A rank-based goodness-of-fit approach to testing for non-additivity in the two-way layout with no replications

Abstract

One of the major problems for which satisfactory small-sample rank-based test procedures are only recently being developed is that of evaluating the possible presence of interaction in the standard two-way layout. This is especially true when there is only one observation on each treatment-block combination. In this paper we take a goodness-of-fit approach to this problem using the idea of grouping “similar” block rank permutations to obtain a workable number of collapsed categories. This grouping is based on the concepts of decomposable and indecomposable classes of rank vectors considered by Comtet (C.R. Acad. Sci. Paris 275 (1972) 569; in Advanced Combinatorics: the Art of Finite and Infinite Expansions, D. Reidel, Boston, 1974, p. 262). Alignment within treatment levels is utilized to adjust for the possible presence of treatment effects prior to the application of the goodness-of-fit procedure to test for interaction. We present the results of a substantial Monte Carlo simulation power study of the proposed procedure.