Bias and Precision of Measures of Association for a Fixed-Effect Multivariate Analysis of Variance Model

The sampling distributions of five popular measures of association with and without two bias adjusting methods were examined for the single factor fixed-effects multivariate analysis of variance model. The number of groups, sample sizes, number of outcomes, and the strength of association were manipulated. The results indicate that all five unadjusted measures of association can be extremely biased when sample sizes are small and the bias increases as the number of groups and outcome variables increase. The Tatsuoka (1973) adjustment procedure minimized the bias in a limited number of contexts, while the Serlin (1982) procedure provided an adequate adjustment for most contexts studied. The precision of both the adjusted and unadjusted effect-size measures was similar, with the Serlin approach having slightly better precision than the Tatsuoka procedure.