The purpose of this study was to develop the Johnson-Neyman Procedure (JN-Procedure) appropriate to multiple groups and covariables, and demonstrate its use in the analysis of group differences. A sequence of significance tests which makes it possible to identify the most parsimonious analysis of group differences appropriate to a given set of data is presented. In addition, there is an orignial mathematical derivation of the JN-Procedure appropriate to multiple groups and covariates, and a demonstration of its superiority to ANCOVA when group regressions are heterogeneous. (Author)