in the scientific system.

Theoretical framework

In designing our study, we used two theories. Firstly, we used the ‘diffusion of innovation theory’ of Rogers [ 20 ]. This theory describes the dissemination of an innovation as a process consisting of four elements: 1) an innovation is 2) communicated through certain channels 3) over time 4) among the members of a social system [ 20 ]. In the current study, the innovation consists of the idea that we should stop with the default use of NHST and instead consider using alternative methods for drawing conclusions from empirical data. The science system forms the social structure in which the innovation should take place. The most important members, and potential adopters of the innovation, we identified are researchers, lecturers, editors of scientific journals and representatives of funding agencies. Rogers describes phases in the adoption process, which coincide with characteristics of the (potential) adopters of the idea: 1) innovators, 2) early adopters, 3) early majority adopters, 4) late majority adopters and 5) laggards. Innovators are the first to adopt an innovation. There are few innovators but these few are very important for bringing in new ideas. Early adopters form the second group to adopt an innovation. This group includes opinion leaders and role models for other stakeholders. The largest group consists of the early and late majority who follow the early adopters, and then there is a smaller group of laggards who resist the innovation until they are certain the innovation will not fail. The process of innovation adoption by individuals is described as a normal distribution ( Fig 1 ). For these five groups, the adoption of a new idea is influenced by the following five characteristics of the innovative idea and 1) its relative advantage, 2) its compatibility with current experiences, 3) its complexity, 4) its flexibility, and 5) its visibility [ 20 ]. Members of all four stakeholder groups could play an important role in the diffusion of the innovation of replacing NHST by its alternatives.

An external file that holds a picture, illustration, etc.
Object name is pone.0258330.g001.jpg

The innovativeness dimension, measured by the time at which an individual from an adopter category adopts an innovation. Each category is one of more standard deviations removed from the average time of adoption [ 20 ].

Another important theory for our study is the ‘theory of planned behavior’, that was developed in the 1960s [ 21 ]. This theory describes how human behavior in a certain context can be predicted and explained. The theory was updated in 2010, under the name ‘the reasoned action approach’ [ 22 ]. A central factor in this theory is the intention to perform a certain behavior, in this case, to change the default use of NHST. According to the theory, people’s intentions determine their behaviors. An intention indexes to what extent someone is motivated to perform the behavior. Intentions are determined by three independent determinants: the person’s attitudes toward the behavior—the degree to which a person sees the behavior as favorable or unfavorable, perceived subjective norms regarding the behavior—the perceived social pressure to perform the behavior or not, and perceptions of control regarding the behavior—the perceived ease or difficulty of performing the behavior. Underlying (i.e. responsible for) these three constructs are corresponding behavioral, normative, and control beliefs [ 21 , 22 ] (see Fig 2 ).

An external file that holds a picture, illustration, etc.
Object name is pone.0258330.g002.jpg

Both theories have served as a lens for both data collection and analysis. We used sensitizing concepts [ 23 ] within the framework of the grounded theory approach [ 24 ] from both theories as a starting point for this qualitative study, and more specifically, for the topic list for the interviews and focus groups, providing direction and guidance for the data collection and data analysis.

Many of the concepts of Rogers’ and Fishbein and Ajzen’s theory can be seen as facilitators and barriers for embracing and implementing innovation in the scientific system.

A qualitative study among stakeholders using semi-structured interviews and focus groups was performed. Data collection and analysis were guided by the principle of constant comparison traditional to the grounded theory approach we followed [ 24 ]. The grounded theory is a methodology that uses inductive reasoning, and aims to construct a theory through the collection and analysis of data. Constant comparison is the iterative process whereby each part of the data that emerges from the data analysis is compared with other parts of the data to thoroughly explore and validate the data. Concepts that have been extracted from the data are tagged with codes that are grouped into categories. These categories constitute themes, which (may) become the basis for a new theory. Data collection and analysis were continued until no new information was gained and data saturation had likely occurred within the identified themes.

The target population consisted of stakeholders relevant to our topic: junior and senior researchers, lecturers in statistics, editors of scientific journals and program leaders of funding agencies (see Tables Tables1 1 and and2). 2 ). We approached participants in the field of medical sciences, health- and life sciences and psychology. In line with the grounded theory approach, theoretical sampling was used to identify and recruit eligible participants. Theoretical sampling is a form of purposive sampling. This means that we aimed to purposefully select participants, based on their characteristics that fit the parameters of the research questions [ 25 ]. Recruitment took place by approaching persons in our professional networks and or the networks of the approached persons.

*The numbers between brackets represents the number of participants that were also interviewed.

Data collection

We conducted individual semi-structured interviews followed by focus groups. The aim of the interviews was to gain insight into the views of participants on the use of NHST and alternative methods and to examine potential barriers and facilitators related to these methods. The aim of the focus groups was to validate and further explore interview findings and to develop a comprehensive understanding of participants’ views and beliefs.

For the semi-structured interviews, we used a topic list (see Appendix 1 in S1 Appendix ). Questions addressed participants’ knowledge and beliefs about the concept of NHST, their familiarity with NHST, perceived attractiveness and drawbacks of the use of NHST, knowledge of the current NHST debate, knowledge of and views on alternative procedures and their views on the future of NHST. The topic list was slightly adjusted based on the interviews with editors and representatives from funding agencies (compared to the topic list for interviews with researchers and lecturers). Questions particularly focused on research and education were replaced by questions focused on policy (see Appendix 1 in S1 Appendix ).

The interviews were conducted between October 2017 and June 2018 by two researchers (L.v.G. and J.S.), both trained in qualitative research methods. Interviews lasted about one hour (range 31–86 minutes) and were voice-recorded. One interview was conducted by telephone; all others were face to face and took place at a location convenient for the participants, in most cases the participants’ work location.

Focus groups

During the focus groups, important themes that emerged from the interviews were discussed and explored. These include perceptions on NHST and alternatives and essential conditions to shift away from the default use of NHST.

Five focus groups included representatives from the different stakeholder groups. One focus group was homogenous, including solely lecturers. The focus groups consisted of ‘old’ as well as ‘new’ participants, that is, some of the participants of the focus groups were also in the interview sample. We also selected persons that were open for further contribution to the NHST debate and were willing to help think about (implementing) alternatives for NHST.

The focus groups were conducted between September and December 2018 by three researchers (L.v.G., J.S. and A.d.K.), all trained in qualitative research methods. The focus groups lasted about one-and-a-half hours (range 86–100 minutes).

Data analysis

All interviews and focus groups were transcribed verbatim. Atlas.ti 8.0 software was used for data management and analysis. All transcripts were read thoroughly several times to identify meaningful and relevant text fragments and analyzed by two researchers (J.S. and L.v.G.). Deductive predefined themes and theoretical concepts were used to guide the development of the topic list for the semi-structured interviews and focus groups, and were used as sensitizing concepts [ 23 ] in data collection and data analysis. Inductive themes were identified during the interview process and analysis of the data [ 26 ].

Transcripts were open-, axial- and selectively coded by two researchers (J.S. and L.v.G.). Open coding is the first step in the data-analysis, whereby phenomena found in the text are identified and named (coded). With axial coding, connections between codes are drawn. Selective coding is the process of selecting one central category and relating all other categories to that category, capturing the essence of the research. The constant comparison method [ 27 ] was applied allowing emerging (sub)themes to be fully explored. First, the two researchers independently developed a set of initial codes. Subsequently, findings were discussed until consensus was reached. Codes were then grouped into categories that were covered under subthemes, belonging to main themes. Finally, a theory substantiating the prevailing use of NHST was developed based on the main themes and subthemes.

