[R] significance test for difference of two correlations

Gabor Grothendieck ggrothendieck at gmail.com
Thu Jul 26 18:38:00 CEST 2007

```There is R code for both the Fisher transform and the corresponding bootstrap
procedure in the vignette for the proto package:
http://cran.r-project.org/doc/vignettes/proto/proto.pdf

On 7/26/07, Viechtbauer Wolfgang (STAT)
<Wolfgang.Viechtbauer at stat.unimaas.nl> wrote:
> 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
>
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