# [R] significance test for difference of two correlations

Viechtbauer Wolfgang (STAT) Wolfgang.Viechtbauer at STAT.unimaas.nl
Thu Jul 26 18:18:36 CEST 2007

```Let r_1 be the correlation between the two variables for the first group with n_1 subjects and let r_2 be the correlation for the second group with n_2 subjects. Then a simple way to test H0: rho_1 = rho_2 is to convert r_1 and r_2 via Fisher's variance stabilizing transformation ( z = 1/2 * ln[ (1+r)/(1-r)] ) and then calculate:

(z_1 - z_2) / sqrt( 1/(n_1 - 3) + 1/(n_2 - 3) )

which is (approximately) N(0,1) under H0. So, using alpha = .05, you can reject H0 if the absolute value of the test statistic above is larger than 1.96.

--
Wolfgang Viechtbauer
Department of Methodology and Statistics
University of Maastricht, The Netherlands
http://www.wvbauer.com/

----Original Message----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Timo Stolz Sent:
Thursday, July 26, 2007 16:13 To: r-help at stat.math.ethz.ch
Subject: [R] significance test for difference of two correlations

> Dear R users,
>
> how can I test, whether two correlations differ significantly. (I
> want to prove, that variables are correlated differently, depending
> on the group a person is in.)
>
> Greetings from Freiburg im Breisgau (Germany),
> Timo Stolz

```