This paper proposes and presents a method that would enable the use of dummy variable regression techniques for the analysis of sample data appropriate for analysis with the traditional one factor analysis of variance techniques with one, equal and unequal replications per treatment combination. The proposed method, applying the extra sum of squares principle develops F ratio-test statistics for testing the significance of factor effects in analysis of variance models. The method also shows how using the extra sum of squares principle builds more parsimonious explanatory models for dependent or criterion variables of interest. In addition, unlike the traditional approach with analysis of variance models, the proposed method easily enables the simultaneous estimation of total or absolute and the so-called direct and indirect effects of independent or explanatory variables on the dependent or criterion variables. The proposed methods are illustrated with some sample data and shown to yield essentially the same results as would the one factor analysis of variance techniques when the later methods are equally applicable.