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

• Published in: Biometrical journal Vol. 43; no. 2; pp. 135 - 146
• Main Authors: Hartung, Joachim, Makambi, Kepher Henry, Argaç, Dog̃an
• Format: Journal Article
• Language: English
• Published: Berlin WILEY-VCH Verlag Berlin GmbH 01.05.2001; WILEY‐VCH Verlag Berlin GmbH; Wiley-VCH
• Subjects: ANOVA F-test; Attained power; Attained significance level; Between-group variance; Exact sciences and technology; Linear inference, regression; Mathematics; Meta-analysis; Multivariate analysis; Probability and statistics; Random effects model; Risk difference; Sciences and techniques of general use; Statistics; F test; Data analysis; Covariance analysis; Meta analysis; Risk; Statistical estimation; Multivariate analysis; Variance analysis; Heteroscedasticity; Hypothesis test; Heterogeneity; One way analysis of variance; Random effect; Linear estimation; Sampling
• ISSN: 0323-3847; 1521-4036
• DOI: 10.1002/1521-4036(200105)43:2<135::AID-BIMJ135>3.0.CO;2-H

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.