A Nonparametric Analogy of Analysis of Covariance

Abstract

A nonparametric test of the hypothesis of no treatment effect is suggested for a situation where measures of the severity of the condition treated can be obtained and ranked both pre- and post-treatment. The test allows use to be made of the pre-treatment rank as a "concomitant variable," and is based on the nature and degree of permutation of the post-treatment ranks relative to the pre-treatment ranks. Evidence is given which shows that the distribution of the suggested test statistic rapidly approaches the F distribution as the number of subjects is increased. For small samples, a randomization test may be performed.