This does not necessarily mean that the researcher accepts the null hypothesis as true—only that there is not currently enough evidence to conclude that it is true. The p value is one of the most misunderstood quantities in psychological research Cohen, [1].
Even professional researchers misinterpret it, and it is not unusual for such misinterpretations to appear in statistics textbooks! The most common misinterpretation is that the p value is the probability that the null hypothesis is true—that the sample result occurred by chance.
For example, a misguided researcher might say that because the p value is. But this is incorrect. The p value is really the probability of a result at least as extreme as the sample result if the null hypothesis were true. So a p value of. You can avoid this misunderstanding by remembering that the p value is not the probability that any particular hypothesis is true or false. Instead, it is the probability of obtaining the sample result if the null hypothesis were true.
Specifically, the stronger the sample relationship and the larger the sample, the less likely the result would be if the null hypothesis were true. That is, the lower the p value. This should make sense. If there were really no sex difference in the population, then a result this strong based on such a large sample should seem highly unlikely. If there were no sex difference in the population, then a relationship this weak based on such a small sample should seem likely.
And this is precisely why the null hypothesis would be rejected in the first example and retained in the second. Of course, sometimes the result can be weak and the sample large, or the result can be strong and the sample small.
In these cases, the two considerations trade off against each other so that a weak result can be statistically significant if the sample is large enough and a strong relationship can be statistically significant even if the sample is small. Table The columns of the table represent the three levels of relationship strength: weak, medium, and strong. The rows represent four sample sizes that can be considered small, medium, large, and extra large in the context of psychological research.
Thus each cell in the table represents a combination of relationship strength and sample size. If it contains the word No , then it would not be statistically significant for either.
There is one cell where the decision for d and r would be different and another where it might be different depending on some additional considerations, which are discussed in Section If you keep this lesson in mind, you will often know whether a result is statistically significant based on the descriptive statistics alone. It is extremely useful to be able to develop this kind of intuitive judgment. One reason is that it allows you to develop expectations about how your formal null hypothesis tests are going to come out, which in turn allows you to detect problems in your analyses.
The simplistic definition is that the null hypothesis is the opposite of the hypothesis being tested. The researcher suspects the hypothesis to be true and thus is doing research to support the hypothesis , but the null hypothesis is the hypothesis the researcher tries to disprove.
While a Bayesian analysis is suited to estimate that the probability that a hypothesis is correct, like NHST, it does not prove a theory on itself, but adds its plausibility Lindley, Reporting everything can however hinder the communication of the main result s , and we should aim at giving only the information needed, at least in the core of a manuscript.
Here I propose to adopt optimal reporting in the result section to keep the message clear, but have detailed supplementary material. For the reader to understand and fully appreciate the results, nothing else is needed.
Because science progress is obtained by cumulating evidence Rosenthal, , scientists should also consider the secondary use of the data.
It is also essential to report the context in which tests were performed — that is to report all of the tests performed all t, F, p values because of the increase type one error rate due to selective reporting multiple comparisons and p-hacking problems - Ioannidis, I can see from the history of this paper that the author has already been very responsive to reviewer comments, and that the process of revising has now been quite protracted.
That makes me reluctant to suggest much more, but I do see potential here for making the paper more impactful. So my overall view is that, once a few typos are fixed see below , this could be published as is, but I think there is an issue with the potential readership and that further revision could overcome this.
I suspect my take on this is rather different from other reviewers, as I do not regard myself as a statistics expert, though I am on the more quantitative end of the continuum of psychologists and I try to keep up to date. I think I am quite close to the target readership , insofar as I am someone who was taught about statistics ages ago and uses stats a lot, but never got adequate training in the kinds of topic covered by this paper.
The fact that I am aware of controversies around the interpretation of confidence intervals etc is simply because I follow some discussions of this on social media. I am therefore very interested to have a clear account of these issues. This paper contains helpful information for someone in this position, but it is not always clear, and I felt the relevance of some of the content was uncertain. So here are some recommendations:. I wondered about changing the focus slightly and modifying the title to reflect this to say something like: Null hypothesis significance testing: a guide to commonly misunderstood concepts and recommendations for good practice.
