Statistics for dummies null hypothesis

The set of values outside the region of acceptance is called the region of rejection. If the test statistic falls within the region of rejection, the null hypothesis is rejected. These approaches are equivalent. Some statistics texts use the P-value approach; others use the region of acceptance approach.

In subsequent lessons, this tutorial will present examples that illustrate each approach. A test of a statistical hypothesis, where the region of rejection is on only one side of the sampling distribution , is called a one-tailed test.

For example, suppose the null hypothesis states that the mean is less than or equal to The alternative hypothesis would be that the mean is greater than The region of rejection would consist of a range of numbers located on the right side of sampling distribution; that is, a set of numbers greater than A test of a statistical hypothesis, where the region of rejection is on both sides of the sampling distribution, is called a two-tailed test.

For example, suppose the null hypothesis states that the mean is equal to The alternative hypothesis would be that the mean is less than 10 or greater than The region of rejection would consist of a range of numbers located on both sides of sampling distribution; that is, the region of rejection would consist partly of numbers that were less than 10 and partly of numbers that were greater than It looks like you're using Internet Explorer 11 or older.

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

The p -value only tells you how likely the data you have observed is to have occurred under the null hypothesis. Have a language expert improve your writing. Check your paper for plagiarism in 10 minutes. Do the check. Generate your APA citations for free! APA Citation Generator. Home Knowledge Base Statistics The p-value explained.

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What is a p-value? How do you calculate a p-value? What is statistical significance? In the NHST framework, the level of significance is in practice assimilated to the alpha level, which appears as a simple decision rule: if the p-value is less or equal to alpha, the null is rejected. It is however a common mistake to assimilate these two concepts. The figure was prepared with G-power for a one-sided one-sample t-test, with a sample size of 32 subjects, an effect size of 0.

Therefore, one can only reject the null hypothesis if the test statistics falls into the critical region s , or fail to reject this hypothesis. In the latter case, all we can say is that no significant effect was observed, but one cannot conclude that the null hypothesis is true. This is another common mistake in using NHST: there is a profound difference between accepting the null hypothesis and simply failing to reject it Killeen, By failing to reject, we simply continue to assume that H0 is true, which implies that one cannot argue against a theory from a non-significant result absence of evidence is not evidence of absence.

CI have been advocated as alternatives to p-values because i they allow judging the statistical significance and ii provide estimates of effect size. Assuming the CI a symmetry and width are correct but see Wilcox, , they also give some indication about the likelihood that a similar value can be observed in future studies. If sample sizes however differ between studies, CI do not however warranty any a priori coverage. The most common mistake is to interpret CI as the probability that a parameter e.

The alpha value has the same interpretation as testing against H0, i. This implies that CI do not allow to make strong statements about the parameter of interest e. To make a statement about the probability of a parameter of interest e.

NHST has always been criticized, and yet is still used every day in scientific reports Nickerson, One question to ask oneself is what is the goal of a scientific experiment at hand? 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. This test is used as a test of goodness of fit and is ideal when the size of the sample is small.

It compares the cumulative distribution function for a variable with a specified distribution. The null hypothesis assumes no difference between the observed and theoretical distribution and the value of test statistic 'D' is calculated as:. Acceptance Criteria: If calculated value is less than critical value accept null hypothesis. Rejection Criteria: If calculated value is greater than table value reject null hypothesis. In a study done from various streams of a college 60 students, with equal number of students drawn from each stream, are we interviewed and their intention to join the Drama Club of college was noted.

It was expected that 12 students from each class would join the Drama Club.