A Lattice-Based Approach to Matched Pairs

摘要

In a matched pairs statistical test, items in each given pair of n experimental units are randomly assigned to either the control or the treatment group. A randomization test can then be used to assess the efficacy of the treatment by computing the p-value of a certain test statistic. That is, we are interested in determining the probability, under the randomization assumption, of obtaining a value for the test, statistic at least as extreme as that observed. Exact calculation of this tail probability theoretically involves looking at 2~n possible interchanges of data values between treatment and control groups. We view this problem in terms of a certain (distributive) lattice. An algorithm for generating relevant values of the test statistic is based on studying the Hasse diagram of this lattice. A rooted spanning tree of the Hasse diagram is then used to guide the generation algorithm, which produces values of the test statistic in monotone order.