R help - Nov 2010 - Significance of the difference between two correlation coefficients

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

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Thanks for providing the example but it would be useful to know who I am 
communicating with or from which institute, but nevermind ...

I don't know much about this subject but a quick google search gives 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.

Regards, Adai



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
>

Adaikalavan Ramasamy wrote:
> 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 ){
> ...
William Revelle also mentioned the r.test in the psych package.

I would add here that inference on second-order quantities, such as
correlation coefficients and variances, is not robust to the assumption
of a normally-distributed population.  (Inference on first-order
quantities such as means and regression coefficients, IS pretty robust
to that assumption.) A good general alternative is the bootstrap,
implemented in R in the boot package.

Norm Matloff