title: The behavior of the P-value when the alternative hypothesis is true.
abstract: The P-value is a random variable derived from the distribution of the test statistic used to analyze a data set and to test a null hypothesis. Under the null hypothesis, the P-value based on a continuous test statistic has a uniform distribution over the interval [0, 1], regardless of the sample size of the experiment. In contrast, the distribution of the P-value under the alternative hypothesis is a function of both sample size and the true value or range of true values of the tested parameter. The characteristics, such as mean and percentiles, of the P-value distribution can give valuable insight into how the P-value behaves for a variety of parameter values and sample sizes. Potential applications of the P-value distribution under the alternative hypothesis to the design, analysis, and interpretation of results of clinical trials are considered.
authors.affiliation: Division of Biometrics I, Food and Drug Administration, Rockville, Maryland 20852, USA.
authors.forename: H M
authors.initials: HM
authors.lastname: Hung
authors.forename: R T
authors.initials: RT
authors.lastname: O'Neill
authors.forename: P
authors.initials: P
authors.lastname: Bauer
authors.forename: K
authors.initials: K
authors.lastname: Köhne
mesh_terms: D001699:Biometry; D002986:Clinical Trials as Topic / Q000706:statistics & numerical data*; D006801:Humans; D011336:Probability; D016032:Randomized Controlled Trials as Topic / Q000706:statistics & numerical data