On rank transformation techniques for balanced incomplete repeated-measures designs

Asymptotic properties of statistics designed to detect general alternatives in compound symmetric balanced incomplete repeated-measures designs with fixed treatment effects are investigated. Included in this study are the analysis of variance (ANOVA) F statistic, its rank transform, and Durbin's statistic. By making asymptotic relative efficiency comparisions among these statistics when they have been computed with and without mean alignment, valuable new insight into their large-sample performance characteristics is gained. Evidence is presented corroborating recent empirical studies that suggest that mean alignment can improve the performance of rank transformation statistics. Finally, it is noted that the rank transform of the ANOVA F statistic when it is computed using mean aligned data is generally the most efficient among the statistics studied here.