Ethical issues

This research was conducted in accordance with the Dutch "General Data Protection Regulation" and the “Netherland’s code of conduct for research integrity”. The research protocol had been submitted for review and approved by the ethical review committee of the VU Faculty of Behavioral and Movement Sciences. In addition, the project had been submitted to the Medical Ethics Committee (METC) of the Amsterdam University Medical Centre who decided that the project is not subject to the Medical Research (Human Subjects) Act ( WMO). At the start of data collection, all participants signed an informed consent form.

A full study protocol, including a detailed data analysis plan, was preregistered ( https://osf.io/4qg38/ ). At the start of this study, preregistration forms for qualitative studies were not developed yet. Therefore, preregistration for this study is based on an outdated form. Presently, there is a preregistration form available for qualitative studies [ 28 ]. Information about data collection, data management, data sharing and data storage is described in a Data Management Plan. Sensitive data is stored in Darkstor, an offline archive for storing sensitive information or data (information that involves i.e., privacy or copyright). As the recordings and transcripts of the interviews and focus groups contain privacy-sensitive data, these files are archived in Darkstor and can be accessed only on request by authorized individuals (i.e., the original researcher or a research coordinator) (Data requests can be send to ln.uv@mdr ). Non-sensitive data is stored in DANS ( https://doi.org/10.17026/dans-2at-nzfs ) (Data Archiving and Networked Services; the Netherlands institute for permanent access to digital research resources).

Participant characteristics

Twenty-nine individual interviews and six focus groups were conducted. The focus groups included four to six participants per session. A total of 47 participants were included in the study (13 researchers, 15 lecturers, 11 editors of scientific journals and 8 representatives of funding agencies). Twenty-nine participants were interviewed. Twenty-seven participants took part in the focus group. Nine of the twenty-seven participants were both interviewed and took part in the focus groups. Some participants had multiple roles (i.e., editor and researcher, editor and lecturer or lecturer and researcher) but were classified based on their primary role (assistant professors were classified as lecturers). The lecturers in statistics in our sample were not statisticians themselves. Although they all received training in statistics, they were primarily trained as psychologists, medical doctors, or health scientists. Some lecturers in our sample taught an applied subject, with statistics as part of it. Other lectures taught Methodology and Statistics courses. Statistical skills and knowledge among lecturers varied from modest to quite advanced. Statistical skills and knowledge among participants from the other stakeholder groups varied from poor to quite advanced. All participants were working in the Netherlands. A general overview of the participants is presented in Table 1 . Participant characteristics split up by interviews and focus groups are presented in Table 2 .

Three main themes with sub-themes and categories emerged ( Fig 3 ): the green-colored compartments hold the three main themes: The scientific climate , The scientific duty and Reactivity . Each of these three main themes consists of subthemes, depicted by the yellow-colored compartments. In turn, some (but not all) of the 9 subthemes also have categories. These ‘lower level’ findings are not included in the figure but will be mentioned in the elaboration on the findings and are depicted in Appendix 2 in S1 Appendix . Fig 3 shows how the themes are related to each other. The blue arrows indicate that the themes are interrelated; factors influence each other. The scientific climate affects the way stakeholders perceive and fulfil their scientific duty, the way stakeholders give substance to their scientific duty shapes and maintain the scientific climate. The scientific duty and the scientific climate cause a state of reactivity. Many participants have adopted a ’wait and see’ attitude regarding behavioral changes with respect to statistical methods. They feel dependent on someone else’s action. This leads to a reactive (instead of a proactive) attitude and a low sense of responsibility. ‘Reactivity’ is the core theme, explaining the most critical problem with respect to the continuous and ubiquitous use of NHST.

An external file that holds a picture, illustration, etc.
Object name is pone.0258330.g003.jpg

Main themes and subthemes are numbered. Categories are mentioned in the body of the text in bold. ‘P’ stands for participant; ‘I’ stands for interviewer.

1. The scientific climate

The theme, ‘the scientific climate’, represents researchers’ (Dutch) perceptions of the many written and unwritten rules they face in the research environment. This theme concerns the opportunities and challenges participants encounter when working in the science system. Dutch academics feel pressured to publish fast and regularly, and to follow conventions and directions of those on whom they depend. They feel this comes at the expense of the quality of their work. Thus, the scientific climate in the Netherlands has a strong influence on the behavior of participants regarding how they set their priorities and control the quality of their work.

1 . 1 Quality control . Monitoring the quality of research is considered very important. Researchers, funding agencies and editors indicate they rely on their own knowledge, expertise, and insight, and those of their colleagues, to guarantee this quality. However, editors or funding agencies are often left with little choice when it comes to compiling an evaluation committee or a review panel. The choice is often like-knows-like-based. Given the limited choice, they are forced to trust the opinion of their consultants, but the question is whether this is justified.

I: “The ones who evaluate the statistics, do they have sufficient statistical knowledge?” P: “Ehhr, no, I don’t think so.” I: “Okay, interesting. So, there are manuscripts published of which you afterwards might think….” P: “Yes yes.” (Interview 18; Professor/editor, Medical Sciences)

1 . 2 Convention . The scientific system is built on mores and conventions, as this participant describes:

P: “There is science, and there is the sociology of science, that is, how we talk to each other, what we believe, how we connect. And at some point, it was agreed upon that we would talk to each other in this way.” (Interview 28, researcher, Medical Sciences)

And to these conventions, one (naturally) conforms. Stakeholders copy behavior and actions of others within their discipline, thereby causing particular behaviors and values to become conventional or normative. One of those conventions is the use of NHST and p-values. Everyone is trained with NHST and is used to applying this method. Another convention is the fact that significant results mean ‘success’, in the sense of successful research and being a successful researcher. Everyone is aware that ‘p is smaller than 0.05’ means the desired results are achieved and that publication and citation chances are increased.

P: “You want to find a significant result so badly. (…) Because people constantly think: I must find a significant result, otherwise my study is worthless.” (Focus group 4, lecturer, Medical Sciences)

Stakeholders rigidly hold on to the above-mentioned conventions and are not inclined to deviate from existing norms; they are, in other words, quite conservative . ‘We don’t know any better’ has been brought up as a valid argument by participants from various stakeholder groups to stick to current rules and conventions. Consequently, the status quo in the scientific system is being maintained.

P: “People hold on to….” I: ‘Everyone maintains the system?’ P: ‘Yes, we kind of hang to the conservative manner. This is what we know, what someone, everyone, accepts.” (Interview 17, researcher, Health Sciences)

Everyone is trained with NHST and considers it an accessible and easy to interpret method. The familiarity and perceived simplicity of NHST, user-friendly software such as SPSS and the clear cut-off value for significance are important facilitators for the use of NHST and at the same time barriers to start using alternative methods. Applied researchers stressed the importance of the accessibility of NHST as a method to test hypotheses and draw conclusions. This accessibility also justifies the use of NHST when researchers want to communicate their study results and messages in understandable ways to their readership.

P: “It is harder, also to explain, to use an alternative. So, I think, but maybe I’m overstepping, but if you want to go in that direction [alternative methods] it needs to be better facilitated for researchers. Because at the moment… I did some research, but, you know, there are those uncommon statistical packages.” (Interview 16, researcher/editor, Medical Sciences)

1 . 3 Publication pressure . Most researchers mentioned that they perceive publication pressure. This motivates them to use NHST and hope for significant results, as ‘significant p-values’ increase publication chances. They perceive a high workload and the way the scientific reward system is constructed as barriers for behavioral change pertaining to the use of statistical methods; potential negative consequences for publication and career chances prevent researchers from deviating from (un)written rules.

