Comparison of aligned Friedman rank and parametric methods for testing interactions in split-plot designs

摘要

Parametric methods are commonly used despite evidence that model assumptions are often violated. Various statistical procedures have been suggested for analyzing data from multiple-group repeated measures (i,e., split-plot) designs when parametric model assumptions are violated (e.g., Akritas and Arnold (J. Amer. Statist. Assoc. 89 (1994) 336); Brunner and Langer (Biometrical J. 42 (2000) 663)), including the use of Friedman ranks. The effects of Friedman ranking on data and the resultant test statistics for single sample repeated measures designs have been examined (e.g., Hat-well and Serlin (Comput. Statist. Data Anal, 17 (1994) 35; Comm. Statist. Simulation Comput. 26 (1997) 605); Zimmerman and Zumbo (J. Experiment. Edue. 62 (1993) 75)). However, there have been fewer investigations concerning Friedman ranks applied to multiple groups of repeated measures data (e.g., Beasley (J. Educ. Behav. Statist, 25 (2000) 20); Rasmussen (British J. Math. Statist. Psych. 42 (1989) 91)). We investigate the use of Friedman ranks for testing the interaction in a split-plot design as a robust alternative to parametric procedures. We demonstrated that the presence of a repeated measures main effect may reduce the power of interaction tests performed on Friedman ranks. Aligning the data before applying Friedman ranks was shown to produce more statistical power than simply analyzing Friedman ranks. Results from a simulation study showed that aligning the data (i.e., removing main effects) before applying Friedman ranks and then performing either a univariate or multivariate test can provide more statistical power than parametric tests if the error distributions are skewed.