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• Null and Alternative Hypotheses | Definitions & Examples

Null and Alternative Hypotheses | Definitions & Examples

Published on 5 October 2022 by Shaun Turney . Revised on 6 December 2022.

The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test :

• Null hypothesis (H 0 ): There’s no effect in the population .
• Alternative hypothesis (H A ): There’s an effect in the population.

The effect is usually the effect of the independent variable on the dependent variable .

Table of contents

Answering your research question with hypotheses, what is a null hypothesis, what is an alternative hypothesis, differences between null and alternative hypotheses, how to write null and alternative hypotheses, frequently asked questions about null and alternative hypotheses.

The null and alternative hypotheses offer competing answers to your research question . When the research question asks “Does the independent variable affect the dependent variable?”, the null hypothesis (H 0 ) answers “No, there’s no effect in the population.” On the other hand, the alternative hypothesis (H A ) answers “Yes, there is an effect in the population.”

The null and alternative are always claims about the population. That’s because the goal of hypothesis testing is to make inferences about a population based on a sample . Often, we infer whether there’s an effect in the population by looking at differences between groups or relationships between variables in the sample.

You can use a statistical test to decide whether the evidence favors the null or alternative hypothesis. Each type of statistical test comes with a specific way of phrasing the null and alternative hypothesis. However, the hypotheses can also be phrased in a general way that applies to any test.

The null hypothesis is the claim that there’s no effect in the population.

If the sample provides enough evidence against the claim that there’s no effect in the population ( p ≤ α), then we can reject the null hypothesis . Otherwise, we fail to reject the null hypothesis.

Although “fail to reject” may sound awkward, it’s the only wording that statisticians accept. Be careful not to say you “prove” or “accept” the null hypothesis.

Null hypotheses often include phrases such as “no effect”, “no difference”, or “no relationship”. When written in mathematical terms, they always include an equality (usually =, but sometimes ≥ or ≤).

Examples of null hypotheses

The table below gives examples of research questions and null hypotheses. There’s always more than one way to answer a research question, but these null hypotheses can help you get started.

*Note that some researchers prefer to always write the null hypothesis in terms of “no effect” and “=”. It would be fine to say that daily meditation has no effect on the incidence of depression and p 1 = p 2 .

The alternative hypothesis (H A ) is the other answer to your research question . It claims that there’s an effect in the population.

Often, your alternative hypothesis is the same as your research hypothesis. In other words, it’s the claim that you expect or hope will be true.

The alternative hypothesis is the complement to the null hypothesis. Null and alternative hypotheses are exhaustive, meaning that together they cover every possible outcome. They are also mutually exclusive, meaning that only one can be true at a time.

Alternative hypotheses often include phrases such as “an effect”, “a difference”, or “a relationship”. When alternative hypotheses are written in mathematical terms, they always include an inequality (usually ≠, but sometimes > or <). As with null hypotheses, there are many acceptable ways to phrase an alternative hypothesis.

Examples of alternative hypotheses

The table below gives examples of research questions and alternative hypotheses to help you get started with formulating your own.

Null and alternative hypotheses are similar in some ways:

• They’re both answers to the research question
• They both make claims about the population
• They’re both evaluated by statistical tests.

However, there are important differences between the two types of hypotheses, summarized in the following table.

To help you write your hypotheses, you can use the template sentences below. If you know which statistical test you’re going to use, you can use the test-specific template sentences. Otherwise, you can use the general template sentences.

The only thing you need to know to use these general template sentences are your dependent and independent variables. To write your research question, null hypothesis, and alternative hypothesis, fill in the following sentences with your variables:

Does independent variable affect dependent variable ?

• Null hypothesis (H 0 ): Independent variable does not affect dependent variable .
• Alternative hypothesis (H A ): Independent variable affects dependent variable .

Test-specific

Once you know the statistical test you’ll be using, you can write your hypotheses in a more precise and mathematical way specific to the test you chose. The table below provides template sentences for common statistical tests.

Note: The template sentences above assume that you’re performing one-tailed tests . One-tailed tests are appropriate for most studies.

The null hypothesis is often abbreviated as H 0 . When the null hypothesis is written using mathematical symbols, it always includes an equality symbol (usually =, but sometimes ≥ or ≤).

The alternative hypothesis is often abbreviated as H a or H 1 . When the alternative hypothesis is written using mathematical symbols, it always includes an inequality symbol (usually ≠, but sometimes < or >).

A research hypothesis is your proposed answer to your research question. The research hypothesis usually includes an explanation (‘ x affects y because …’).

A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the null and alternative hypotheses. In a well-designed study , the statistical hypotheses correspond logically to the research hypothesis.

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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.

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Hypothesis Testing (cont...)

Hypothesis testing, the null and alternative hypothesis.

In order to undertake hypothesis testing you need to express your research hypothesis as a null and alternative hypothesis. The null hypothesis and alternative hypothesis are statements regarding the differences or effects that occur in the population. You will use your sample to test which statement (i.e., the null hypothesis or alternative hypothesis) is most likely (although technically, you test the evidence against the null hypothesis). So, with respect to our teaching example, the null and alternative hypothesis will reflect statements about all statistics students on graduate management courses.

The null hypothesis is essentially the "devil's advocate" position. That is, it assumes that whatever you are trying to prove did not happen ( hint: it usually states that something equals zero). For example, the two different teaching methods did not result in different exam performances (i.e., zero difference). Another example might be that there is no relationship between anxiety and athletic performance (i.e., the slope is zero). The alternative hypothesis states the opposite and is usually the hypothesis you are trying to prove (e.g., the two different teaching methods did result in different exam performances). Initially, you can state these hypotheses in more general terms (e.g., using terms like "effect", "relationship", etc.), as shown below for the teaching methods example:

Depending on how you want to "summarize" the exam performances will determine how you might want to write a more specific null and alternative hypothesis. For example, you could compare the mean exam performance of each group (i.e., the "seminar" group and the "lectures-only" group). This is what we will demonstrate here, but other options include comparing the distributions , medians , amongst other things. As such, we can state:

Now that you have identified the null and alternative hypotheses, you need to find evidence and develop a strategy for declaring your "support" for either the null or alternative hypothesis. We can do this using some statistical theory and some arbitrary cut-off points. Both these issues are dealt with next.

