Improving Some Multiple Comparison Procedures

Abstract

Genizi and Hochberg (1978) recommended using Contrast Set Preserving (CSP) procedures in the class of $T(Q)$ procedures for multiple comparisons in general unbalanced designs based on partial results. They did not, however, propose a general method for selecting a specific CSP procedure, or for replacing a given non-CSP procedure with a better CSP one. In this work we identify a certain orthogonal transformation of non-CSP procedures into CSP ones and give a sufficient condition for the uniform dominance (shorter confidence intervals for all contrasts) of the latter over the former. Two important implications of the given condition are: (i) Applying the given transformation to Spjotvoll and Stoline's (1973) $T$'-procedure in any unbalanced ANOVA gives a uniformly improved procedure. (ii) In any arbitrary design, our transformation gives uniform improvement if the original procedure is "nearly CSP."