D. Robinson and J. Levin (1997) proposed what they called a two-step procedure for analyzing statistical data in which researchers first evaluate the probability of an observed effect statistically (i.e., statistical significance), and, if and only if, it can be concluded that the underlying finding is too improbable to be due to chance, then they assess its magnitude or effect size (practical significance). This technique is extremely useful when conducting null hypothesis significance tests that have sufficient statistical power. However, if statistical power is lacking, then the first step, which serves as the "gatekeeper" for computing effect sizes, may lead to the nonreporting of a nontrival effect. When multiple tests of statistical significance are conducted, adjustments for inflated Type I error rates should be made to ensure that the actual error rate does not exceed its nominal value. Unfortunately, when multiple tests are undertaken with an adjusted alpha, the statistical power of any particular test is lowered. This paper expands on the Robinson and Levin model by proposing a three-step procedure when five or more hypothesis tests are of interest within the same experiment. In this case, the third step involves the use of a binomial test of result direction (including confidence intervals and effect sizes) to determine whether the number of results falling in a certain direction represents chance by assuming that the probability of any particular result direction is 0.5 under the null hypothesis. (Contains 1 figure, 2 tables, and 85 references.) (Author/SLD)