Presented and discussed in this paper is the use of dummy variable multiple regression techniques in the analysis of samples drawn from several related or dependent populations ordinarily appropriate for random effects and mixed effects two factor analysis of variances model with one observation per-cell or treatment combinations. Using the extra sum of squares principle the method develops necessary sums of squares, degrees of freedom and the F-ratios required test to the significance of factor level effects thereby helping resolve the problem of one observation per treatment combination, encountered in the usual two factor analysis of variance models with one observation per cell. The method provides estimates of the overall and factor mean effects comparable to those obtained with the two factor analysis of variance methods. In addition, the method also provides estimates of the total or absolute effects as well as the direct and indirect effects of the independent variables or factors on the dependent or criterion variable which are not ordinarily obtainable with the usual analysis of variance techniques. The proposed method is illustrated with some sample data and shown to compare favourably with the usual Friedman’s two-way analysis of variance test by ranks often used for the same purpose.