p-Values as Random Variables; Expected p-Values

Harold Sackrowitz & Ester Samuel-Cahn

P-values for hypotheses are considered as random variables. Their expected value (EPV) is expressed in a simple form. In simple examples they are directly computable, also under the alternative hypothesis, and in more complicated examples they are easily simulated. Their major advantage is that they do not depend on any significant level. It is suggested that the use of EPV can replace the use of power, which is always significance level dependent EPV can also be used for comparison of tests when more than one test is available for a given hypothesis. Examples are given, as well as tables which relate significance level and power to EPV. A comparison of the two-sample one-sided Kolmogorov-Smirnov, Mann-Whitney and t tests is included, for a variety of underlying distributions.

September, 1997
Published in: 
The American Statistician 53 (1999), 326-331