Directional Alternative Hypotheses in Data Homogeneity Analysis

This paper deals with the use of permutation tests in the analysis of data homogeneity. The proposed solution is based on a nonparametric approach that involves the use of a combined permutation test. The strategy corresponds to Pesarin’s Nonparametric Combination (NPC) method. This non-classical approach to statistical inference allows for the formulation of complex alternative hypotheses.

The paper presents a proposal for testing directional hypotheses based on data presented in contingency tables. The proposed method does not have the limitations of the chi-square test regarding the expected frequencies in the cells of the contingency table. Moreover, in the case of a permutation homogeneity test with complex directional alternative hypotheses, the interpretation of results is more detailed than in the chi-square homogeneity test.

A two-step algorithm of the complex permutation procedure is used to assess the overall achieved significance level (ASL). The applied nonparametric statistical inference procedure uses a combining function. A simulation study was conducted to determine the size and power of the test. A Monte Carlo simulation was used to compare the empirical power of tests with different forms of combining functions. The advantage of the proposed method is its applicability even for small sample sizes. The idea of the proposed method is illustrated using data from the European Social Survey (ESS) project.