P: “I would like to learn it [alternative methods], but it might very well be that I will not be able to apply it, because I will not get my paper published. I find that quite tricky.” (Interview 1, Assistant Professor, Health Sciences)

2. The scientific duty

Throughout the interviews, participants reported a sense of duty in several variations. “What does it mean to be a scientific researcher?” seemed to be a question that was reflected upon during rather than prior to the interview, suggesting that many scientists had not really thought about the moral and professional obligations of being a scientist in general—let alone what that would mean for their use of NHST. Once they had given it some thought, the opinions concerning what constitutes the scientific duty varied to a large extent. Some participants attached great importance to issues such as reproducibility and transparency in scientific research and continuing education and training for researchers. For others, these topics seemed to play a less important role. A distinction was made between moral and professional obligations that participants described concerning their scientific duty.

2 . 1 Moral obligation . The moral obligation concerns issues such as doing research in a thorough and honest way, refraining from questionable research practices (QRPs) and investing in better research. It concerns tasks and activities that are not often rewarded or acknowledged.

Throughout the interviews and the focus groups, participants very frequently touched upon the responsibility they felt for doing ‘the right thing’ and making the right choice in doing research and using NHST, in particular. The extent to which they felt responsible varied among participants. When it comes to choices during doing research—for example, drawing conclusions from data—participants felt a strong sense of responsibility to do this correctly. However, when it comes to innovation and new practices, and feeling responsible for your own research, let alone improving scientific practice in general, opinions differed. This quotation from one of the focus groups illustrates that:

P1: “If you people [statisticians, methodologists] want me to improve the statistics I use in my research, then you have to hand it to me. I am not going to make any effort to improve that myself. “P3: “No. It is your responsibility as an academic to keep growing and learning and so, also to start familiarizing yourself when you notice that your statistics might need improvement.” (Focus group 2, participant 1 (PhD researcher, Medical Sciences) and 3 (Associate Professor, Health Sciences)

The sense of responsibility for improving research practices regarding the use of NHST was strongly felt and emphasized by a small group of participants. They emphasized the responsibility of the researcher to think, interpret and be critical when interpreting the p -value in NHST. It was felt that you cannot leave that up to the reader. Moreover, scrutinizing and reflecting upon research results was considered a primary responsibility of a scientist, and failing to do so, as not living up to what your job demands you to do:

P: “Yes, and if I want to be very provocative—and I often want that, because then people tend to wake up and react: then I say that hiding behind alpha.05 is just scientific laziness. Actually, it is worse: it is scientific cowardice. I would even say it is ‘relieving yourself from your duty’, but that may sound a bit harsh…” (Interview 2, Professor, Health Sciences)

These participants were convinced that scientists have a duty to keep scientific practice in general at the highest level possible.

The avoidance of questionable research practices (QRPs) was considered a means or a way to keep scientific practices high level and was often touched upon during the interviews and focus groups as being part of the scientific duty. Statisticians saw NHST as directly facilitating QRPs and providing ample examples of how the use of NHST leads to QRPs, whereas most applied researchers perceived NHST as the common way of doing research and were not aware of the risks related to QRPs. Participants did mention the violation of assumptions underlying NHST as being a QRP. Then, too, participants considered overinterpreting results as a QRP, including exaggerating the degree of significance. Although participants stated they were careful about interpreting and reporting p-values, they ‘admitted’ that statistical significance was a starting point for them. Most researchers indicated they search for information that could get their study published, which usually includes a low p-value (this also relates to the theme ‘Scientific climate’).

P: “We all know that a lot of weight is given to the p-value. So, if it is not significant, then that’s the end of it. If it ís significant, it just begins.” (Interview 5, lecturer, Psychology)

The term ‘sloppy science’ was mentioned in relation to efforts by researchers to reduce the p -value (a.k.a. p-hacking, data-dredging, and HARKing. HARKing is an acronym that refers to the questionable research question of Hypothesizing After the Results are Known. It occurs when researchers formulate a hypothesis after the data have been collected and analyzed, but make it look like it is an a priori hypothesis [ 29 ]). Preregistration and replication were mentioned as being promising solutions for some of the problems caused by NHST.

2 . 2 . Professional obligation . The theme professional obligation reflects participants’ expressions about what methodological knowledge scientists should have about NHST. In contrast moral obligations, there appeared to be some consensus about scientists’ professional obligations. Participants considered critical evaluation of research results a core professional obligation. Also, within all the stakeholder groups, participants agreed that sufficient statistical knowledge is required for using NHST, but they varied in their insights in the principles, potential and limitations of NHST. This also applied to the extent to which participants were aware of the current debate about NHST.

Participants considered critical thinking as a requirement for fulfilling their professional obligation. It specifically refers to the process of interpreting outcomes and taking all relevant contextual information into consideration. Critical thinking was not only literally referred to by participants, but also emerged by interpreting text fragments on the emphasis within their research. Researchers differed quite strongly in where the emphasis of their research outcomes should be put and what kind of information is required when reporting study results. Participants mentioned the proven effectiveness of a particular treatment, giving a summary of the research results, effect sizes, clinical relevance, p-values, or whether you have made a considerable contribution to science or society.

P: “I come back to the point where I said that people find it arbitrary to state that two points difference on a particular scale is relevant. They prefer to hide behind an alpha of 0.05, as if it is a God given truth, that it counts for one and for all. But it is just as well an invented concept and an invented guideline, an invented cut-off value, that isn’t more objective than other methods?” (Interview 2, Professor, Health Sciences)

For some participants, especially those representing funding agencies, critical thinking was primarily seen as a prerequisite for the utility of the research. The focus, when formulating the research question and interpreting the results, should be on practical relevance and the contribution the research makes to society.

The term ‘ignorance’ arose in the context of the participants’ concern regarding the level of statistical knowledge scientists and other stakeholders have versus what knowledge they should have to adequately apply statistical analysis in their research. The more statistically competent respondents in the sample felt quite strongly about how problematic the lack of knowledge about NHST is among those who regularly use it in their research, let alone the lack of knowledge about alternative methods. They felt that regularly retraining yourself in research methods is an essential part of the professional obligation one has. Applied researchers in the sample agreed that a certain level of background knowledge on NHST was required to apply it properly to research and acknowledged their own ignorance. However, they had different opinions about what level of knowledge is required. Moreover, not all of them regarded it as part of their scientific duty to be informed about all ins and outs of NHST. Some saw it as the responsibility of statisticians to actively inform them (see also the subtheme periphery). Some participants were not aware of their ignorance or stated that some of their colleagues are not aware of their ignorance, i.e., that they are unconsciously incompetent and without realizing it, poorly understood what the p-value and associated outcome measures actually mean.

P: “The worst, and I honestly think that this is the most common, is unconsciously incompetent, people don’t even understand that…” I: “Ignorance.” P: “Yes, but worse, ignorant and not even knowing you are ignorant.” (Interview 2, Professor, Health Sciences)

The lack of proper knowledge about statistical procedures was especially prevalent in the medical sciences. Participants working in or with the medical sciences all confirmed that there is little room for proper statistical training for medical students and that the level of knowledge is fairly low. NHST is often used because of its simplicity. It is especially attractive for medical PhD students because they need their PhD to get ahead in their medical career instead of pursuing a scientific career.

