The analysis of repeated measurements: A quantitative research synthesis

Abstract

Meta‐analytic methods were used to summarize the results of Monte Carlo studies investigating the Type I error and power properties of various univariate and multivariate procedures for testing within‐subjects effects in split‐plot repeated measures designs. Results indicated that all test procedures were generally robust to violations of the multivariate normality assumption, but varied in terms of their Type I error control when the sphericity assumption was not satisfied. For balanced designs, the usual F and ê adjusted F tests (Greenhouse & Geisser, 1959) were generally robust to moderate degrees of covariance heterogeneity, whereas the multivariate procedures were slightly more affected by departures from this assumption. When the design was unbalanced, however, all procedures were sensitive to the presence of heterogeneous covariance matrices, particularly when testing the within‐subjects interaction effect. Power rates varied little as a function of assumption violations. However, this finding may be due to the restricted range of many of the variables included in the meta‐analysis of the power data as well as the strong and overshadowing relationship between the degree of non‐centrality and power rates. For balanced designs, the use of either an ê‐adjusted univariate or a multivariate approach is recommended; for unbalanced designs, researchers should consider adopting one of several robust alternatives that have recently been suggested in the literature.