Significance levels

The level of statistical significance is often expressed as the so-called p -value . Depending on the statistical test you have chosen, you will calculate a probability (i.e., the p -value) of observing your sample results (or more extreme) given that the null hypothesis is true . Another way of phrasing this is to consider the probability that a difference in a mean score (or other statistic) could have arisen based on the assumption that there really is no difference. Let us consider this statement with respect to our example where we are interested in the difference in mean exam performance between two different teaching methods. If there really is no difference between the two teaching methods in the population (i.e., given that the null hypothesis is true), how likely would it be to see a difference in the mean exam performance between the two teaching methods as large as (or larger than) that which has been observed in your sample?

So, you might get a p -value such as 0.03 (i.e., p = .03). This means that there is a 3% chance of finding a difference as large as (or larger than) the one in your study given that the null hypothesis is true. However, you want to know whether this is "statistically significant". Typically, if there was a 5% or less chance (5 times in 100 or less) that the difference in the mean exam performance between the two teaching methods (or whatever statistic you are using) is as different as observed given the null hypothesis is true, you would reject the null hypothesis and accept the alternative hypothesis. Alternately, if the chance was greater than 5% (5 times in 100 or more), you would fail to reject the null hypothesis and would not accept the alternative hypothesis. As such, in this example where p = .03, we would reject the null hypothesis and accept the alternative hypothesis. We reject it because at a significance level of 0.03 (i.e., less than a 5% chance), the result we obtained could happen too frequently for us to be confident that it was the two teaching methods that had an effect on exam performance.

Whilst there is relatively little justification why a significance level of 0.05 is used rather than 0.01 or 0.10, for example, it is widely used in academic research. However, if you want to be particularly confident in your results, you can set a more stringent level of 0.01 (a 1% chance or less; 1 in 100 chance or less).

One- and two-tailed predictions

When considering whether we reject the null hypothesis and accept the alternative hypothesis, we need to consider the direction of the alternative hypothesis statement. For example, the alternative hypothesis that was stated earlier is:

The alternative hypothesis tells us two things. First, what predictions did we make about the effect of the independent variable(s) on the dependent variable(s)? Second, what was the predicted direction of this effect? Let's use our example to highlight these two points.

Sarah predicted that her teaching method (independent variable: teaching method), whereby she not only required her students to attend lectures, but also seminars, would have a positive effect (that is, increased) students' performance (dependent variable: exam marks). If an alternative hypothesis has a direction (and this is how you want to test it), the hypothesis is one-tailed. That is, it predicts direction of the effect. If the alternative hypothesis has stated that the effect was expected to be negative, this is also a one-tailed hypothesis.

Alternatively, a two-tailed prediction means that we do not make a choice over the direction that the effect of the experiment takes. Rather, it simply implies that the effect could be negative or positive. If Sarah had made a two-tailed prediction, the alternative hypothesis might have been:

In other words, we simply take out the word "positive", which implies the direction of our effect. In our example, making a two-tailed prediction may seem strange. After all, it would be logical to expect that "extra" tuition (going to seminar classes as well as lectures) would either have a positive effect on students' performance or no effect at all, but certainly not a negative effect. However, this is just our opinion (and hope) and certainly does not mean that we will get the effect we expect. Generally speaking, making a one-tail prediction (i.e., and testing for it this way) is frowned upon as it usually reflects the hope of a researcher rather than any certainty that it will happen. Notable exceptions to this rule are when there is only one possible way in which a change could occur. This can happen, for example, when biological activity/presence in measured. That is, a protein might be "dormant" and the stimulus you are using can only possibly "wake it up" (i.e., it cannot possibly reduce the activity of a "dormant" protein). In addition, for some statistical tests, one-tailed tests are not possible.

Rejecting or failing to reject the null hypothesis

Let's return finally to the question of whether we reject or fail to reject the null hypothesis.

If our statistical analysis shows that the significance level is below the cut-off value we have set (e.g., either 0.05 or 0.01), we reject the null hypothesis and accept the alternative hypothesis. Alternatively, if the significance level is above the cut-off value, we fail to reject the null hypothesis and cannot accept the alternative hypothesis. You should note that you cannot accept the null hypothesis, but only find evidence against it.

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Statistics By Jim

Making statistics intuitive

Statistical Hypothesis Testing Overview

By Jim Frost 59 Comments

In this blog post, I explain why you need to use statistical hypothesis testing and help you navigate the essential terminology. Hypothesis testing is a crucial procedure to perform when you want to make inferences about a population using a random sample. These inferences include estimating population properties such as the mean, differences between means, proportions, and the relationships between variables.

This post provides an overview of statistical hypothesis testing. If you need to perform hypothesis tests, consider getting my book, Hypothesis Testing: An Intuitive Guide .

Why You Should Perform Statistical Hypothesis Testing

Hypothesis testing is a form of inferential statistics that allows us to draw conclusions about an entire population based on a representative sample. You gain tremendous benefits by working with a sample. In most cases, it is simply impossible to observe the entire population to understand its properties. The only alternative is to collect a random sample and then use statistics to analyze it.

While samples are much more practical and less expensive to work with, there are trade-offs. When you estimate the properties of a population from a sample, the sample statistics are unlikely to equal the actual population value exactly.  For instance, your sample mean is unlikely to equal the population mean. The difference between the sample statistic and the population value is the sample error.

Differences that researchers observe in samples might be due to sampling error rather than representing a true effect at the population level. If sampling error causes the observed difference, the next time someone performs the same experiment the results might be different. Hypothesis testing incorporates estimates of the sampling error to help you make the correct decision. Learn more about Sampling Error .

For example, if you are studying the proportion of defects produced by two manufacturing methods, any difference you observe between the two sample proportions might be sample error rather than a true difference. If the difference does not exist at the population level, you won’t obtain the benefits that you expect based on the sample statistics. That can be a costly mistake!

Let’s cover some basic hypothesis testing terms that you need to know.