P: “I am not familiar with other ways of doing research. I would really like to learn, but I do not know where I could go. And I do not know whether there are better ways. So sometimes I do read studies of which I think: ‘this is something I could investigate with a completely different test. Apparently, this is also possible, but I don’t know how.’ Yes, there are courses, but I do not know what they are. And here in the medical center, a lot of research is done by medical doctors and these people have hardly been taught any statistics. Maybe they will get one or two statistics courses, they know how to do a t-test and that is about it. (…) And the courses have a very low level of statistics, so to say.” (Interview 1, Assistant Professor, Health Sciences)

Also, the term ‘ awareness ’ arose. Firstly, it refers to being conscious about the limitations of NHST. Secondly, it refers to the awareness of the ongoing discussions about NHST and more broadly, about the replication crisis. The statisticians in the sample emphasized the importance of knowing that NHST has limitations and that it cannot be considered the holy grail of data analysis. They also emphasized the importance of being aware of the debate. A certain level of awareness was considered a necessary requirement for critical thinking. There was variation in that awareness. Some participants were quite informed and were also fairly engaged in the discussion whereas others were very new to the discussion and larger contextual factors, such as the replication crisis.

I: “Are you aware of the debate going on in academia on this topic [NHST]? P: “No, I occasionally see some article sent by a colleague passing by. I have the idea that something is going on, but I do not know how the debate is conducted and how advanced it is. (Interview 6, lecturer, Psychology)

With respect to the theme, ‘the scientific duty’, participants differed to what extent they felt responsible for better and open science, for pioneering, for reviewing, and for growing and learning as a scientist. Participants had one commonality: although they strived for adherence to the norms of good research, the rampant feeling is that this is very difficult, due to the scientific climate. Consequently, participants perceive an internal conflict : a discrepancy between what they want or believe , and what they do . Participants often found themselves struggling with the responsibility they felt they had. Making the scientifically most solid choice was often difficult due to feasibility, time constraints, or certain expectations from supervisors (this is also directly related to the themes ‘Scientific climate’ and ‘Reactivity’). Thus, the scientific climate strongly influences the behavior of scientists regarding how they set their priorities and fulfill their scientific duties. The strong sense of scientific duty was perceived by some participants as a facilitator and by others as a barrier for the use of alternative methods.

3. Reactivity

A consequence of the foregoing factors is that most stakeholders have adopted a reactive attitude and behave accordingly. People are disinclined to take responsibility and await external signals and initiatives of others. This might explain why NHST is being continuously used and remains the default procedure to make inferences about population effects.

The core theme ‘reactivity’ can be explained by the following subthemes and categories:

3 . 1 Periphery . The NHST-problem resides in the periphery in several ways. First, it is a subject that is not given much priority. Secondly, some applied researchers and editors believe that methodological knowledge, as it is not their field of expertise, should not be part of their job requirement. This also applies to the NHST debate. Thirdly, and partly related to the second point, there is a lack of cooperation within and between disciplines.

The term ‘ priority’ was mentioned often when participants were asked to what extent the topic of NHST was subject of discussion in their working environment. Participants indicated that (too) little priority is given to statistics and the problems related to the subject. There is simply a lot going on in their research field and daily work, so there are always more important or urgent issues on the agenda.

P: “Discussions take place in the periphery; many people find it complicated. Or are just a little too busy.” (Interview 5, lecturer, Psychology)

As the NHST debate is not prioritized, initiatives with respect to this issue are not forthcoming. Moreover, researchers and lecturers claim there is neither time nor money available for training in statistics in general or acquiring more insight and skills with respect to (the use of) alternative methods. Busy working schedules were mentioned as an important barrier for improving statistical knowledge and skills.

P: “Well you can use your time once, so it is an issue low on the priority list.” (Focus group 5, researcher, Medical Sciences)

The NHST debate is perceived as the domain of statisticians and methodologists. Also, cooperation between different domains and domain-specific experts is perceived as complicated, as different perceptions and ways of thinking can clash. Therefore, some participants feel that separate worlds should be kept separate; put another way: stick to what you know!

P: “This part is not our job. The editorial staff, we have the assignment to ensure that it is properly written down. But the discussion about that [alternatives], that is outside our territory.” (Interview 26, editor, Medical Sciences)

Within disciplines, individuals tend to act on their own, not being aware that others are working on the same subject and that it would be worthwhile to join forces. The interviews and focus groups exposed that a modest number of participants actively try to change the current situation, but in doing that, feel like lone voices in the wilderness.

P1: “I mean, you become a lone voice in the wilderness.” P2: “Indeed, you don’t want that.” P1: “I get it, but no one listens. There is no audience.” (Focus Group 3, P1: MD, lecturer, medical Sciences, P2: editor, Medical Sciences)

To succeed at positive change, participants emphasized that it is essential that people (interdisciplinary) cooperate and join forces, rather than operate on individual levels, focusing solely on their own working environment.

The caution people show with respect to taking initiative is reenforced by the fear of encountering resistance from their working environment when one voices that change regarding the use of NHST is needed. A condition that was mentioned as essential to bring about change was tactical implementation , that is, taking very small steps. As everyone is still using NHST, taking big steps brings the risk of losing especially the more conservative people along the way. Also, the adjustment of policy, guidelines and educational programs are processes for which we need to provide time and scope.

P: “Everyone still uses it, so I think we have to be more critical, and I think we have to look at some kind of culture change, that means that we are going to let go of it (NHST) more and we will also use other tests, that in the long term will overthrow NHST. I: and what about alternatives? P: I think you should never be too fanatic in those discussion, because then you will provoke resistance. (…) That is not how it works in communication. You will touch them on a sore spot, and they will think: ‘and who are you?’ I: “and what works?” P: “well, gradualness. Tell them to use NHST, do not burn it to the ground, you do not want to touch peoples work, because it is close to their hearts. Instead, you say: ‘try to do another test next to NHST’. Be a pioneer yourself.” (Interview 5, lecturer, Psychology)

3 . 2 . Efficacy . Most participants stated they feel they are not in the position to initiate change. On the one hand, this feeling is related to their hierarchical positions within their working environments. On the other hand, the feeling is caused by the fact that statistics is perceived as a very complex field of expertise and people feel they lack sufficient knowledge and skills, especially about alternative methods.

Many participants stated they felt little sense of empowerment, or self-efficacy. The academic system is perceived as hierarchical, having an unequal balance of power. Most participants believe that it is not in their power to take a lead in innovative actions or to stand up against establishment, and think that this responsibility lies with other stakeholders, that have more status .

P: “Ideally, there would be a kind of an emergency letter from several people whose names open up doors, in which they indicate that in the medical sciences we are throwing away money because research is not being interpreted properly. Well, if these people that we listen to send such an emergency letter to the board of The Netherlands Organization for Health Research and Development [the largest Dutch funding agency for innovation and research in healthcare], I can imagine that this will initiate a discussion.” (…) I: “and with a big name you mean someone from within the science system? P: well, you know, ideally a chairman, or chairmen of the academic medical center. At that level. If they would put a letter together. Yes, that of course would have way more impact. Or some prominent medical doctors, yes, that would have more impact, than if some other person would send a letter yes.” (Interview 19, representative from funding agency, Physical Sciences)

Some participants indicated that they did try to make a difference but encountered too much resistance and therefore gave up their efforts. PhD students feel they have insufficient power to choose their own directions and make their own choices.

P: I am dependent on funding agencies and professors. In the end, I will write a grant application in that direction that gives me the greatest chance of eventually receiving that grant. Not primarily research that I think is the most optimal (…) If I know that reviewers believe the p-value is very important, well, of course I write down a method in which the p-value is central.” (Focus group 2, PhD-student, Medical Sciences)

With a sense of imperturbability, most participants accept that they cannot really change anything.

