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### If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?

A basic limitation of null hypothesis significance testing is that it does not allow a researcher to gather evidence in favor of the null (Source) I see this claim repeated in multiple places, but I ...
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### Definition of alternative hypothesis

Which of these properties is required of the alternative hypothesis, by definition, in the general case: a) If the alternative hypothesis is true, then the null hypothesis would necessarily tend ...
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### Misunderstanding a P-value?

So I've been reading a lot about how to correctly interpret a P-value, and from what I've read, the p-value says NOTHING about the probability that the null hypothesis is true or false. However, when ...
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### The rationale behind the “fail to reject the null” jargon in hypothesis testing?

In hypothesis testing with a Null and the Alternative hypothesis (assuming that these two cases are mutually inclusive of all the possible "truths"), we usually base our hypothesis selection criterion ...
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### Is there a consensus on adjusting alpha for multiple contrasts if the main effect is significant?

After talking to a couple of statisticians, reading some book sections, internet articles, and forums like this, I am still unclear about multiplicity adjustments of post hoc tests and contrasts. Let'...
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### What fraction to use in the formulation of a hypothesis test ? - Population fraction versus sample fraction

Imagine that I am studying racial discrimination. In particular, whether a white candidate (for a job) is chosen more often than an equally qualified minority candidate. I ask people to choose ...
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### How can we reject null hypothesis based on p-values? [closed]

In textbook statistical tests, we usually calculate the probability of observing the data we observed given that the null hypothesis is true, i.e. $P[D|H_0]$. If this probability is small (e.g. \$<0....
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### what “rejecting a null hypothesis” actually means?

I have a sample dateset consists two variables as "Score"(independent continuous) consists score of students in maths and school(dependent categorical)having 3 categories as "S1","S2","S3". I'd ...
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### When a one-tailed test passes but a two-tailed test does not

(Sorry if this is obvious or is a duplicate. I couldn't find one.) Suppose two researchers are studying whether average height of some population has changed significantly. Researcher 1 hypothesizes ...
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### Using p-value to compute the probability of hypothesis being true; what else is needed?

Question: One common misunderstanding of p-values is that they represent the probability of the null hypothesis being true. I know that's not correct and I know that p-values only represent the ...
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### Null hypothesis for the one- and two-tailed test

From the Online Stat Book, Chapter 11.5: The null hypothesis for the two-tailed test is π = 0.5. By contrast, the null hypothesis for the one-tailed test is π ≤ 0.5. Why is that so? The null ...
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### Is this null hypothesis wrong?

The Wikipedia article Null hypothesis says in its opening paragraph: In inferential statistics, the term "null hypothesis" is a general statement or default position that there is no relationship ...
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### Interpreting hypothesis testing result (assuming that the null hypothesis is true) [duplicate]

I have a doubt on how to interpret a result of a hypothesis test. For example, a scenario where I have an existing configuration and also a new configuration. I am trying to check if with the new ...