Background information : Difference between Descriptive and Inferential Statistics and Populations, Parameters, and Samples in Inferential Statistics

Hypothesis Testing

Hypothesis testing is a statistical analysis that uses sample data to assess two mutually exclusive theories about the properties of a population. Statisticians call these theories the null hypothesis and the alternative hypothesis. A hypothesis test assesses your sample statistic and factors in an estimate of the sample error to determine which hypothesis the data support.

When you can reject the null hypothesis, the results are statistically significant, and your data support the theory that an effect exists at the population level.

The effect is the difference between the population value and the null hypothesis value. The effect is also known as population effect or the difference. For example, the mean difference between the health outcome for a treatment group and a control group is the effect.

Typically, you do not know the size of the actual effect. However, you can use a hypothesis test to help you determine whether an effect exists and to estimate its size. Hypothesis tests convert your sample effect into a test statistic, which it evaluates for statistical significance. Learn more about Test Statistics .

An effect can be statistically significant, but that doesn’t necessarily indicate that it is important in a real-world, practical sense. For more information, read my post about Statistical vs. Practical Significance .

Null Hypothesis

The null hypothesis is one of two mutually exclusive theories about the properties of the population in hypothesis testing. Typically, the null hypothesis states that there is no effect (i.e., the effect size equals zero). The null is often signified by H 0 .

In all hypothesis testing, the researchers are testing an effect of some sort. The effect can be the effectiveness of a new vaccination, the durability of a new product, the proportion of defect in a manufacturing process, and so on. There is some benefit or difference that the researchers hope to identify.

However, it’s possible that there is no effect or no difference between the experimental groups. In statistics, we call this lack of an effect the null hypothesis. Therefore, if you can reject the null, you can favor the alternative hypothesis, which states that the effect exists (doesn’t equal zero) at the population level.

You can think of the null as the default theory that requires sufficiently strong evidence against in order to reject it.

For example, in a 2-sample t-test, the null often states that the difference between the two means equals zero.

When you can reject the null hypothesis, your results are statistically significant. Learn more about Statistical Significance: Definition & Meaning .

Related post : Understanding the Null Hypothesis in More Detail

Alternative Hypothesis

The alternative hypothesis is the other theory about the properties of the population in hypothesis testing. Typically, the alternative hypothesis states that a population parameter does not equal the null hypothesis value. In other words, there is a non-zero effect. If your sample contains sufficient evidence, you can reject the null and favor the alternative hypothesis. The alternative is often identified with H 1 or H A .

For example, in a 2-sample t-test, the alternative often states that the difference between the two means does not equal zero.

You can specify either a one- or two-tailed alternative hypothesis:

If you perform a two-tailed hypothesis test, the alternative states that the population parameter does not equal the null value. For example, when the alternative hypothesis is H A : μ ≠ 0, the test can detect differences both greater than and less than the null value.

A one-tailed alternative has more power to detect an effect but it can test for a difference in only one direction. For example, H A : μ > 0 can only test for differences that are greater than zero.

Related posts : Understanding T-tests and One-Tailed and Two-Tailed Hypothesis Tests Explained

P-values are the probability that you would obtain the effect observed in your sample, or larger, if the null hypothesis is correct. In simpler terms, p-values tell you how strongly your sample data contradict the null. Lower p-values represent stronger evidence against the null. You use P-values in conjunction with the significance level to determine whether your data favor the null or alternative hypothesis.

Related post : Interpreting P-values Correctly

Significance Level (Alpha)

For instance, a significance level of 0.05 signifies a 5% risk of deciding that an effect exists when it does not exist.

Use p-values and significance levels together to help you determine which hypothesis the data support. If the p-value is less than your significance level, you can reject the null and conclude that the effect is statistically significant. In other words, the evidence in your sample is strong enough to be able to reject the null hypothesis at the population level.

Related posts : Graphical Approach to Significance Levels and P-values and Conceptual Approach to Understanding Significance Levels

Types of Errors in Hypothesis Testing

Statistical hypothesis tests are not 100% accurate because they use a random sample to draw conclusions about entire populations. There are two types of errors related to drawing an incorrect conclusion.

• False positives: You reject a null that is true. Statisticians call this a Type I error . The Type I error rate equals your significance level or alpha (α).
• False negatives: You fail to reject a null that is false. Statisticians call this a Type II error. Generally, you do not know the Type II error rate. However, it is a larger risk when you have a small sample size , noisy data, or a small effect size. The type II error rate is also known as beta (β).

Statistical power is the probability that a hypothesis test correctly infers that a sample effect exists in the population. In other words, the test correctly rejects a false null hypothesis. Consequently, power is inversely related to a Type II error. Power = 1 – β. Learn more about Power in Statistics .

Related posts : Types of Errors in Hypothesis Testing and Estimating a Good Sample Size for Your Study Using Power Analysis

Which Type of Hypothesis Test is Right for You?

There are many different types of procedures you can use. The correct choice depends on your research goals and the data you collect. Do you need to understand the mean or the differences between means? Or, perhaps you need to assess proportions. You can even use hypothesis testing to determine whether the relationships between variables are statistically significant.

To choose the proper statistical procedure, you’ll need to assess your study objectives and collect the correct type of data . This background research is necessary before you begin a study.

Related Post : Hypothesis Tests for Continuous, Binary, and Count Data

Statistical tests are crucial when you want to use sample data to make conclusions about a population because these tests account for sample error. Using significance levels and p-values to determine when to reject the null hypothesis improves the probability that you will draw the correct conclusion.

To see an alternative approach to these traditional hypothesis testing methods, learn about bootstrapping in statistics !

If you want to see examples of hypothesis testing in action, I recommend the following posts that I have written:

• How Effective Are Flu Shots? This example shows how you can use statistics to test proportions.
• Fatality Rates in Star Trek . This example shows how to use hypothesis testing with categorical data.
• Busting Myths About the Battle of the Sexes . A fun example based on a Mythbusters episode that assess continuous data using several different tests.
• Are Yawns Contagious? Another fun example inspired by a Mythbusters episode.

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Reader Interactions

January 14, 2024 at 8:43 am

Hello professor Jim, how are you doing! Pls. What are the properties of a population and their examples? Thanks for your time and understanding.

