Nonparametric procedures for partially paired data in two groups

A fully nonparametric method is developed for comparing samples with partially paired data. Partially-paired (correlated) data naturally arise, for example, as a result of missing values, in incomplete block designs or meta analysis. In the nonparametric setup, treatment effects are characterized in terms of functionals of distribution functions and the only assumption needed is that the marginal distributions are non-degenerate. The setup accommodates binary, ordered categorical, discrete and continuous data in a seamless fashion. The use of nonparametric effects addresses the Behrens–Fisher problem from the nonparametric point of view and allows construction of confidence intervals. Although the nonparametric methods are mainly asymptotic, methods for small sample approximations are also proposed. Size and power simulation results show numerical evidence of favorable performance of the nonparametric methods. The new nonparametric method has overwhelming power advantage when treatment effects are in the shape of the distributions and they perform comparably well with parametric methods for location-type alternatives. Data from randomized trials in public health are used to illustrate the application of the method.