Lastly, the complexity of the subject is an obstacle for behavioral change. Statistics is perceived as a difficult subject. Participants indicate that they have a lack of knowledge and skills and that they are unsure about their own abilities. This applies to the ‘standard’ statistical methods (NHST), but to a greater extent to alternative methods. Many participants feel that they do not have the capacity to pursue a true understanding of (alternative) statistical methods.

P: “Statistics is just very hard. Time and again, research demonstrates that scientists, even the smartest, have a hard time with statistics.” (Focus group 3, PhD researcher, Psychology)

3 . 3 . Interdependency . As mentioned, participants feel they are not in a sufficiently strong position to take initiative or to behave in an anti-establishment manner. Therefore, they await external signals from people within the scientific system with more status, power, or knowledge. This can be people within their own stakeholder group, or from other stakeholder groups. As a consequence of this attitude, a situation arises in which peoples’ actions largely depend on others. That is, a complex state of interdependency evolves: scientists argue that if the reward system does not change, they are not able to alter their statistical behavior. According to researchers, editors and funding agencies are still very much focused on NHST and especially (significant) p-values, and thus, scientists wait for editors and funders to adjust their policy regarding statistics:

P: “I wrote an article and submitted it to an internal medicine journal. I only mentioned confidence intervals. Then I was asked to also write down the p-values. So, I had to do that. This is how they [editors] can use their power. They decide.” (Interview 1, Assistant Professor, Health Sciences)

Editors and funders in their turn claim they do not maintain a strict policy. Their main position is that scientists should reach consensus about the best statistical procedure, and they will then adjust their policy and guidelines.

P: “We actually believe that the research field itself should direct the quality of its research, and thus, also the discussions.” (Interview 22, representative from funding agency, Neurosciences)

Lecturers, for their part, argue that they cannot revise their educational programs due to the academic system, and university policies are adapted to NHST and p-values.

As most participants seem not to be aware of this process, a circle of interdependency arises that is difficult to break.

P: “Yes, the stupid thing about this perpetual circle is that you are educating people, let’s say in the department of cardiology. They must of course grow, and so they need to publish. If you want to publish you must meet the norms and values of the cardiology journals, so they will write down all those p-values. These people are trained and in twenty years they are on the editorial board of those journals, and then you never get rid of it [the p-value].” (Interview 18, Professor, editor, Medical Sciences)

3 . 4 . Degree of eagerness . Exerting certain behavior or behavioral change is (partly) determined by the extent to which people want to employ particular behavior, their behavioral intention [ 22 ]. Some participants indicated they are willing to change their behavior regarding the use of statistical methods, but only if it is absolutely necessary, imposed or if they think that the current conventions have too many negative consequences. Thus, true, intrinsic will-power to change behavior is lacking among these participants. Instead, they have a rather opportunistic attitude, meaning that their behavior is mostly driven by circumstances, not by principles.

P: “If tomorrow an alternative is offered by people that make that call, than I will move along. But I am not the one calling the shots on this issue.” (Interview 26, editor, Medical Sciences)

In addition, pragmatism often outweighs the perceived urgency to change. Participants argue they ‘just want to do their jobs’ and consider the practical consequences mainly in their actions. This attitude creates a certain degree of inertia. Although participants claim they are willing to change their behavior, this would contain much more than ‘doing their jobs, and thus, in the end, the NHST-debate is subject to ‘coffee talk’. People are open to discussion, but when it comes to taking action (and motivating others to do so), no one takes action.

P: “The endless analysis of your data to get something with a p-value less than 0.05… There are people that are more critical about that, and there are people that are less critical. But that is a subject for during the coffee break.” (Interview 18, professor, editor, Medical Sciences)

The goal of our study was to acquire in-depth insight into reasons why so many stakeholders from the scientific system keep using NHST as the default method to draw conclusions, despite its many well-documented drawbacks. Furthermore, we wanted to gain insight into the reasons for their reluctance to apply alternative methods. Using a theoretical framework [ 20 , 21 ], several interrelated facilitators and barriers associated with the use of NHST and alternative methods were identified. The identified factors are subsumed under three main themes: the scientific climate, the scientific duty and reactivity. The scientific climate is dominated by conventions, behavioral rules, and beliefs, of which the use of NHST and p-values is part. At the same time, stakeholders feel they have a (moral or professional) duty. For many participants, these two sides of the same coin are incompatible, leading to internal conflicts. There is a discrepancy between what participants want and what they do . As a result of these factors, the majority feels dependent on others and have thereby become reactive. Most participants are not inclined to take responsibility themselves but await action and initiatives from others. This may explain why NHST is still the standard and used by almost everyone involved.

The current study is closely related to the longstanding debate regarding NHST which recently increased to a level not seen before. In 2015, the editors of the journal ‘Basic and Applied Social Psychology’ (BASP) prohibited the use of NHST (and p-values and confidence intervals) [ 30 ]. Subsequently, in 2016, the American Statistical Association published the so-called ‘Statement on p-values’ in the American Statistician. This statement consists of critical standpoints regarding the use of NHST and p-values and warns against the abuse of the procedure. In 2019, the American Statistician devoted an entire edition to the implementation of reforms regarding the use of NHST; in more than forty articles, scientists debated statistical significance, advocated to embrace uncertainty, and suggested alternatives such as the use of s-values, False Positive Risks, reporting results as effect sizes and confidence intervals and more holistic approaches to p-values and outcome measures [ 31 ]. In addition, in the same year, several articles appeared in which an appeal was made to stop using statistical significance testing [ 32 , 33 ]. A number of counter-reactions were published [ 34 – 36 ], stating (i.e.) that banning statistical significance and, with that, abandoning clear rules for statistical analyses may create new problems with regard to statistical interpretation, study interpretations and objectivity. Also, some methodologists expressed the view that under certain circumstances the use of NHST and p-values is not problematic and can in fact provide useful answers [ 37 ]. Until recently, the NHST-debate was limited to mainly methodologists and statisticians. However, a growing number of scientists are getting involved in this lively debate and believe that a paradigm shift is desirable or even necessary.

The aforementioned publications have constructively contributed to this debate. In fact, since the publication of the special edition of the American Statistician, numerous scientific journals published editorials or revised, to a greater or lesser extent, their author guidelines [ 38 – 45 ]. Furthermore, following the American Statistical Association (ASA), the National Institute of Statistical Sciences (NISS) in the United States has also taken up the reform issue. However, real changes are still barely visible. It takes a long time before these kinds of initiatives translate into behavioral changes, and the widespread adoption by most of the scientific community is still far from accomplished. Debate alone will not lead to real changes, and therefore, our efforts to elucidate behavioral barriers and facilitators could provide a framework for potential effective initiatives that could be taken to reduce the default use of NHST. In fact, the debate could counteract behavioral change. If there is no consensus among statisticians and methodologists (the innovators), changing behavior cannot be expected from stakeholders with less statistical and methodological expertise. In other words, without agreement among innovators, early adopters might be reluctant to adopt the innovation.

Research has recently been conducted to explore the potential of behavioral change to improve Open Science behaviors. The adoption of open science behavior has increased in the last years, but uptake has been slow, due to firm barriers such as a lack of awareness about the subject, concerns about constrainment of the creative process, worries about being “scooped” and holding on to existing working practices [ 46 ]. The development regarding open science practices and the parallels these lines of research shows with the current study, might be of benefit to subserve behavioral change regarding the use of statistical methods.

