The Coefficients of a Maximum Contrast as Interpretable Statistics.

A fundamental fact of the analysis of variance statistical procedure is that if the omnibus F test of an effect is significant, then there exists at least one contrast of that effect that will be significantly different from zero according to the S-method of Scheffe. The caveat to this rule is that the significant contrast(s) may not be of any interest to or interpretable by the investigator. Frustration does arise when the investigator determines the omnibus F test to be significant and then fails to find any meaningful group comparisons to be significant. The purpose of this paper is to discuss the coefficients of a contrast which will yield the largest test statistic according to the S-method. Then according to the fundamental theorem, this contrast will be significantly different from zero and, additionally, should offer the investigator some assistance in developing a parsimonious interpretation of the data. The S-method is a post-hoc method of comparing experimental groups and is often referred to as a data-snooping or sifting device. The techniques discussed here are also of the data-snooping species and may be employed to generate new hypotheses or to amend the existing theory of a practical problem. (Author/CTM)