Testing Variance Components in Mixed Models with GeneralizedpValues

A procedure for testing one-sided hypotheses on variance components in a balanced random effects model is developed. The testing is performed on the basis of a generalized p value and involves a one-dimensional numerical integration. In the special case for which the conventional methods provide an exact test, this test is equivalent to the usual F test. The test is also generalized Bayes in the sense that, under a certain diffuse prior, the p value is numerically the same as the posterior probability of the null hypothesis.