Improving Some Multiple Comparison Procedures

Alexander Felzenbaum, Sergiu Hart and Yosef Hochberg

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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."

AMS 1980 subject classifications: Primary 62F99, 62F25

Keywords: Generalized t-method, unbalanced designs, contrasts, orthogonal transformations