January 14, 2024 at 12:57 pm

Please read my post about Populations vs. Samples for more information and examples.

Also, please note there is a search bar in the upper-right margin of my website. Use that to search for topics.

July 5, 2023 at 7:05 am

Hello, I have a question as I read your post. You say in p-values section

“P-values are the probability that you would obtain the effect observed in your sample, or larger, if the null hypothesis is correct. In simpler terms, p-values tell you how strongly your sample data contradict the null. Lower p-values represent stronger evidence against the null.”

But according to your definition of effect, the null states that an effect does not exist, correct? So what I assume you want to say is that “P-values are the probability that you would obtain the effect observed in your sample, or larger, if the null hypothesis is **incorrect**.”

July 6, 2023 at 5:18 am

Hi Shrinivas,

The correct definition of p-value is that it is a probability that exists in the context of a true null hypothesis. So, the quotation is correct in stating “if the null hypothesis is correct.”

Essentially, the p-value tells you the likelihood of your observed results (or more extreme) if the null hypothesis is true. It gives you an idea of whether your results are surprising or unusual if there is no effect.

Hence, with sufficiently low p-values, you reject the null hypothesis because it’s telling you that your sample results were unlikely to have occurred if there was no effect in the population.

I hope that helps make it more clear. If not, let me know I’ll attempt to clarify!

May 8, 2023 at 12:47 am

Thanks a lot Ny best regards

May 7, 2023 at 11:15 pm

Hi Jim Can you tell me something about size effect? Thanks

May 8, 2023 at 12:29 am

Here’s a post that I’ve written about Effect Sizes that will hopefully tell you what you need to know. Please read that. Then, if you have any more specific questions about effect sizes, please post them there. Thanks!

January 7, 2023 at 4:19 pm

Hi Jim, I have only read two pages so far but I am really amazed because in few paragraphs you made me clearly understand the concepts of months of courses I received in biostatistics! Thanks so much for this work you have done it helps a lot!

January 10, 2023 at 3:25 pm

Thanks so much!

June 17, 2021 at 1:45 pm

Can you help in the following question: Rocinante36 is priced at ₹7 lakh and has been designed to deliver a mileage of 22 km/litre and a top speed of 140 km/hr. Formulate the null and alternative hypotheses for mileage and top speed to check whether the new models are performing as per the desired design specifications.

April 19, 2021 at 1:51 pm

Its indeed great to read your work statistics.

I have a doubt regarding the one sample t-test. So as per your book on hypothesis testing with reference to page no 45, you have mentioned the difference between “the sample mean and the hypothesised mean is statistically significant”. So as per my understanding it should be quoted like “the difference between the population mean and the hypothesised mean is statistically significant”. The catch here is the hypothesised mean represents the sample mean.

Please help me understand this.

Regards Rajat

April 19, 2021 at 3:46 pm

Thanks for buying my book. I’m so glad it’s been helpful!

The test is performed on the sample but the results apply to the population. Hence, if the difference between the sample mean (observed in your study) and the hypothesized mean is statistically significant, that suggests that population does not equal the hypothesized mean.

For one sample tests, the hypothesized mean is not the sample mean. It is a mean that you want to use for the test value. It usually represents a value that is important to your research. In other words, it’s a value that you pick for some theoretical/practical reasons. You pick it because you want to determine whether the population mean is different from that particular value.

I hope that helps!

November 5, 2020 at 6:24 am

Jim, you are such a magnificent statistician/economist/econometrician/data scientist etc whatever profession. Your work inspires and simplifies the lives of so many researchers around the world. I truly admire you and your work. I will buy a copy of each book you have on statistics or econometrics. Keep doing the good work. Remain ever blessed

November 6, 2020 at 9:47 pm

Hi Renatus,

Thanks so much for you very kind comments. You made my day!! I’m so glad that my website has been helpful. And, thanks so much for supporting my books! 🙂

November 2, 2020 at 9:32 pm

Hi Jim, I hope you are aware of 2019 American Statistical Association’s official statement on Statistical Significance: https://www.tandfonline.com/doi/full/10.1080/00031305.2019.1583913 In case you do not bother reading the full article, may I quote you the core message here: “We conclude, based on our review of the articles in this special issue and the broader literature, that it is time to stop using the term “statistically significant” entirely. Nor should variants such as “significantly different,” “p < 0.05,” and “nonsignificant” survive, whether expressed in words, by asterisks in a table, or in some other way."

With best wishes,

November 3, 2020 at 2:09 am

I’m definitely aware of the debate surrounding how to use p-values most effectively. However, I need to correct you on one point. The link you provide is NOT a statement by the American Statistical Association. It is an editorial by several authors.

There is considerable debate over this issue. There are problems with p-values. However, as the authors state themselves, much of the problem is over people’s mindsets about how to use p-values and their incorrect interpretations about what statistical significance does and does not mean.

If you were to read my website more thoroughly, you’d be aware that I share many of their concerns and I address them in multiple posts. One of the authors’ key points is the need to be thoughtful and conduct thoughtful research and analysis. I emphasize this aspect in multiple posts on this topic. I’ll ask you to read the following three because they all address some of the authors’ concerns and suggestions. But you might run across others to read as well.

Five Tips for Using P-values to Avoid Being Misled How to Interpret P-values Correctly P-values and the Reproducibility of Experimental Results

September 24, 2020 at 11:52 pm

HI Jim, i just want you to know that you made explanation for Statistics so simple! I should say lesser and fewer words that reduce the complexity. All the best! 🙂

September 25, 2020 at 1:03 am

Thanks, Rene! Your kind words mean a lot to me! I’m so glad it has been helpful!

September 23, 2020 at 2:21 am

Honestly, I never understood stats during my entire M.Ed course and was another nightmare for me. But how easily you have explained each concept, I have understood stats way beyond my imagination. Thank you so much for helping ignorant research scholars like us. Looking forward to get hardcopy of your book. Kindly tell is it available through flipkart?

September 24, 2020 at 11:14 pm

I’m so happy to hear that my website has been helpful!

I checked on flipkart and it appears like my books are not available there. I’m never exactly sure where they’re available due to the vagaries of different distribution channels. They are available on Amazon in India.

