10 questions linked to/from Formal definition of p-value
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### Why is the p-value defined the way it is (as opposed to a more intuitive measure)?

As I understand it the p-value for some hypothesis H and some test-statistic T is defined as the probability of observing a test-statistic T' which is at least as extreme as T, conditional on H being ...
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### Difference/relationship between power and significance

What is the conceptual difference between statistical power and statistical significance? Are they the same? Is one used for the other?
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### How can I get a significant overall ANOVA but no significant pairwise differences with Tukey's procedure?

I performed with R an ANOVA and I got significant differences. However when checking which pairs were significantly different using the Tukey's procedure I did not get any of them. How can this be ...
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### Does p-value ever depend on the alternative?

Our tag definition of the $p$-value says In frequentist hypothesis testing, the $p$-value is the probability of a result as extreme (or more) than the observed result, under the assumption that the ...
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### Why does $\mu > 0$ (or even $\mu > \epsilon$) "seem easier” to substantiate than $\mu \neq 0$?

Consider a random variable $X$ following a normal distribution $N(\mu,\sigma^2)$. Suppose that we have drawn iid samples of $X$, obtaining a data set with a sample mean $\bar{x}>0$. We want to test ...
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### Comparing two, or more, independent paired t-tests

Can we compare the results from two, or more, independent paired t-tests? For example: I want to test if drug 1 and drug 2 are effective to reduce weight. I have a control group (that will consume a ...
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### R Tukey HSD Anova: Anova significant, Tukey not? [duplicate]

i created a simple anova with three groups in R and get a significant Result. After that i do a Tukey HSD Test and now nothing is significant. How can that be? Pr(>F): 0.0316 Group | p adj 1 - 2 ...
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### Surprising behavior of the power of Fisher exact test (permutation tests)

I met a paradoxical behavior of so-called "exact tests" or "permutation tests", the prototype of which is Fisher test. Here it is. Imagine you have two groups of 400 individuals (e.g. 400 control vs ...
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In a hypothesis test, the null hypothesis $H_0$ is rejected in favor of $H_1$ if $|\bar X|>\mu$. When tests found that $\bar x$ is the mean of the samples, a p-value is computed using  p=\Pr(|\...