Nonparametric Analysis of Covariance by Matching

The basic problem under consideration is the comparison of treatments with respect to a response Y when a covariable X is taken into account. Various methods involving matching may be regarded as compromises between the standard analysis of covariance and the standard analysis of independent matched pairs. First, there is no need to restrict attention to independent matched pairs, but rather all matched pairs may be incorporated. Then, if X is concomitant, that is, if its distribution is the same regardless of treatment, methods may be used which are based ultimately on randomization although in practice they are based on analysis of variance. When X is not concomitant, methods related to partial correlation (between Y and 'treatment', given X) are applicable. All methods considered may use either the actual magnitudes of Y or analogues of their ranks.