Z_{H}: An updated version of Steiger's Z and web-based calculator for testing the statistical significance of the difference between dependent correlations

This calculator is used to calculate the difference between dependent correlations, or correlations that involve a common variable. For example, you could use this calculator to determine whether the correlation between GPA and Verbal IQ (r_{1}) is higher than the correlation between GPA and Non-verbal IQ (r_{2}). In this example, you would also need a third correlation (r_{3}), which though not of interest to the research question, statistically restricts the level of deviation between the other two correlations and needs to be accounted for. You would not use this calculator if the two correlations you wish to compare fail to share a common measure. For example, you would use a Significance Test for the Difference between Two INDEPENDENT Correlations if you wanted to compare the correlation between one pair of variables (SAT scores and Verbal IQ) with the correlation between a completely different pair of variables (GPA and Non-verbal IQ).

This calculator is adapted from formulas presented by Steiger (1980). Specifically, I use the formula for "Z one star bar" or Z_{1}^{*}. The calculations are complex but follow Steiger's sample "Case A" on p. 249, with two minor exceptions. One, there is a typo in part of the article's example. Using Steiger's calculations, the solution for s_{31.32} (which I refer to as s in my calculations) should have been .0042, not .042 (p. 249, left column, middle). Two, the provided formula for calculating r uses simple averaging [.5(r_{1}+r_{2})]. To yield a more accurate indicator of r, I have used Fisher's r-to-Z tranformation, averaged, and reversed back from Z-to-r. Nonetheless, the computation of s in the Z_{1}^{*} formula is relatively robust against minor deviations. In using this calculator, you are responsible for hand-checking all calculations.

Steiger, J. H. (1980). Tests for comparing elements of a correlation matrix. Psychological Bulletin, 87, 245-251.

Hoerger, M. (2013). Z_{H}: An updated version of Steiger's Z and web-based calculator for testing the statistical significance of the difference between dependent correlations. Retrieved from http://www.psychmike.com/dependent_correlations.php