Abstract: In this article, we use the bootstrap to estimate the power of a distribution-free rank test introduced by Mack and Skillings (1980) for the hypothesis of no treatment effect in a randomized block design, or a two-way analysis of variance model with no interaction. Since ties affect the distribution of rank tests and because the sample size in each cell is usually too small, the resampling must be done from a smoothed version of the empirical distribution function of residuals. The theory will show that the type of smoothing is crucial to attain asymptotic consistency under local alternatives. A small sample simulation shows that a particular implementation of the bootstrap does well.
Key words and phrases: Kernel estimates, sample size determination, testing in two-way ANOVA, rank test, smooth bootstrap, Friedman test, power estimation.