Introduction to Statistics: An Intuitive Guide (Amazon IN) Hypothesis Testing: An Intuitive Guide (Amazon IN)

July 26, 2020 at 11:57 am

Dear Jim I am a teacher from India . I don’t have any background in statistics, and still I should tell that in a single read I can follow your explanations . I take my entire biostatistics class for botany graduates with your explanations. Thanks a lot. May I know how I can avail your books in India

July 28, 2020 at 12:31 am

Right now my books are only available as ebooks from my website. However, soon I’ll have some exciting news about other ways to obtain it. Stay tuned! I’ll announce it on my email list. If you’re not already on it, you can sign up using the form that is in the right margin of my website.

June 22, 2020 at 2:02 pm

Also can you please let me if this book covers topics like EDA and principal component analysis?

June 22, 2020 at 2:07 pm

This book doesn’t cover principal components analysis. Although, I wouldn’t really classify that as a hypothesis test. In the future, I might write a multivariate analysis book that would cover this and others. But, that’s well down the road.

My Introduction to Statistics covers EDA. That’s the largely graphical look at your data that you often do prior to hypothesis testing. The Introduction book perfectly leads right into the Hypothesis Testing book.

June 22, 2020 at 1:45 pm

Thanks for the detailed explanation. It does clear my doubts. I saw that your book related to hypothesis testing has the topics that I am studying currently. I am looking forward to purchasing it.

Regards, Take Care

June 19, 2020 at 1:03 pm

For this particular article I did not understand a couple of statements and it would great if you could help: 1)”If sample error causes the observed difference, the next time someone performs the same experiment the results might be different.” 2)”If the difference does not exist at the population level, you won’t obtain the benefits that you expect based on the sample statistics.”

I discovered your articles by chance and now I keep coming back to read & understand statistical concepts. These articles are very informative & easy to digest. Thanks for the simplifying things.

June 20, 2020 at 9:53 pm

I’m so happy to hear that you’ve found my website to be helpful!

To answer your questions, keep in mind that a central tenant of inferential statistics is that the random sample that a study drew was only one of an infinite number of possible it could’ve drawn. Each random sample produces different results. Most results will cluster around the population value assuming they used good methodology. However, random sampling error always exists and makes it so that population estimates from a sample almost never exactly equal the correct population value.

So, imagine that we’re studying a medication and comparing the treatment and control groups. Suppose that the medicine is truly not effect and that the population difference between the treatment and control group is zero (i.e., no difference.) Despite the true difference being zero, most sample estimates will show some degree of either a positive or negative effect thanks to random sampling error. So, just because a study has an observed difference does not mean that a difference exists at the population level. So, on to your questions:

1. If the observed difference is just random error, then it makes sense that if you collected another random sample, the difference could change. It could change from negative to positive, positive to negative, more extreme, less extreme, etc. However, if the difference exists at the population level, most random samples drawn from the population will reflect that difference. If the medicine has an effect, most random samples will reflect that fact and not bounce around on both sides of zero as much.

2. This is closely related to the previous answer. If there is no difference at the population level, but say you approve the medicine because of the observed effects in a sample. Even though your random sample showed an effect (which was really random error), that effect doesn’t exist. So, when you start using it on a larger scale, people won’t benefit from the medicine. That’s why it’s important to separate out what is easily explained by random error versus what is not easily explained by it.

I think reading my post about how hypothesis tests work will help clarify this process. Also, in about 24 hours (as I write this), I’ll be releasing my new ebook about Hypothesis Testing!

May 29, 2020 at 5:23 am

Hi Jim, I really enjoy your blog. Can you please link me on your blog where you discuss about Subgroup analysis and how it is done? I need to use non parametric and parametric statistical methods for my work and also do subgroup analysis in order to identify potential groups of patients that may benefit more from using a treatment than other groups.

May 29, 2020 at 2:12 pm

Hi, I don’t have a specific article about subgroup analysis. However, subgroup analysis is just the dividing up of a larger sample into subgroups and then analyzing those subgroups separately. You can use the various analyses I write about on the subgroups.

Alternatively, you can include the subgroups in regression analysis as an indicator variable and include that variable as a main effect and an interaction effect to see how the relationships vary by subgroup without needing to subdivide your data. I write about that approach in my article about comparing regression lines . This approach is my preferred approach when possible.

April 19, 2020 at 7:58 am

sir is confidence interval is a part of estimation?

April 17, 2020 at 3:36 pm

Sir can u plz briefly explain alternatives of hypothesis testing? I m unable to find the answer

April 18, 2020 at 1:22 am

Assuming you want to draw conclusions about populations by using samples (i.e., inferential statistics ), you can use confidence intervals and bootstrap methods as alternatives to the traditional hypothesis testing methods.

March 9, 2020 at 10:01 pm

Hi JIm, could you please help with activities that can best teach concepts of hypothesis testing through simulation, Also, do you have any question set that would enhance students intuition why learning hypothesis testing as a topic in introductory statistics. Thanks.

March 5, 2020 at 3:48 pm

Hi Jim, I’m studying multiple hypothesis testing & was wondering if you had any material that would be relevant. I’m more trying to understand how testing multiple samples simultaneously affects your results & more on the Bonferroni Correction

March 5, 2020 at 4:05 pm

I write about multiple comparisons (aka post hoc tests) in the ANOVA context . I don’t talk about Bonferroni Corrections specifically but I cover related types of corrections. I’m not sure if that exactly addresses what you want to know but is probably the closest I have already written. I hope it helps!

January 14, 2020 at 9:03 pm

Thank you! Have a great day/evening.

January 13, 2020 at 7:10 pm

Any help would be greatly appreciated. What is the difference between The Hypothesis Test and The Statistical Test of Hypothesis?

January 14, 2020 at 11:02 am

They sound like the same thing to me. Unless this is specialized terminology for a particular field or the author was intending something specific, I’d guess they’re one and the same.

April 1, 2019 at 10:00 am

so these are the only two forms of Hypothesis used in statistical testing?

April 1, 2019 at 10:02 am

Are you referring to the null and alternative hypothesis? If so, yes, that’s those are the standard hypotheses in a statistical hypothesis test.

