The Analysis of Repeated Measurements with Mixed-Model Adjusted F Tests

• Published in: Educational and psychological measurement Vol. 64; no. 2; pp. 224 - 242
• Main Authors: Kowalchuk, Rhonda K., Keselman, H. J., Algina, James, Wolfinger, Russell D.
• Format: Journal Article
• Language: English
• Published: London SAGE Publications 01.04.2004; Thousand Oaks, CA Sage Publications; New Delhi Sage; SAGE PUBLICATIONS, INC
• Subjects: Analysis; Biological and medical sciences; Error of Measurement; Evaluation Methods; Fundamental and applied biological sciences. Psychology; Interaction; Psychological tests; Psychology. Psychoanalysis. Psychiatry; Psychology. Psychophysiology; Psychometrics. Statistics. Methodology; Sample Size; Statistical Analysis; Statistics. Mathematics; Unbalanced Designs; Weights & measures; small sample settings; Welch-James adjusted-df test; Kenward-Roger’s adjusted-df test; mixed-model analyses; repeated measurements; Statistical method; Significance test; Repeated measurement; Statistical test; Sample size
• ISSN: 0013-1644; 1552-3888
• DOI: 10.1177/0013164403260196

One approach to the analysis of repeated measures data allows researchers to model the covariance structure of their data rather than presume a certain structure, as is the case with conventional univariate and multivariate test statistics. This mixed-model approach, available through SAS PROC MIXED, was compared to a Welch-James type statistic. The Welch-James approach is known to provide generally robust tests of treatment effects in a repeated measures between-by within-subjects design under assumption violations given certain sample size requirements. The mixed-model F tests were based on Kenward-Roger’s adjusted degrees of freedom solution, an approach specifically proposed for small sample settings. The authors investigated Type I error control for repeated measures main and interaction effects in unbalanced designs when normality and covariance homogeneity assumptions did not hold. The mixed-model Kenward-Roger’s adjusted F tests showed superior Type I error control in small sample size conditions in which the Welch-James type statistic was nonrobust; power rates, however, did not favor one approach over the other.