Three criticisms of overreliance on results from statistical significance tests are noted. It is suggested that: (1) statistical significance tests are often tautological; (2) some uses can involve comparisons that are not completely sensible; and (3) using statistical significance tests to evaluate both methodological assumptions (e.g., the homogeneity of variance or of regression assumptions) and substantive hypotheses creates inescapable dilemmas. Three strategies for augmenting statistical significance testing are elaborated. First, a review of effect sizes is presented. Second, a method for evaluating statistical significance in a sample size context is discussed. Finally, strategies for empirically evaluating whether results will replicate are reviewed, with an emphasis on explaining one computer-intensive resampling strategy (the bootstrap method). It is inconsistent to use sample results to estimate population values, but to be unwilling to consult the sample to estimate the variability and shape of samples drawn from the population. Three tables and one figure illustrate the discussion, and a 79-item list of references is included. (Author/SLD)