title: Tests that are robust against variance heterogeneity in k x 2 designs with unequal cell frequencies.
abstract: Heterogeneity of variance produces serious bias in conventional analysis of variance tests of significance when cell frequencies are unequal. Welch in 1938 and 1947 proposed an adjusted t test for the difference between two means when cell frequencies and population variances are both unequal. This article describes two ways to use the Welch t to evaluate the significance of the main effect for two treatments across k levels of a concomitant factor in a two-way design. Monte Carlo results document the bias in conventional analysis of variance tests and the stable and appropriately conservative results from applications of the Welch t to evaluation of treatment effects in the two-way design.
authors.affiliation: Department of Psychiatry and Behavioral Sciences, University of Texas Medical School, Houston 77225, USA.
authors.forename: J E
authors.initials: JE
authors.lastname: Overall
authors.forename: R S
authors.initials: RS
authors.lastname: Atlas
authors.forename: J M
authors.initials: JM
authors.lastname: Gibson
mesh_terms: D000704:Analysis of Variance; D015982:Bias; D002986:Clinical Trials as Topic / Q000706:statistics & numerical data*; D006801:Humans; D009010:Monte Carlo Method