Are alternative variables in a set differently associated with a target variable? Statistical tests and practical advice for dealing with dependent correlations.

The analysis of multiple bivariate correlations is often carried out by conducting simple tests to check whether each of them is significantly different from zero. In addition, pairwise differences are often judged by eye or by comparing the p-values of the individual tests of significance despite the existence of statistical tests for differences between correlations. This paper uses simulation methods to assess the accuracy (empirical Type I error rate), power, and robustness of 10 tests designed to check the significance of the difference between two dependent correlations with overlapping variables (i.e., the correlation between X₁ and Y and the correlation between X₂ and Y). Five of the tests turned out to be inadvisable because their empirical Type I error rates under normality differ greatly from the nominal alpha level of .05 either across the board or within certain sub-ranges of the parameter space. The remaining five tests were acceptable and their merits were similar in terms of all comparison criteria, although none of them was robust across all forms of non-normality explored in the study. Practical recommendations are given for the choice of a statistical test to compare dependent correlations with overlapping variables.