两个相关系数差异的显著性检验

Question

在GNU R中，如何测试两个相关系数是否有显著不同？

也就是说，如果相同变量(例如，年龄和收入)之间的影响在两个不同的总体(子样本)中不同。

有关背景信息，请参阅How do I compare correlation coefficients of the same variables across different groups和Significance test on the difference of Spearman's correlation coefficient (均位于CrossValidated)。

Answer 1

如果您想要比较多对系数(基于Significance of the difference between two correlation coefficients和Quantitative Analysis and Politics, PDF)，下面是一个适用于GNU R的现成函数：

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)
  }
}

Answer 2

cocor包提供了测试两个独立的或相关的相关系数是否显著不同的函数。还有一个可用于软件包的web界面：http://comparingcorrelations.org