[R] significance test for difference of two correlations

[Viechtbauer Wolfgang (STAT)]

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