P-values in hypothesis testing are uniformly distributed when derived from a continuous null distribution, as they represent the probability of observing a test statistic as extreme as the one calculated. To generate a p-value, one can produce a uniform random number and apply the inverse cumulative distribution function (CDF) of the null distribution, resulting in a p-value that reflects this uniformity. However, this uniformity may not hold true for discrete distributions or certain acceptance/rejection regions. The discussion emphasizes the need for an intuitive understanding of this concept, especially for those outside of statistical fields. Overall, the uniform distribution of p-values is contingent on the nature of the test statistic and the underlying distribution.
