| Abstract: | This paper is a continuation of one (1992) in which the author studied the paradoxes that can arise when a nonparametric statistical test is used to give an ordering of k samples and the subsets of those samples. This article characterizes the projection paradoxes that can occur when using contingency tables, complete block designs, and tests of dichotomous behaviour of several samples. This is done by examining the “dictionaries” of possible orderings of each of these procedures. Specifically, it is shown that contingency tables and complete block designs, like the Kruskal-Wallis nonparametric test on k samples, minimize the number and kinds of projection paradoxes that can occur; however, using a test of dichotomous behaviour of several samples does not. An analysis is given of two procedures used to determine the ordering of a pair of samples from a set of k samples. It is shown that these two procedures may not have anything in common. |
