An Extended ANOVA F-Test with Applications to the Heterogeneity Problem in Meta-Analysis

The classical F-test in the one-way random effects ANOVA model is extended to solve the long outstanding problem of testing the between-group variance on values also different from zero. This is done first for homoscedastic and heteroscedastic cases in not necessarily balanced models and secondly for balanced homoscedastic models. By simulation, the tests are shown to attain acceptable significance levels and high power even in data that do not follow the usual ANOVA model. An important application of the tests is given by the heterogeneity questions concerning the treatment effects across studies in meta-analysis.