P-values in hypothesis testing are uniformly distributed under the null hypothesis, particularly in continuous distributions. When generating p-values, one can create a uniform random number and apply the inverse cumulative distribution function (CDF) of the null distribution to obtain a p-value. This method holds true for left tail tests, where the p-value corresponds to the CDF evaluated at the test statistic. However, this uniformity may not apply to tests with discrete distributions or different acceptance/rejection regions.
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If you wanted to generate random numbers from whatever the null distribution is, you would first generate a uniform random number and then apply the inverse cdf of the null distribution to get a random value. That value would be a (one-sided) p-value.alan2 said:Help. I need an intuitive, non-mathematical explanation of why p-values from hypothesis testing are uniformly distributed. I was talking to a social scientist and got a blank stare. I couldn't come up with anything except the proof. Thanks.
alan2 said:Help. I need an intuitive, non-mathematical explanation of why p-values from hypothesis testing are uniformly distributed.
tnich said:If you wanted to generate random numbers from whatever the null distribution is, you would first generate a uniform random number and then apply the inverse cdf of the null distribution to get a random value. That value would be a (one-sided) p-value.