A Comparison between the LEHMACHER & WALL Rank Tests and Pyhel's Permutation Test for the Analysis of r Independent Samples of Response Curves

Abstract

Key words : Rank test, response curves, Pyhel-permutation t s t , split-plot design. Int,roductionNonparametric solutions for the problem of comparing r independent samples of response profiles are mostly based on some rank transformations of the original data either using complete rankings of the first or second order differences of the response curves or block rankings of the original profiles (KRAUTH 1973 (1981) give a method t o perform permutation tests of interaction -and (simple) main effects 8s well 8s aposteriori (pairwise) comparisons using HOLM'S (1979) sequential procedure. The test statistics for the split-plot design are derived by using intuitive arguments along the lines of HOEFFDING (1952), but can a180 he given a theoretically satisfying characterization as maxima invariants (PYHEL 1978). These permutation tests, like the ANOVA P-tests, also have the property of testing each interaction or main effect irrespective of all other effects in the design. The test statistics are listed in table 1. The groups of admissible permutations of the observations under the respective null hypothesis are summarized, too.As usual, r independent samples (plot factor) of sizes n,,, h = 1 , . . . , r of response profiles i = l , , .