Calculation for the Test of the Difference
Between Two Dependent Correlations
with No Variable in Common
Kristopher J. Preacher

Calculation for the test of the difference between two dependent correlations with no variable in common
Ihno A. Lee (Stanford University)
Kristopher J. Preacher (Vanderbilt University)

This web utility may be cited in APA style in the following manner:

Lee, I. A., & Preacher, K. J. (2013, October). Calculation for the test of the difference between two dependent correlations with no variable in common [Computer software]. Available from http://quantpsy.org.

This interactive calculator yields the result of a test of the equality of two correlation coefficients obtained from the same sample, with the two correlations sharing no variable in common. For example, this would include testing correlations between X and Y at times 1 and 2, where Xt1 and Xt2 reflect two separate variables (as do Yt1 and Yt2). The result is a z-score which may be compared in a 1-tailed or 2-tailed fashion to the unit normal distribution. By convention, values greater than |1.96| are considered significant if a 2-tailed test is performed.

How it's done

First, each correlation coefficient is converted into a z-score using Fisher's r-to-z transformation. Then, we make use of Steiger's (1980) Equations 2 and 11 to compute the asymptotic covariance of the estimates. These quantities are used in an asymptotic z-test.

Enter the two correlation coefficients to be compared (rjk and rhm), along with four other correlations from the matrix (rjh, rjm, rkh, and rkm) and the sample size, into the boxes below. Then click on "calculate." The p-values associated with both a 1-tailed and 2-tailed test will be displayed in the "p" boxes.

 r n Output: rjk: z-score: rhm: 1-tail p: rjh: 2-tail p: rjm: rkh: rkm: Status:

References

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

Acknowledgments

Original version posted October, 2013. Free JavaScripts provided by The JavaScript Source and John C. Pezzullo.