Multiple Comparisons in Higher Dimensional Designs

Abstract

Several explications of multiple comparisons are available for the usual one-way analysis of variance (ANOVA) situation; Miller's (1966) text might be the most definitive. Most standard texts on statistical analysis typically present one.or more methods for the one-way ANOVA situation. A presentation of multiple comparisons in a regression framework was made by Williams (1976) wherein most of the more common multiple comparison procedures were considered.
For research situations more complex than the simple one-way ANOVA, most texts are silent. This silence is understandable; the issues, equations and other considerations become much more complex. Further, if the uncertainties of two or more issues are compounded, the morass of detail can be more than most authors wish to attempt a resolution for general readership. Winer (1971) presents some detail for more complex research situations that might shed light on the reluctance of traditional researchers to address the issue. The computations are often sufficient to ward off all but the most hardy. Perhaps the lack of writing regarding multiple comparisons in more complex situations than one-way ANOVA should serve as a warning, but "fools rush in where angels fear to tread"; lacking wings, we'll rush right in.