April 1, 2019 at 9:57 am

year very insightful post, thanks for the write up

October 27, 2018 at 11:09 pm

hi there, am upcoming statistician, out of all blogs that i have read, i have found this one more useful as long as my problem is concerned. thanks so much

October 27, 2018 at 11:14 pm

Hi Stano, you’re very welcome! Thanks for your kind words. They mean a lot! I’m happy to hear that my posts were able to help you. I’m sure you will be a fantastic statistician. Best of luck with your studies!

October 26, 2018 at 11:39 am

Dear Jim, thank you very much for your explanations! I have a question. Can I use t-test to compare two samples in case each of them have right bias?

October 26, 2018 at 12:00 pm

Hi Tetyana,

You’re very welcome!

The term “right bias” is not a standard term. Do you by chance mean right skewed distributions? In other words, if you plot the distribution for each group on a histogram they have longer right tails? These are not the symmetrical bell-shape curves of the normal distribution.

If that’s the case, yes you can as long as you exceed a specific sample size within each group. I include a table that contains these sample size requirements in my post about nonparametric vs parametric analyses .

Bias in statistics refers to cases where an estimate of a value is systematically higher or lower than the true value. If this is the case, you might be able to use t-tests, but you’d need to be sure to understand the nature of the bias so you would understand what the results are really indicating.

I hope this helps!

April 2, 2018 at 7:28 am

Simple and upto the point 👍 Thank you so much.

April 2, 2018 at 11:11 am

Hi Kalpana, thanks! And I’m glad it was helpful!

March 26, 2018 at 8:41 am

Am I correct if I say: Alpha – Probability of wrongly rejection of null hypothesis P-value – Probability of wrongly acceptance of null hypothesis

March 28, 2018 at 3:14 pm

You’re correct about alpha. Alpha is the probability of rejecting the null hypothesis when the null is true.

Unfortunately, your definition of the p-value is a bit off. The p-value has a fairly convoluted definition. It is the probability of obtaining the effect observed in a sample, or more extreme, if the null hypothesis is true. The p-value does NOT indicate the probability that either the null or alternative is true or false. Although, those are very common misinterpretations. To learn more, read my post about how to interpret p-values correctly .

March 2, 2018 at 6:10 pm

I recently started reading your blog and it is very helpful to understand each concept of statistical tests in easy way with some good examples. Also, I recommend to other people go through all these blogs which you posted. Specially for those people who have not statistical background and they are facing to many problems while studying statistical analysis.

Thank you for your such good blogs.

March 3, 2018 at 10:12 pm

Hi Amit, I’m so glad that my blog posts have been helpful for you! It means a lot to me that you took the time to write such a nice comment! Also, thanks for recommending by blog to others! I try really hard to write posts about statistics that are easy to understand.

January 17, 2018 at 7:03 am

I recently started reading your blog and I find it very interesting. I am learning statistics by my own, and I generally do many google search to understand the concepts. So this blog is quite helpful for me, as it have most of the content which I am looking for.

January 17, 2018 at 3:56 pm

Hi Shashank, thank you! And, I’m very glad to hear that my blog is helpful!

January 2, 2018 at 2:28 pm

thank u very much sir.

January 2, 2018 at 2:36 pm

You’re very welcome, Hiral!

November 21, 2017 at 12:43 pm

Thank u so much sir….your posts always helps me to be a #statistician

November 21, 2017 at 2:40 pm

Hi Sachin, you’re very welcome! I’m happy that you find my posts to be helpful!

November 19, 2017 at 8:22 pm

great post as usual, but it would be nice to see an example.

November 19, 2017 at 8:27 pm

Thank you! At the end of this post, I have links to four other posts that show examples of hypothesis tests in action. You’ll find what you’re looking for in those posts!

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That actually explain what's on your next test, alternative hypothesis, from class:, preparatory statistics.

The alternative hypothesis is a statement that proposes a specific effect, relationship, or difference that researchers expect to find in a study, contrasting the null hypothesis, which suggests no effect or relationship. It serves as the basis for hypothesis testing and is critical in determining whether observed data provides sufficient evidence to reject the null hypothesis in favor of an alternative outcome.

congrats on reading the definition of Alternative Hypothesis . now let's actually learn it.

5 Must Know Facts For Your Next Test

• The alternative hypothesis is denoted as H1 or Ha and suggests that there is an effect or a difference present in the data.
• In hypothesis testing, if the p-value is less than the significance level, it provides evidence against the null hypothesis and supports the alternative hypothesis.
• There are two types of alternative hypotheses: one-tailed (indicating direction) and two-tailed (indicating any difference), depending on the research question.
• The formulation of the alternative hypothesis is essential in guiding the design and analysis of experiments and studies.
• Rejecting the null hypothesis in favor of the alternative does not prove that the alternative is true; it only suggests that the data supports it more than the null.

Review Questions

• The alternative hypothesis is a critical component of hypothesis testing as it presents what researchers aim to prove. During testing, data collected can either support rejecting the null hypothesis or fail to provide enough evidence for it. A successful rejection means that results align more closely with the alternative hypothesis, guiding future research directions and influencing decision-making based on statistical evidence.
• When planning a study, researchers can formulate an alternative hypothesis by clearly defining what they expect to find. They must decide if they want a one-tailed alternative hypothesis, which indicates a specific direction of effect (e.g., 'Group A will perform better than Group B'), or a two-tailed one that considers any potential difference (e.g., 'Group A will differ from Group B'). This formulation should align with research objectives and expected outcomes.
• Failing to reject the null hypothesis means that there isn't enough statistical evidence to support the alternative hypothesis. This situation doesn't prove that the alternative hypothesis is false; instead, it suggests that either there is truly no effect or relationship present, or that the study may have lacked sufficient power or appropriate design to detect it. Understanding this nuance helps researchers interpret their findings and informs decisions about further research or adjustments needed in study design.

Related terms

Null Hypothesis : The null hypothesis is a statement that assumes no effect or no difference exists between groups or variables being studied, serving as a benchmark for comparison.

