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In null-hypothesis significance testing, the p-value [note 1] is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct. [2] [3] A very small p-value means that such an extreme observed outcome would be very unlikely under the null hypothesis.
In 2016, the American Statistical Association (ASA) published a statement on p-values, saying that "the widespread use of 'statistical significance' (generally interpreted as 'p ≤ 0.05') as a license for making a claim of a scientific finding (or implied truth) leads to considerable distortion of the scientific process". [57]
The p-value is not the probability that the observed effects were produced by random chance alone. [2] The p-value is computed under the assumption that a certain model, usually the null hypothesis, is true. This means that the p-value is a statement about the relation of the data to that hypothesis. [2]
In statistics, a generalized p-value is an extended version of the classical p-value, which except in a limited number of applications, provides only approximate solutions. Conventional statistical methods do not provide exact solutions to many statistical problems, such as those arising in mixed models and MANOVA , especially when the problem ...
The cumulative distribution function (shown as F(x)) gives the p values as a function of the q values. The quantile function does the opposite: it gives the q values as a function of the p values. Note that the portion of F(x) in red is a horizontal line segment.
Killeen acknowledges this lack of information, but suggests that p-rep better captures the way naive experimenters conceptualize p-values and statistical hypothesis testing. Among the criticisms of p-rep is the fact that while it attempts to estimate replicability, it ignores results from other studies which can accurately guide this estimate. [4]
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A p-value that satisfies this guarantee is also called a post-hoc p-value. As p ′ {\displaystyle p^{\prime }} is a post-hoc p-value if and only if p ′ = 1 / E {\displaystyle p^{\prime }=1/E} for some e-value E {\displaystyle E} , it is possible to view this as an alternative definition of an e-value.