Although analysis of variance is the most popular statistical tool to researchers in the behavioral sciences, the casual user has recognized only recently that there is no single correct way to perform such an analysis. This paper is concerned with hypotheses tested in the two-way, fixed model under a variety of conditions: (1) with and without restrictions, and (2) with unbalanced, proportional and balanced cell frequencies. Standard texts and canned computer programs are surveyed and their recommendations are expressed in a common notation. Recommendations based on these results are given, along with the rationale for the recommendations. (Author)