Statistical inference based on incomplete blocks designs

Abstract

In an earlier paper (Shane and Puri, 1969), the authors developed a class of asymptotically nonparametric tests for a bivariate paired comparison model. This paper unifies and complements the results of the previous paper by deriving a class of genuinely distribution free tests for the same problem but under the more general framework of $p(\ge2)$-­variate situations. This is done by exploiting the theory of permutation distribution under sign invariant transformations to a class of rank order statistics. Asymptotic properties of these permutation rank order tests are studied and certain stochastic equivalence relationship with a similar class of multisample extensions of the $p$-variate one sample rank order tests proposed by Sen and Puri (1967) are derived. The asymptotic power properties of these tests are also studied.