A general approach to stepup multiple test procedures for free-combinations families

• Published in: Journal of statistical planning and inference Vol. 82; no. 1; pp. 35 - 54
• Main Authors: Grechanovsky, Eugene, Pinsker, Ilia
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Lausanne Elsevier B.V 01.12.1999; New York,NY Elsevier Science; Amsterdam
• Subjects: Applications; Approximate critical values; Biology, psychology, social sciences; Comparative powers; Exact sciences and technology; General test algorithm; Mathematics; Multivariate analysis; Nonparametric inference; Probability and statistics; Procedural p-values; Sciences and techniques of general use; Statistics; Stepup tests; 62J15; General test algorithm; Approximate critical values; Procedural p-values; Comparative powers; Stepup tests; Biometrics; Hypothesis test; Data analysis; Error estimation; Error rate; Multivariate analysis; Algorithm
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/S0378-3758(99)00030-0

Dunnett and Tamhane (1992, J. Amer. Statist. Assoc. 87, 162–170) proposed a stepup multiple test procedure for simultaneous testing of k hypotheses satisfying the free-combinations condition under the normal setup in the equicorrelated case and later extended it for the non-equicorrelated case (1995, Biometrics, 51, 217–227). However, our counterexample shows that the last one does not control the familywise error rate. We suggest a new approach to constructing stepup procedures which yields as particular cases the procedures by Hochberg (1988, Biometrika, 75, 800–802), Rom (1990, Biometrika, 77, 663–665) and Dunnett and Tamhane (1992) though not by Dunnett and Tamhane (1995). Furthermore, using this approach we develop a stepup test procedure for the non-equicorrelated case that generalizes the Dunnett and Tamhane (1992) procedure but differs from the Dunnett and Tamhane (1995) one. A new test algorithm for the generalized procedure has no break rules and in general makes k tests associated with k nodes on the graph of subset intersection hypotheses whose positions are dictated by the observations. Under the normality assumption, we suggest approximations for sharp critical values and for p-values. The performance of the procedure is illustrated by examples.