The intent of the study was to determine the extent to which test statistics computed by the unweighted means analysis are F-distributed. Applicability criteria were sought in terms of the number of factor levels and the degree to which cell frequencies differ. The unweighted means analysis, a frequently used approximate analysis, was contrasted with three least squares solutions. Evidence was relatively strong in favor of a least squares analysis if one is to conduct a two-factor analysis of variance for fixed effects. However, results confirmed that the approximate solution can be used with some confidence on main effects but not interactions when cell frequencies do not differ by more than four to one and factors exist at no more than four levels. (Author)