Defining Johnson-Neyman Regions of Significance in the Three-Covariate ANCOVA Using Mathematica

The Johnson-Neyman ANCOVA, used when nonhomogeneity of within-group regressions is present, poses special computational and plotting problems when three covariates are used. These problems can be overcome by using (a) an appropriate design and contrast matrix for the general linear model and (b) the Mathematica software system of computation to handle the symbolic and graphical processing requirements. Four-dimensional graphical representation of the polynomials which result are contour plotted in a three-dimensional space in order to define the regions of significance for contrasts. It is also shown that for some values of the covariate orthogonal contrasts are produced.