Determining the Most Significant Parametric Function for a Given Linear Hypothesis

Abstract

After a hypothesis about some linear statistical model has been tested and rejected (e.g., in an ANOVA), many researchers employ the Scheffe procedure to locate the source(s) of the rejection. This procedure guarantees that there is at least one linear combination of the model parameters (consistent with the hypothesis) that is significantly different from its hypothesized value. This most significant parametric function is not always easy to find, however, because it may not manifest itself in simple functions (such as pairwise contrasts between groups) or in “obvious” functions (such as those suggested by the graph of an interaction). A general solution to this problem is presented along with a practical example of its application.