The described obstacles to change behavior are related to features of both the ‘innovative idea’ and the potential adopters of the idea. First, there are characteristics of ‘the innovation’ that form barriers. The first barrier is the complexity of the innovation: most participants perceive alternative methods as difficult to understand and to use. A second barrier concerns the feasibility of trying the innovation; most people do not feel flexible about trying out or experimenting with the new idea. There is a lack of time and monetary resources to get acquainted with alternative methods (for example, by following a course). Also, the possible negative consequences of the use of alternatives (lower publications chances, the chance that the statistical method and message is too complicated for one’s readership) is holding people back from experimenting with these alternatives. And lastly, it is unclear for most participants what the visibility of the results of the new idea are. Up until now, the debate has mainly taken place among a small group of statisticians and methodologists. Many researchers are still not aware of the NHST debate and the idea to shift away from NHST and use alternative methods instead. Therefore, the question is how easily the benefits of the innovation can be made visible for a larger part of the scientific community. Thus, our study shows that, although the compatibility of the innovation is largely consistent with existing values (participants are critical about (the use of) NHST and the p-value and believe that there are better alternatives to NHST), important attributes of the innovative idea negatively affect the rate of adoption and consequently the diffusion of the innovation.

Due to the barriers mentioned above, most stakeholders do not have the intention to change their behavior and adopt the innovative idea. From the theory of planned behavior [ 21 ], it is known that behavioral intentions directly relate to performances of behaviors. The strength of the intention is shaped by attitudes, subjective norms, and perceived power. If people evaluate the suggested behavior as positive (attitude), and if they think others want them to perform the behavior (subjective norm), this leads to a stronger intention to perform that behavior. When an individual also perceives they have enough control over the behavior, they are likely to perform it. Although most participants have a positive attitude towards the behavior, or the innovative idea at stake, many participants think that others in their working environment believe that they should not perform the behavior—i.e., they do not approve of the use of alternative methods (social normative pressure). This is expressed, for example, in lower publication chances, negative judgements by supervisors or failing the requirements that are imposed by funding agencies. Thus, the perception about a particular behavior—the use of alternative methods—is negatively influenced by the (perceived) judgment of others. Moreover, we found that many participants have a low self-efficacy, meaning that there is a perceived lack of behavioral control, i.e., their perceived ability to engage in the behavior at issue is low. Also, participants feel a lack of authority (in the sense of knowledge and skills, but also power) to initiate behavioral change. The existing subjective norms and perceived behavioral control, and the negative attitudes towards performing the behavior, lead to a lower behavioral intention, and, ultimately, a lower chance of the performance of the actual behavior.

Several participants mentioned there is a need for people of stature (belonging to the group of early adopters) to take the lead and break down perceived barriers. Early adopters serve as role models and have opinion leadership, and form the next group (after the innovators, in this case statisticians and methodologists) to adopt an innovative idea [ 20 ] ( Fig 2 ). If early adopters would stand up, conveying a positive attitude towards the innovation, breaking down the described perceived barriers and facilitating the use of alternatives (for example by adjusting policy, guidelines and educational programs and making available financial resources for further training), this could positively affect the perceived social norms and self-efficacy of the early and late majority and ultimately laggards, which could ultimately lead to behavioral change among all stakeholders within the scientific community.

A strength of our study is that it is the first empirical study on views on the use of NHST, its alternatives and reasons for the prevailing use of NHST. Another strength is the method of coding which corresponds to the thematic approach from Braun & Clarke [ 47 ], which allows the researcher to move beyond just categorizing and coding the data, but also analyze how the codes are related to each other [ 47 ]. It provides a rich description of what is studied, linked to theory, but also generating new hypotheses. Moreover, two independent researchers coded all transcripts, which adds to the credibility of the study. All findings and the coding scheme were discussed by the two researchers, until consensus was reached. Also, interview results were further explored, enriched and validated by means of (mixed) focus groups. Important themes that emanated from the interviews, such as interdependency, perceptions on the scientific duty, perceived disadvantages of alternatives or the consequences of the current scientific climate, served as starting points and main subjects of the focus groups. This set-up provided more data, and more insight about the data and validation of the data. Lastly, the use of a theoretical framework [ 20 , 21 ] to develop the topic list, guide the interviews and focus groups, and guide their analysis is a strength as it provides structure to the analysis and substantiation of the results.

A limitation of this study is its sampling method. By using the network of members of the project group, and the fact that a relatively high proportion of those invited to participate refused because they thought they knew too little about the subject to be able to contribute, our sample was biased towards participants that are (somewhat) aware of the NHST debate. Our sample may also consist of people that are relatively critical towards the use of NHST, compared to the total population of researchers. It was not easy to include participants who were indifferent about or who were pro-NHST, as those were presumably less willing to make time and participate in this study. Even in our sample we found that the majority of our participants solely used NHST and perceived it as difficult if not impossible to change their behavior. These perceptions are thus probably even stronger in the target population. Another limitation, that is inherent to qualitative research, is the risk of interviewer bias. Respondents are unable, unwilling, or afraid to answer questions in good conscience, and instead provide socially desirable answers. In the context of our research, people are aware that, especially as a scientist, it does not look good to be conservative, complacent, or ignorant, or not to be open to innovation and new ideas. Therefore, some participants might have given a too favorable view of themselves. The interviewer bias can also take the other direction when values and expectations of the interviewer consciously or unconsciously influence the answers of the respondents. Although we have tried to be as neutral and objective as possible in asking questions and interpreting answers, we cannot rule out the chance that our views and opinions on the use of NHST have at times steered the respondents somewhat, potentially leading to the foregoing desirable answers.

Generalizability is a topic that is often debated in qualitative research methodology. Many researchers do not consider generalizability the purpose of qualitative research, but rather finding in-depth insights and explanations. However, this is an unjustified simplification, as generalizing of findings from qualitative research is possible. Three types of generalization in qualitative research are described: representational generalization (whether what is found in a sample can be generalized to the parent population of the sample), inferential generalization (whether findings from the study can be generalized to other settings), and theoretical generalization (where one draws theoretical statements from the findings of the study for more general application) [ 48 ]. The extent to which our results are generalizable is uncertain, as we used a theoretical sampling method, and our study was conducted exclusively in the Netherlands. We expect that the generic themes (reactivity, the scientific duty and the scientific climate) are applicable to academia in many countries across the world (inferential generalization). However, some elements, such as the Dutch educational system, will differ to a more or lesser extent from other countries (and thus can only be representationally generalized). In the Netherlands there is, for example, only one educational route after secondary school that has an academic orientation (scientific education, equivalent to the US university level education). This route consists of a bachelor’s program (typically 3 years), and a master’s program (typically 1, 2 or 3 years). Not every study program contains (compulsory) statistical courses, and statistical courses differ in depth and difficulty levels depending on the study program. Thus, not all the results will hold for other parts of the world, and further investigation is required.

Our findings demonstrate how perceived barriers to shift away from NHST set a high threshold for behavioral change and create a circle of interdependency. Behavioral change is a complex process. As ‘the stronger the intention to engage in a behavior, the more likely should be its performance’[ 21 ], further research on this subject should focus on how to influence the intention of behavior; i.e. which perceived barriers for the use of alternatives are most promising to break down in order to increase the intention for behavioral change. The present study shows that negative normative beliefs and a lack of perceived behavioral control regarding the innovation among individuals in the scientific system is a substantial problem. When social norms change in favor of the innovation, and control over the behavior increases, then the behavioral intention becomes a sufficient predictor of behavior [ 49 ]. An important follow-up question will therefore be: how can people be enthused and empowered, to ultimately take up the use of alternative methods instead of NHST? Answering this question can, in the long run, lead to the diffusion of the innovation through the scientific system as a whole.

