A computational procedure devised to combine the virtues of the analysis of covariance technique and the Neyman-Johnson technique is outlined. The usual analysis of covariance procedure is carried out through the test of hypothesis B. If hypothesis B is rejected, one can: 1) continue to test for hypothesis C if a crude test of the significance of the difference in criterion scores is all that is needed; or 2) turn to the Neyman-Johnson "region of significance" if one is interested in refinement. A numerical example was chosen from the Veterans' Study. Regression planes were calculated for a group of male veterans and a group of male nonveterans at Miller University using ACPE scores and high school rank as predictors, and first year college average as the criterion. Analysis of covariance results are given. (SGK).