Exploratory research with large numbers of variables and even larger numbers of relationships is likely to result in frequent Type II errors; that is falsely accepting an incorrect null hypotheses. There are three ways of reducing Type II errors: (1) choosing a lower significance level, which then increases the probability of Type I error; (2) replicating the experiment, which is usually expensive; and (3) applying second-order significance tests. The procedures for applying second-order significance tests are described and exemplified by analysis of data from an aptitude-treatment interaction experiment. (CTM)