A test for serial correlation in univariate repeated-measures analysis

A popular design in biostatistics and psychometrics is the time-factor experiment involving one grouping factor, e.g. treatment or drug, and one repeated-measures factor, e.g. time or visit. If F tests involving the repeated-measures factor are to be valid, univariate analytic procedures require special assumptions for covariance matrices across groups. The robustness of these univariate procedures is investigated when the covariance matrices do not satisfy these assumptions but have a frequently occurring form, namely the serial correlation or simplex pattern. A table is presented which shows that, for some matrices that fit the pattern, the main-effect repeated-measures estimated actual probability level is more than three times the .05 nominal level. A likelihood ratio test for the serial correlation pattern is presented, along with an example from the field of biostatistics.