Tests That are Robust against Variance Heterogeneity in k × 2 Designs with Unequal Cell Frequencies
- 1 June 1995
- journal article
- research article
- Published by SAGE Publications in Psychological Reports
- Vol. 76 (3) , 1011-1017
- https://doi.org/10.2466/pr0.1995.76.3.1011
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.Keywords
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