Studentized maximum root procedures for coherent analyses of two-factor fixed-effects designs.

Abstract

The authors provide generalizations of R. J. Boik's (1993) studentized maximum root (SMR) procedure that allow for simultaneous inference on families of product contrasts including simple effect contrasts and differences among simple effect contrasts in coherent analyses of data from 2-factor fixed-effects designs. Unlike the F-based simultaneous test procedures (STPs) proposed by M. A. Betz and K. R. Gabriel (1978) for coherent analyses allowing for inferences on all factorial contrasts, SMR STPs are designed for analyses where each contrast of interest is a product contrast, which is usually the case in analyses of data from factorial experiments. When both factors have more than 2 levels, SMR STPs always provide more power and precision than F STPs for inferences on product contrasts.