The analysis of repeated measurements: a comparison of mixed-model satterthwaite f tests and a nonpooled adjusted degrees of freedom multivariate test

Abstract

Mixed-model analysis is the newest approach to the analysis of repeated measurements. The approach is supposed to be advantageous (i.e., efficient and powerful) because it allows users to model the covariance structure of their data prior to assessing treatment effects. The statistics for this method are based on an F-distribution with degrees of freedom often just approximated by the residual degrees of freedom. However, previous results indicated that these statistics can produce biased Type I error rates under conditions believed to characterize behavioral science research, This study investigates a more complex degrees of freedom method based on Satterthwaite's technique of matching moments. The resulting mixed-model F-tests are compared with a Welch-James-type test which has been found to be generally robust to assumption violations. Simulation results do not universally favor one approach over the other, although additional considerations are discussed outlining the relative merits of each approach.

Keywords:

• Repeated measurements
• Mixed-model analyses
• Welch-James adjusted-df test
• Unbalanced nonspherical designs