# [R] Significance of the difference between two correlation coefficients

William Revelle lists at revelle.net
Tue Nov 30 02:48:34 CET 2010

```At 5:02 PM +0000 11/29/10, Adaikalavan Ramasamy wrote:
>Thanks for providing the example but it would be useful to know who
>I am communicating with or from which institute, but nevermind ...
>
>me the following site: http://davidmlane.com/hyperstat/A50760.html
>
>Using the info from that website, I can code up the following to
>give the two-tailed p-value of difference in correlations:
>
>  diff.corr <- function( r1, n1, r2, n2 ){
>
>    Z1 <- 0.5 * log( (1+r1)/(1-r1) )
>    Z2 <- 0.5 * log( (1+r2)/(1-r2) )
>
>    diff   <- Z1 - Z2
>    SEdiff <- sqrt( 1/(n1 - 3) + 1/(n2 - 3) )
>    diff.Z  <- diff/SEdiff
>
>    p <- 2*pnorm( abs(diff.Z), lower=F)
>    cat( "Two-tailed p-value", p , "\n" )
>  }
>
>  diff.corr( r1=0.5, n1=100, r2=0.40, n2=80 )
>  ## Two-tailed p-value 0.4103526
>
>  diff.corr( r1=0.1, n1=100, r2=-0.1, n2=80 )
>  ## Two-tailed p-value 0.1885966
>
>The p-value here is slightly different from the Vassar website
>because the website rounds it's "diff.Z" values to 2 digits.
>
>

See also r.test in the psych package which will test for the
difference between two independent correlations as well as the more
complicated case of two dependent correlations.

>  r.test(n=100,r12=.5,r34=.4, n2=80)
Correlation tests
Call:r.test(n = 100, r12 = 0.5, r34 = 0.4, n2 = 80)
Test of difference between two independent correlations
z value 0.82    with probability  0.41
>

r.test(n=100, .1,-.1,n2=80)

>  r.test(n=100, .1,-.1,n2=80)
Correlation tests
Call:r.test(n = 100, r12 = 0.1, r34 = -0.1, n2 = 80)
Test of difference between two independent correlations
z value 1.31    with probability  0.19
>

Bill

>
>On 29/11/2010 15:30, syrvn wrote:
>>
>>Hi,
>>
>>based on the sample size I want to calculate whether to correlation
>>coefficients are significantly different or not. I know that as a first step
>>both coefficients
>>have to be converted to z values using fisher's z transformation. I have
>>done this already but I dont know how to further proceed from there.
>>
>>unlike for correlation coefficients I know that the difference for z values
>>is mathematically defined but I do not know how to incorporate the sample
>>size.
>>
>>I found a couple of websites that provide that service but since I have huge
>>data sets I need to automate this procedure.
>>
>>(http://faculty.vassar.edu/lowry/rdiff.html)
>>
>>Can anyone help?
>>
>>Cheers,
>>syrvn
>>
>
>______________________________________________
>R-help at r-project.org mailing list
>https://stat.ethz.ch/mailman/listinfo/r-help