Abstract: We develop a robust inference for one-way repeated measures designs with multiple replications per cell assuming exchangeability of the err ors within each subject. R-estimators of the treatment effects are obtained by mini mizing a dispersion function. We develop asymptotically equivalent test procedures based on drop in dispersion, and two quadratics which depend on R-estimates and the gradient vector. Multiple comparison procedures are developed based on the R-estimators. Test results based on a baseball data set concerning three different base running methods are presented and compared with normal theory and Friedman rank sum techniques. Asymptotic relative efficiencies of the rank tests, with respect to the normal-theory counterpart, are discussed. Comparisons with alternative robust tests are also discussed. A small scale simulation study is conducted to investigate the small sample behavior of the rank-based tests.
Key words and phrases: Asymptotic linearity, dispersion function, multiple comparisons, R-estimates.