The relationship between analysis of variance (ANOVA) methods and their analogs (analysis of covariance and multiple analyses of variance and covariance--collectively referred to as OVA methods) and the more general analytic case is explored. A small heuristic data set is used, with a hypothetical sample of 20 subjects, randomly assigned to five conditions of exposure to an experimental instructional method. Students were also grouped into high or low ability levels. The data illustrate that: (1) regression approaches to ANOVA can be superior to classical ANOVA with respect to statistical power against Type II error; and (2) classical regression analysis can be used to test hypotheses typically but incorrectly associated only with ANOVA, such as polynomial trend and interaction hypotheses. Unlike OVA methods, which require that the researcher discard information by converting all dependent variables to the nominal level of scale, classical regression methods do not require that predictors be nominally scaled. Thus, when researchers have data including higher than normally scaled predictors, regression can yield results that more accurately reflect the reality that the researcher purportedly wishes to study. Nine tables and one graph illustrate the data. Control cards for a computer program are appended. (Author/SLD)