P-Value : The p-value is a statistical measure that helps determine the significance of results obtained in a study, specifically indicating the probability of observing the collected data assuming the null hypothesis is true.

Significance Level : The significance level, often denoted as alpha (α), is a threshold used to determine whether to reject the null hypothesis, commonly set at 0.05 or 0.01.

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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.

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 ).

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.

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.

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Alternative Hypothesis: Definition, Types and Examples

In statistical hypothesis testing, the alternative hypothesis is an important proposition in the hypothesis test. The goal of the hypothesis test is to demonstrate that in the given condition, there is sufficient evidence supporting the credibility of the alternative hypothesis instead of the default assumption made by the null hypothesis.

Both hypotheses include statements with the same purpose of providing the researcher with a basic guideline. The researcher uses the statement from each hypothesis to guide their research. In statistics, alternative hypothesis is often denoted as H a or H 1 .

Table of Content

What is a Hypothesis?

Alternative hypothesis, types of alternative hypothesis, difference between null and alternative hypothesis, formulating an alternative hypothesis, example of alternative hypothesis, application of alternative hypothesis.

“A hypothesis is a statement of a relationship between two or more variables.” It is a working statement or theory that is based on insufficient evidence.

While experimenting, researchers often make a claim, that they can test. These claims are often based on the relationship between two or more variables. “What causes what?” and “Up to what extent?” are a few of the questions that a hypothesis focuses on answering. The hypothesis can be true or false, based on complete evidence.

While there are different hypotheses, we discuss only null and alternate hypotheses. The null hypothesis, denoted H o , is the default position where variables do not have a relation with each other. That means the null hypothesis is assumed true until evidence indicates otherwise. The alternative hypothesis, denoted H 1 , on the other hand, opposes the null hypothesis. It assumes a relation between the variables and serves as evidence to reject the null hypothesis.

Example of Hypothesis:

Mean age of all college students is 20.4 years. (simple hypothesis).

An Alternative Hypothesis is a claim or a complement to the null hypothesis. If the null hypothesis predicts a statement to be true, the Alternative Hypothesis predicts it to be false. Let’s say the null hypothesis states there is no difference between height and shoe size then the alternative hypothesis will oppose the claim by stating that there is a relation.

We see that the null hypothesis assumes no relationship between the variables whereas an alternative hypothesis proposes a significant relation between variables. An alternative theory is the one tested by the researcher and if the researcher gathers enough data to support it, then the alternative hypothesis replaces the null hypothesis.

Null and alternative hypotheses are exhaustive, meaning that together they cover every possible outcome. They are also mutually exclusive, meaning that only one can be true at a time.

There are a few types of alternative hypothesis that we will see:

1. One-tailed test H 1 : A one-tailed alternative hypothesis focuses on only one region of rejection of the sampling distribution. The region of rejection can be upper or lower.

• Upper-tailed test H 1 : Population characteristic > Hypothesized value
• Lower-tailed test H 1 : Population characteristic < Hypothesized value

2. Two-tailed test H 1 : A two-tailed alternative hypothesis is concerned with both regions of rejection of the sampling distribution.

3. Non-directional test H 1 : A non-directional alternative hypothesis is not concerned with either region of rejection; rather, it is only concerned that null hypothesis is not true.

4. Point test H 1 : Point alternative hypotheses occur when the hypothesis test is framed so that the population distribution under the alternative hypothesis is a fully defined distribution, with no unknown parameters; such hypotheses are usually of no practical interest but are fundamental to theoretical considerations of statistical inference and are the basis of the Neyman–Pearson lemma.

the differences between Null Hypothesis and Alternative Hypothesis is explained in the table below:

Formulating an alternative hypothesis means identifying the relationships, effects or condition being studied. Based on the data we conclude that there is a different inference from the null-hypothesis being considered.

• Understand the null hypothesis.
• Consider the alternate hypothesis
• Choose the type of alternate hypothesis (one-tailed or two-tailed)

Alternative hypothesis must be true when the null hypothesis is false. When trying to identify the information need for alternate hypothesis statement, look for the following phrases:

• “Is it reasonable to conclude…”
• “Is there enough evidence to substantiate…”
• “Does the evidence suggest…”
• “Has there been a significant…”

When alternative hypotheses in mathematical terms, they always include an inequality ( usually ≠, but sometimes < or >) . When writing the alternate hypothesis, make sure it never includes an “=” symbol.

To help you write your hypotheses, you can use the template sentences below.

Does independent variable affect dependent variable?

• Null Hypothesis (H 0 ): Independent variable does not affect dependent variable.
• Alternative Hypothesis (H a ): Independent variable affects dependent variable.

Various examples of Alternative Hypothesis includes:

Two-Tailed Example

• Research Question : Do home games affect a team’s performance?
• Null-Hypothesis: Home games do not affect a team’s performance.
• Alternative Hypothesis: Home games have an effect on team’s performance.
• Research Question: Does sleeping less lead to depression?
• Null-Hypothesis: Sleeping less does not have an effect on depression.
• Alternative Hypothesis : Sleeping less has an effect on depression.

One-Tailed Example

• Research Question: Are candidates with experience likely to get a job?
• Null-Hypothesis: Experience does not matter in getting a job.
• Alternative Hypothesis: Candidates with work experience are more likely to receive an interview.
• Alternative Hypothesis : Teams with home advantage are more likely to win a match.

Some applications of Alternative Hypothesis includes:

• Rejecting Null-Hypothesis : A researcher performs additional research to find flaws in the null hypothesis. Following the research, which uses the alternative hypothesis as a guide, they may decide whether they have enough evidence to reject the null hypothesis.
• Guideline for Research : An alternative and null hypothesis include statements with the same purpose of providing the researcher with a basic guideline. The researcher uses the statement from each hypothesis to guide their research.
• New Theories : Alternative hypotheses can provide the opportunity to discover new theories that a researcher can use to disprove an existing theory that may not have been backed up by evidence.

We defined the relationship that exist between null-hypothesis and alternative hypothesis. While the null hypothesis is always a default assumption about our test data, the alternative hypothesis puts in all the effort to make sure the null hypothesis is disproved.

