A Note on Optimality of Certain Rank Tests for Ordered Alternatives in Randomized Blocks

Nonparametric tests for ordered alternatives in randomised block designs based on within block rankings have been proposed by many authors. This note is concerned with the optimality of the choice of so-called regression constants usually considered in such rank tests. Some examples are discussed.     

Non-Parametric Methods for the 2-Period-Cross-Over Design Under Weak Model Assumptions

A nonparametric analysis for the two period cross-over design has first been suggested by Koch (1972) and has been discussed by Hills and Armitage (1979). As known rank tests on sums or differences of the data are applied in this procedure, the results on the one hand are not invariant under monotonous transformations and on the other hand the procedure is only correct for models with additive effects. Therefore, in the present article generalized effects will first be defined in the 2-period cross-over design without the assumption of a linear model and then rank test will be presented which test tese effects without the need of sums or differences of the data. In the appendix the equivalence of the hypothesis for the generalized effects to the known hypotheses for the effects in the linear model will be shown. The application of the procedures will be demonstrated by means of an example in literature.     

Rank Tests for the 2×2 Design with I Blocks

In this paper we suggest rank tests for main effects and for interaction when there are two factors and two levels within each factor and when, in addition, there are I blocks. The asymptotic distributions of the test statistics under H₀ are derived. The application of the tests is illustrated by an example and a simulation study investigates size and power of the tests.     

The Effect of Categorization on a Simple Analysis of Variance Model

Many statistical procedures assume a continuous model in spite of the fact that observations are necessarily discrete. Here we consider a simple ANOVA model—one factor with fixed effects—and assess the effect of categorisation by simulating sizes and calculating asymptotic relative efficiencies. Even for severe categorisation the effects are small.     

Asymptotic Efficiency of the Chi-Square Test for Heterogeneity of Proportions in Some Sparse-Data Cases

We consider the problem of testing for heterogeneity of K proportions when K is not small and the binomial sample sizes may not be large. We assume that the binomial proportions are normally distributed with variance σ². The asymptotic relative efficiency (ARE) of the usual chi-square test is found relative to the likelihood-based tests for σ²=0. The chi-square test is found to have ARE = 1 when the binomial sample sizes are all equal and high relative efficiency for other cases. The efficiency is low only in cases where there is insufficient data to use the chi-square test.