Analyzing Small Samples of Repeated Measures Data with the Mixed-Model Adjusted F Test

This research examines the Type I error rates obtained when using the mixed model with the Kenward-Roger correction and compares them with the Between–Within and Satterthwaite approaches in split-plot designs. A simulated study was conducted to generate repeated measures data with small samples under normal distribution conditions. The data were obtained via three covariance matrices (unstructured, heterogeneous first-order auto-regressive, and random coefficients), the one with the best fit being selected according to the Akaike criterion. The results of the simulation study showed the Kenward-Roger test to be more robust, particularly when the population covariance matrices were unstructured or heterogeneous first-order auto-regressive. The main contribution of this study lies in showing that the Kenward–Roger method corrects the liberal Type I error rates obtained with the Between–Within and Satterthwaite approaches, especially with positive pairings between group sizes and covariance matrices.