So it might be better to just focus on explaining as clearly as possible the problems people have had in interpreting key concepts. I think a title that made it clear this was the content would be more appealing than the current one.
P 3, col 1, para 3, last sentence. I wondered whether it would be useful here to note that in some disciplines different cutoffs are traditional, e.
Having read the section on the Fisher approach and Neyman-Pearson approach I felt confused. As I understand it, I have been brought up doing null hypothesis testing, so am adopting a Fisher approach. But I also talk about setting alpha to. But the explanation of the difference was hard to follow and I found myself wondering whether it would actually make any difference to what I did in practice. Maybe it would be possible to explain this better with the tried-and-tested example of tossing a coin.
So in Fisher approach you do a number of coin tosses to test whether the coin is unbiased Null hypothesis ; you can then work out p as the probability of the null given a specific set of observations, which is the p—value.
The section on acceptance or rejection of H0 was good, though I found the first sentence a bit opaque and wondered if it could be made clearer. Also I wondered if this rewording would be accurate as it is clearer to me : instead of:. I felt most readers would be interested to read about tests of equivalence and Bayesian approaches, but many would be unfamiliar with these and might like to see an example of how they work in practice — if space permitted. I understand about difficulties in comparing CI across studies when sample sizes differ, but I did not find the last sentence on p 4 easy to understand.
Here too I felt some concrete illustration might be helpful to the reader. I have read this submission. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above.
The revisions are OK for me, and I have changed my status to Approved. I believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. On the whole I think that this article is reasonable, my main reservation being that I have my doubts on whether the literature needs yet another tutorial on this subject.
A further reservation I have is that the author, following others, stresses what in my mind is a relatively unimportant distinction between the Fisherian and Neyman-Pearson NP approaches. I see this as being unimportant and not even true. Unless one considers that the person carrying out a hypothesis test original tester is mandated to come to a conclusion on behalf of all scientific posterity, then one must accept that any remote scientist can come to his or her conclusion depending on the personal type I error favoured.
To operate the results of an NP test carried out by the original tester, the remote scientist then needs to know the p-value. The type I error rate is then compared to this to come to a personal accept or reject decision 1. In fact Lehmann 2 , who was an important developer of and proponent of the NP system, describes exactly this approach as being good practice.
See Testing Statistical Hypotheses, 2nd edition P Thus using tail-area probabilities calculated from the observed statistics does not constitute an operational difference between the two systems. A more important distinction between the Fisherian and NP systems is that the former does not use alternative hypotheses 3. Fisher's opinion was that the null hypothesis was more primitive than the test statistic but that the test statistic was more primitive than the alternative hypothesis.
Thus, alternative hypotheses could not be used to justify choice of test statistic. Only experience could do that. Further distinctions between the NP and Fisherian approach are to do with conditioning and whether a null hypothesis can ever be accepted. I have one minor quibble about terminology. As far as I can see, the author uses the usual term 'null hypothesis' and the eccentric term 'nil hypothesis' interchangeably. It would be simpler if the latter were abandoned.
Null hypothesis significance testing NHST is a difficult topic, with misunderstandings arising easily. Many texts, including basic statistics books, deal with the topic, and attempt to explain it to students and anyone else interested.
I would refer to a good basic text book, for a detailed explanation of NHST, or to a specialized article when wishing an explaining the background of NHST. So, what is the added value of a new text on NHST? The independent variable is manipulated by the researcher and the dependent variable is the outcome which is measured. Operationalisation of a hypothesis refers to the process of making the variables physically measurable or testable, e.
Now, if we decide to study this by giving the same group of students a lesson on a Monday morning and on a Friday afternoon and then measuring their immediate recall on the material covered in each session we would end up with the following:. The null hypothesis is, therefore, the opposite of the alternative hypothesis in that it states that there will be no change in behavior. At this point, you might be asking why we seem so interested in the null hypothesis.
Surely the alternative or experimental hypothesis is more important? Well, yes it is. What we do instead is see if we can disprove, or reject, the null hypothesis. McLeod, S. What is a hypothesis.
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