The well-known method of unweighted sums of squares (USSs) is examined using, as an example, a random two-way classification model with interaction. In particular, a better motivation is given to the association between the harmonic mean of the cell frequencies and the USSs. Furthermore, a procedure is developed for determining the adequacy of the USSs as approximate balanced analysis of variance (ANOVA) sums of squares. This procedure is easy to apply and provides a better insight into the effects of design and model's variance components on such an approximation. The proposed methodology can be extended to higher-order models and other types of sums of squares.