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
significance test for difference of two correlations
3 messages · Timo Stolz, Viechtbauer Wolfgang (STAT), Gabor Grothendieck
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
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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