Significance test on the difference of two correlation coefficient

Question

How do you test if two correlation coefficients are signficantly different - in GNU R?

That is, if the effect between the same variables (e.g., age and income) is different in two different populations (subsamples).

For background information see How do I compare correlation coefficients of the same variables across different groups and Significance test on the difference of Spearman's correlation coefficient (both at CrossValidated).

Answer 1

Here is a ready-to-use function for GNU R if you want to compare multiple pairs of coefficients (based on Significance of the difference between two correlation coefficients and Quantitative Analysis and Politics, PDF):

cor.diff.test = function(r1, r2, n1, n2, alternative = c("two.sided", "less", "greater")) {

  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

  if (alternative == "less") {
    return(pnorm(diff.Z, lower.tail=F))
  } else if (alternative == "greater") {
    return(pnorm(-diff.Z, lower.tail=F))
  } else if (alternative == "two.sided") {
    return(2 * pnorm( abs(diff.Z), lower.tail=F))
  } else {
    warning(paste("Invalid alterantive", alternative), domain=NA)
    return(NA)
  }
}