The problem of spurious significance in multivariate exploratory research is discussed. When a very large number of statistical tests are performed, many tests will be significant on the basis of chance alone. To counter this problem, the use of two sign tests to analyze sets of results has been suggested; the chance expectation [CE test] assesses whether the number of obtained significant results exceeds the average number of significant results expected on the basis of chance, and the nonchance expectation [NCE test] assesses whether the number of significant results is highly improbable. The characteristics (Type I error rate and statistical power) of these two tests were studied using computer simulation procedures. Application of the CE and NCE tests was found to be reasonable for large sets of results, regardless of the dependence among results: On the basis of the simulation results, specific recommendations for application of the two tests have been proposed. If these tests identify a significant set of results, then they can be applied to smaller and smaller subsets of the results in order to identify the most likely sources of valid relationships. Example applications of the tests to five educational research investigations are given. (Author/CTM)