NHST has been the leading paradigm for many decades and is deeply rooted in our science system, despite longstanding criticism. The aim of this study was to gain insight as to why we continue to use NHST. Our findings have demonstrated how perceived barriers to make a shift away from NHST set a high threshold for actual behavioral change and create a circle of interdependency between stakeholders in the scientific system. Consequently, people find themselves in a state of reactivity, which limits behavioral change with respect to the use of NHST. The next step would be to get more insight into ways to effectively remove barriers and thereby increase the intention to take a step back from NHST. A paradigm shift within a couple of years is not realistic. However, we believe that by taking small steps, one at a time, it is possible to decrease the scientific community’s strong dependence on NHST and p-values.

Supporting information

S1 appendix, acknowledgments.

The authors are grateful to Anja de Kruif for her contribution to the design of the study and for moderating one of the focus groups.

Funding Statement

This research was funded by the NWO (Nederlandse Organisatie voor Wetenschappelijk Onderzoek; Dutch Organization for Scientific Research) ( https://www.nwo.nl/ ) The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Data Availability

School Guide
Mathematics
Number System and Arithmetic
Trigonometry
Probability
Mensuration
Maths Formulas
Class 8 Maths Notes
Class 9 Maths Notes
Class 10 Maths Notes
Class 11 Maths Notes
Class 12 Maths Notes
Greater Than and Less Than Symbols | Meaning of Signs and Examples
Numerator in Mathematics
Rational and Irrational Numbers
Expanded Form
Perfect Cubes - Definition, List, Chart and Examples
Linear Algebra Symbols
Divisibility Rule of 11
Perfect Numbers
Denominator in Maths
Additive Inverse and Multiplicative Inverse
Measurement
Predecessor and Successor
Binary Multiplication
Area and Perimeter of Shapes | Formula and Examples
Probability and Statistics
Number Symbols
Square Root of 4
Factors of 30
Binary Division

Null Hypothesis

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 a Null Hypothesis?

Symbol of Null Hypothesis

Formula of null hypothesis, types of null hypothesis, principle of null hypothesis, how do you find null hypothesis, what is a null hypothesis.

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.

Definition of Null Hypothesis

Null Hypothesis represent 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.

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.

Examples of Null Hypothesis

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.

$\alpha$

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.

Null Hypothesis and Alternative 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.

Null Hypothesis vs 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.

Example of Alternative and Null Hypothesis

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.

Also, Check

Solved Examples on Null Hypothesis

Example 1: A researcher claims that the average time students spend on homework is 2 hours per night.

Null Hypothesis (H 0 ): The average time students spend on homework is equal to 2 hours per night. Data: A random sample of 30 students has an average homework time of 1.8 hours with a standard deviation of 0.5 hours. Test Statistic and Decision: Using a t-test, if the calculated t-statistic falls within the acceptance region, we fail to reject the null hypothesis. If it falls in the rejection region, we reject the null hypothesis. Conclusion: Based on the statistical analysis, we fail to reject the null hypothesis, suggesting that there is not enough evidence to dispute the claim of the average homework time being 2 hours per night.

Example 2: A company asserts that the error rate in its production process is less than 1%.

Null Hypothesis (H 0 ): The error rate in the production process is 1% or higher. Data: A sample of 500 products shows an error rate of 0.8%. Test Statistic and Decision: Using a z-test, if the calculated z-statistic falls within the acceptance region, we fail to reject the null hypothesis. If it falls in the rejection region, we reject the null hypothesis. Conclusion: The statistical analysis supports rejecting the null hypothesis, indicating that there is enough evidence to dispute the company’s claim of an error rate of 1% or higher.

Null Hypothesis – Practice Problems

Q1. A researcher claims that the average time spent by students on homework is less than 2 hours per day. Formulate the null hypothesis for this claim?

Q2. A manufacturing company states that their new machine produces widgets with a defect rate of less than 5%. Write the null hypothesis to test this claim?

Q3. An educational institute believes that their online course completion rate is at least 60%. Develop the null hypothesis to validate this assertion?

Q4. A restaurant claims that the waiting time for customers during peak hours is not more than 15 minutes. Formulate the null hypothesis for this claim?

Q5. A study suggests that the mean weight loss after following a specific diet plan for a month is more than 8 pounds. Construct the null hypothesis to evaluate this statement?

Null Hypothesis – Frequently Asked Questions

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.

Is it Possible to Prove the Null Hypothesis?

No, statistical testing aims to either reject or fail to reject the null hypothesis based on evidence from sample data. It does not prove the null hypothesis to be true.

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.

Please Login to comment...

Improve your Coding Skills with Practice

What kind of Experience do you want to share?

Want to create or adapt books like this? Learn more about how Pressbooks supports open publishing practices.

13.1 Understanding Null Hypothesis Testing

Learning objectives.

Explain the purpose of null hypothesis testing, including the role of sampling error.
Describe the basic logic of null hypothesis testing.
Describe the role of relationship strength and sample size in determining statistical significance and make reasonable judgments about statistical significance based on these two factors.

The Purpose of Null Hypothesis Testing

In fact, any statistical relationship in a sample can be interpreted in two ways:

There is a relationship in the population, and the relationship in the sample reflects this.
There is no relationship in the population, and the relationship in the sample reflects only sampling error.

The purpose of null hypothesis testing is simply to help researchers decide between these two interpretations.

The Logic of Null Hypothesis Testing

Assume for the moment that the null hypothesis is true. There is no relationship between the variables in the population.
Determine how likely the sample relationship would be if the null hypothesis were true.
If the sample relationship would be extremely unlikely, then reject the null hypothesis in favor of the alternative hypothesis. If it would not be extremely unlikely, then retain the null hypothesis .

Following this logic, we can begin to understand why Mehl and his colleagues concluded that there is no difference in talkativeness between women and men in the population. In essence, they asked the following question: “If there were no difference in the population, how likely is it that we would find a small difference of d = 0.06 in our sample?” Their answer to this question was that this sample relationship would be fairly likely if the null hypothesis were true. Therefore, they retained the null hypothesis—concluding that there is no evidence of a sex difference in the population. We can also see why Kanner and his colleagues concluded that there is a correlation between hassles and symptoms in the population. They asked, “If the null hypothesis were true, how likely is it that we would find a strong correlation of +.60 in our sample?” Their answer to this question was that this sample relationship would be fairly unlikely if the null hypothesis were true. Therefore, they rejected the null hypothesis in favor of the alternative hypothesis—concluding that there is a positive correlation between these variables in the population.

The Misunderstood p Value

The p value is one of the most misunderstood quantities in psychological research (Cohen, 1994). Even professional researchers misinterpret it, and it is not unusual for such misinterpretations to appear in statistics textbooks!

