One of the greatest source of value of research results is variance control attainable by applying a principle code-named “MAXMINCOM”. This principle has three components: Maximization of systematic or desirable variance, minimization of error variance and control of variance arising from the effect of unwanted variables, generally called extraneous variables. When the extraneous or nuisance variables can be removed, the research design takes care of that. When such complete removal of the influence of such extraneous variable is not possible or difficult, such variable are deliberately included so that their influences are considered part of the study. Their influences are removed by partialing out the variance attributed to such variables, from the total variance. Analysis of covariance is one of the statistical analysis techniques that is utilized to accomplish this purpose. Many of the reported application of analysis of covariance have one factor with two levels and one covariate. This has caused so many researchers to think that this is a general rule. When there are more than two levels of a factor for instance; A1, A2, A3, you find the pairs A1 and A2, A1 and A3, A2, and A3, for three different hypotheses. If the aim from the beginning is to compare the treatment effect of A1, A2, and A3, then this can be handled on one single analysis with an appropriate post-hoc-test that can only be applied after the observed mean values for A1, A2, and A3, have been adjusted for the effect of the covariate(s). There has been sharp protest from students’ project supervisors and even external examiners when students take the three levels or more of the factor e.g teaching methods, together, carry out an adjustment of treatment means and applying post-hoc test on adjusted means. Students who carryout such proper procedures have been denied graduation, down-graded and sometimes made to re-analyze and interpret the results for such pairs as different hypotheses. The vehemence with which this rejection of the legitimate procedure is done, necessitated this paper. The purpose was therefore to provide theoretical justification of such detailed analysis, to save mainly the students’ who are the victims of the ignorance of the power of ANCOVA and a clarification for project supervisors, examiners and data analysists, that are confronted or consulted with data from such students and researchers.