Orthogonal Comparisons: A Teaching Example

Abstract

When the omnibus one-way Analysis or Variance (ANOVA) is found to be significant, the research question that "at least two populations have different means" can be accepted, but is found to be lacking. (What most textbooks fail to mention is that this means that the one-way ANOVA question is a fruitless question.) Most textbooks turn to post-hoc analyses as a way to determine "where the significance is." But that Journey is often muddled by: a) discussion of a myriad of post-hoc procedures, b) insufficient parallel examples, c) downplay of the value of planned comparisons, and d) failure to tie orthogonal comparisons to the two-way ANOVA. This paper will attempt to alleviate the above issues, with various examples of four groups.