Calculation for the Test of the Difference

Between Two Dependent Correlations

with No Variable in Common

Between Two Dependent Correlations

with No Variable in Common

© 2010-2023,

Kristopher J. Preacher

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 X_{t1} and X_{t2} reflect two separate variables (as do Y_{t1} and Y_{t2}). 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.

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 (r_{jk} and r_{hm}), along with four other correlations from the matrix (r_{jh}, r_{jm}, r_{kh}, and r_{km}) 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.

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

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