Role of Sample Size and Relationship Strength

Of course, sometimes the result can be weak and the sample large, or the result can be strong and the sample small. In these cases, the two considerations trade off against each other so that a weak result can be statistically significant if the sample is large enough and a strong relationship can be statistically significant even if the sample is small. Table 13.1 “How Relationship Strength and Sample Size Combine to Determine Whether a Result Is Statistically Significant” shows roughly how relationship strength and sample size combine to determine whether a sample result is statistically significant. The columns of the table represent the three levels of relationship strength: weak, medium, and strong. The rows represent four sample sizes that can be considered small, medium, large, and extra large in the context of psychological research. Thus each cell in the table represents a combination of relationship strength and sample size. If a cell contains the word Yes , then this combination would be statistically significant for both Cohen’s d and Pearson’s r . If it contains the word No , then it would not be statistically significant for either. There is one cell where the decision for d and r would be different and another where it might be different depending on some additional considerations, which are discussed in Section 13.2 “Some Basic Null Hypothesis Tests”

Table 13.1 How Relationship Strength and Sample Size Combine to Determine Whether a Result Is Statistically Significant

Although Table 13.1 “How Relationship Strength and Sample Size Combine to Determine Whether a Result Is Statistically Significant” provides only a rough guideline, it shows very clearly that weak relationships based on medium or small samples are never statistically significant and that strong relationships based on medium or larger samples are always statistically significant. If you keep this in mind, you will often know whether a result is statistically significant based on the descriptive statistics alone. It is extremely useful to be able to develop this kind of intuitive judgment. One reason is that it allows you to develop expectations about how your formal null hypothesis tests are going to come out, which in turn allows you to detect problems in your analyses. For example, if your sample relationship is strong and your sample is medium, then you would expect to reject the null hypothesis. If for some reason your formal null hypothesis test indicates otherwise, then you need to double-check your computations and interpretations. A second reason is that the ability to make this kind of intuitive judgment is an indication that you understand the basic logic of this approach in addition to being able to do the computations.

Statistical Significance Versus Practical Significance

Table 13.1 “How Relationship Strength and Sample Size Combine to Determine Whether a Result Is Statistically Significant” illustrates another extremely important point. A statistically significant result is not necessarily a strong one. Even a very weak result can be statistically significant if it is based on a large enough sample. This is closely related to Janet Shibley Hyde’s argument about sex differences (Hyde, 2007). The differences between women and men in mathematical problem solving and leadership ability are statistically significant. But the word significant can cause people to interpret these differences as strong and important—perhaps even important enough to influence the college courses they take or even who they vote for. As we have seen, however, these statistically significant differences are actually quite weak—perhaps even “trivial.”

Key Takeaways

Null hypothesis testing is a formal approach to deciding whether a statistical relationship in a sample reflects a real relationship in the population or is just due to chance.
The logic of null hypothesis testing involves assuming that the null hypothesis is true, finding how likely the sample result would be if this assumption were correct, and then making a decision. If the sample result would be unlikely if the null hypothesis were true, then it is rejected in favor of the alternative hypothesis. If it would not be unlikely, then the null hypothesis is retained.
The probability of obtaining the sample result if the null hypothesis were true (the p value) is based on two considerations: relationship strength and sample size. Reasonable judgments about whether a sample relationship is statistically significant can often be made by quickly considering these two factors.
Statistical significance is not the same as relationship strength or importance. Even weak relationships can be statistically significant if the sample size is large enough. It is important to consider relationship strength and the practical significance of a result in addition to its statistical significance.
Discussion: Imagine a study showing that people who eat more broccoli tend to be happier. Explain for someone who knows nothing about statistics why the researchers would conduct a null hypothesis test.

Practice: Use Table 13.1 “How Relationship Strength and Sample Size Combine to Determine Whether a Result Is Statistically Significant” to decide whether each of the following results is statistically significant.

The correlation between two variables is r = −.78 based on a sample size of 137.
The mean score on a psychological characteristic for women is 25 ( SD = 5) and the mean score for men is 24 ( SD = 5). There were 12 women and 10 men in this study.
In a memory experiment, the mean number of items recalled by the 40 participants in Condition A was 0.50 standard deviations greater than the mean number recalled by the 40 participants in Condition B.
In another memory experiment, the mean scores for participants in Condition A and Condition B came out exactly the same!
A student finds a correlation of r = .04 between the number of units the students in his research methods class are taking and the students’ level of stress.

Cohen, J. (1994). The world is round: p < .05. American Psychologist, 49 , 997–1003.

Hyde, J. S. (2007). New directions in the study of gender similarities and differences. Current Directions in Psychological Science , 16 , 259–263.

Research Methods in Psychology Copyright © 2016 by University of Minnesota is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

Want to create or adapt books like this? Learn more about how Pressbooks supports open publishing practices.

Inferential Statistics

Learning Objectives

Explain the purpose of null hypothesis testing, including the role of sampling error.
Describe the basic logic of null hypothesis testing.
Describe the role of relationship strength and sample size in determining statistical significance and make reasonable judgments about statistical significance based on these two factors.

The Purpose of Null Hypothesis Testing

Unfortunately, sample statistics are not perfect estimates of their corresponding population parameters. This is because there is a certain amount of random variability in any statistic from sample to sample. The mean number of depressive symptoms might be 8.73 in one sample of adults with clinical depression, 6.45 in a second sample, and 9.44 in a third—even though these samples are selected randomly from the same population. Similarly, the correlation (Pearson’s r ) between two variables might be +.24 in one sample, −.04 in a second sample, and +.15 in a third—again, even though these samples are selected randomly from the same population. This random variability in a statistic from sample to sample is called sampling error . (Note that the term error here refers to random variability and does not imply that anyone has made a mistake. No one “commits a sampling error.”)

In fact, any statistical relationship in a sample can be interpreted in two ways:

There is a relationship in the population, and the relationship in the sample reflects this.
There is no relationship in the population, and the relationship in the sample reflects only sampling error.

The purpose of null hypothesis testing is simply to help researchers decide between these two interpretations.

The Logic of Null Hypothesis Testing

Assume for the moment that the null hypothesis is true. There is no relationship between the variables in the population.
Determine how likely the sample relationship would be if the null hypothesis were true.
If the sample relationship would be extremely unlikely, then reject the null hypothesis in favor of the alternative hypothesis. If it would not be extremely unlikely, then retain the null hypothesis .

Following this logic, we can begin to understand why Mehl and his colleagues concluded that there is no difference in talkativeness between women and men in the population. In essence, they asked the following question: “If there were no difference in the population, how likely is it that we would find a small difference of d = 0.06 in our sample?” Their answer to this question was that this sample relationship would be fairly likely if the null hypothesis were true. Therefore, they retained the null hypothesis—concluding that there is no evidence of a sex difference in the population. We can also see why Kanner and his colleagues concluded that there is a correlation between hassles and symptoms in the population. They asked, “If the null hypothesis were true, how likely is it that we would find a strong correlation of +.60 in our sample?” Their answer to this question was that this sample relationship would be fairly unlikely if the null hypothesis were true. Therefore, they rejected the null hypothesis in favor of the alternative hypothesis—concluding that there is a positive correlation between these variables in the population.

The Misunderstood p Value

Role of Sample Size and Relationship Strength

Statistical Significance Versus Practical Significance

Table 13.1 illustrates another extremely important point. A statistically significant result is not necessarily a strong one. Even a very weak result can be statistically significant if it is based on a large enough sample. This is closely related to Janet Shibley Hyde’s argument about sex differences (Hyde, 2007) [3] . The differences between women and men in mathematical problem solving and leadership ability are statistically significant. But the word significant can cause people to interpret these differences as strong and important—perhaps even important enough to influence the college courses they take or even who they vote for. As we have seen, however, these statistically significant differences are actually quite weak—perhaps even “trivial.”

Image Description

Media Attributions

Null Hypothesis by XKCD CC BY-NC (Attribution NonCommercial)
Conditional Risk by XKCD CC BY-NC (Attribution NonCommercial)
Lakens, D. (2017, December 25). About p -values: Understanding common misconceptions. [Blog post] Retrieved from https://correlaid.org/en/blog/understand-p-values/ ↵
Cohen, J. (1994). The world is round: p < .05. American Psychologist, 49 , 997–1003. ↵
Hyde, J. S. (2007). New directions in the study of gender similarities and differences. Current Directions in Psychological Science, 16 , 259–263. ↵