Comparison of Rank-Based Tests for Ordered Alternative Hypotheses in Randomized Complete Block Designs

Abstract

Nonparametric tests are useful when underlying distribution of a population is unknown or samplesize is quiet small to satisfy assumptions of a traditional F test. Nonparametric tests have a goodusage in a sample which consists of observations from various populations, as well. Randomizedblock designs are purposive when experimental subjects vary in natural heterogeneity.Nonparametric tests which are suitable for two-way ANOVA designs where the blocks containingobservations which follow an increasing or a decreasing trend are main focus of this study. Arecently proposed nonparametric test which was developed as an alternative to Jonckheere test ismodified for ordered alternative hypotheses in randomized complete block designs. Thismodification test and several nonparametric tests for detecting ordered alternative hypotheses inrandomized complete block designs are compared empirically in a broad set of Monte Carlosimulations under different conditions. A numerical example is provided to illustrate testprocedures. The modified test provides better performance than Jonckheere test in terms of typeI error and power values whereas Hollander test provides slightly better power values among theother test statistics. In terms of type I error values, it can be stated that the most conservative testis Jonckheere test whereas, estimated type 1 error values of the other test statistics are usuallycloser to nominal level of alpha.