Null-hypothesis always explores new relationships between the independent variables to find potential outcomes from our test data. We should note that for every null hypothesis, one or more alternate hypotheses can be developed.

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FAQs on Alternative Hypothesis

What is hypothesis.

A hypothesis is a statement of a relationship between two or more variables.” It is a working statement or theory that is based on insufficient evidence.

What is an Alternative Hypothesis?

Alternative hypothesis, denoted by H 1 , opposes the null-hypothesis. It assumes a relation between the variables and serves as an evidence to reject the null-hypothesis.

What is the Difference between Null-Hypothesis and Alternative Hypothesis?

Null hypothesis is the default claim that assumes no relationship between variables while alternative hypothesis is the opposite claim which considers statistical significance between the variables.

What is Alternative and Experimental Hypothesis?

Null hypothesis (H 0 ) states there is no effect or difference, while the alternative hypothesis (H 1 or H a ) asserts the presence of an effect, difference, or relationship between variables. In hypothesis testing, we seek evidence to either reject the null hypothesis in favor of the alternative hypothesis or fail to do so.

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• Understanding P values | Definition and Examples

Understanding P-values | Definition and Examples

Published on July 16, 2020 by Rebecca Bevans . Revised on June 22, 2023.

The p value is a number, calculated from a statistical test, that describes how likely you are to have found a particular set of observations if the null hypothesis were true.

P values are used in hypothesis testing to help decide whether to reject the null hypothesis. The smaller the p value, the more likely you are to reject the null hypothesis.

Table of contents

What is a null hypothesis, what exactly is a p value, how do you calculate the p value, p values and statistical significance, reporting p values, caution when using p values, other interesting articles, frequently asked questions about p-values.

All statistical tests have a null hypothesis. For most tests, the null hypothesis is that there is no relationship between your variables of interest or that there is no difference among groups.

For example, in a two-tailed t test , the null hypothesis is that the difference between two groups is zero.

• Null hypothesis ( H 0 ): there is no difference in longevity between the two groups.
• Alternative hypothesis ( H A or H 1 ): there is a difference in longevity between the two groups.

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The p value , or probability value, tells you how likely it is that your data could have occurred under the null hypothesis. It does this by calculating the likelihood of your test statistic , which is the number calculated by a statistical test using your data.

The p value tells you how often you would expect to see a test statistic as extreme or more extreme than the one calculated by your statistical test if the null hypothesis of that test was true. The p value gets smaller as the test statistic calculated from your data gets further away from the range of test statistics predicted by the null hypothesis.

The p value is a proportion: if your p value is 0.05, that means that 5% of the time you would see a test statistic at least as extreme as the one you found if the null hypothesis was true.

P values are usually automatically calculated by your statistical program (R, SPSS, etc.).

You can also find tables for estimating the p value of your test statistic online. These tables show, based on the test statistic and degrees of freedom (number of observations minus number of independent variables) of your test, how frequently you would expect to see that test statistic under the null hypothesis.

The calculation of the p value depends on the statistical test you are using to test your hypothesis :

• Different statistical tests have different assumptions and generate different test statistics. You should choose the statistical test that best fits your data and matches the effect or relationship you want to test.
• The number of independent variables you include in your test changes how large or small the test statistic needs to be to generate the same p value.

No matter what test you use, the p value always describes the same thing: how often you can expect to see a test statistic as extreme or more extreme than the one calculated from your test.

P values are most often used by researchers to say whether a certain pattern they have measured is statistically significant.

Statistical significance is another way of saying that the p value of a statistical test is small enough to reject the null hypothesis of the test.

How small is small enough? The most common threshold is p < 0.05; that is, when you would expect to find a test statistic as extreme as the one calculated by your test only 5% of the time. But the threshold depends on your field of study – some fields prefer thresholds of 0.01, or even 0.001.

The threshold value for determining statistical significance is also known as the alpha value.

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P values of statistical tests are usually reported in the results section of a research paper , along with the key information needed for readers to put the p values in context – for example, correlation coefficient in a linear regression , or the average difference between treatment groups in a t -test.

P values are often interpreted as your risk of rejecting the null hypothesis of your test when the null hypothesis is actually true.

In reality, the risk of rejecting the null hypothesis is often higher than the p value, especially when looking at a single study or when using small sample sizes. This is because the smaller your frame of reference, the greater the chance that you stumble across a statistically significant pattern completely by accident.

P values are also often interpreted as supporting or refuting the alternative hypothesis. This is not the case. The  p value can only tell you whether or not the null hypothesis is supported. It cannot tell you whether your alternative hypothesis is true, or why.

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

• Normal distribution
• Descriptive statistics
• Measures of central tendency
• Correlation coefficient
• Null hypothesis

Methodology

• Cluster sampling
• Stratified sampling
• Types of interviews
• Cohort study
• Thematic analysis

Research bias

• Implicit bias
• Cognitive bias
• Survivorship bias
• Availability heuristic
• Nonresponse bias
• Regression to the mean

A p -value , or probability value, is a number describing how likely it is that your data would have occurred under the null hypothesis of your statistical test .

P -values are usually automatically calculated by the program you use to perform your statistical test. They can also be estimated using p -value tables for the relevant test statistic .

P -values are calculated from the null distribution of the test statistic. They tell you how often a test statistic is expected to occur under the null hypothesis of the statistical test, based on where it falls in the null distribution.

If the test statistic is far from the mean of the null distribution, then the p -value will be small, showing that the test statistic is not likely to have occurred under the null hypothesis.

Statistical significance is a term used by researchers to state that it is unlikely their observations could have occurred under the null hypothesis of a statistical test . Significance is usually denoted by a p -value , or probability value.

Statistical significance is arbitrary – it depends on the threshold, or alpha value, chosen by the researcher. The most common threshold is p < 0.05, which means that the data is likely to occur less than 5% of the time under the null hypothesis .

When the p -value falls below the chosen alpha value, then we say the result of the test is statistically significant.

No. The p -value only tells you how likely the data you have observed is to have occurred under the null hypothesis .

If the p -value is below your threshold of significance (typically p < 0.05), then you can reject the null hypothesis, but this does not necessarily mean that your alternative hypothesis is true.

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