Distribution-free tests for cluster samples of ordinal responses

Abstract

A simulation comparison is done of Mann–Whitney U test extensions recently proposed for simple cluster samples or for repeated ordinal responses. These are based on two approaches: the permutation approach of Fay and Gennings (four tests, two exact), and Edwardes’ approach (two asymptotic tests, one new). Edwardes’ approach permits confidence interval estimation, unlike the permutation approach. An appropriate parameter for estimation is P( X< Y)− P( X> Y), where X is the rank of a response from group 1 and Y is from group 2. The permutation tests are shown to be unsuitable for some survey data, since they are sensitive to a difference in cluster intra-correlations when there is no distribution difference between groups at the individual level. The exact permutation tests are of little use for less than seven clusters, precisely where they are most needed. Otherwise, the permutation tests perform well.