Comparing Correlated but Nonoverlapping Correlations

Abstract

A common situation in psychological research involves the comparison of two correlations on the same sample of subjects, in which the correlations are nonoverlapping in the sense of having a variable in common (e.g., ru and r2) rather than r,3 and r,2). The classic statistic for this situation is the Pearson- Filon statistic, (PF) which is based on the difference of rs. A much more accurate statistic is the version of this statistic based on the difference of Fisher r-to-Z transformed rs, (ZPF). Both PF and ZPF involve an easily computed but visually unattractive expression for the large-N sampling correlation between the correlations and thus may not be especially easy to motivate or teach. We develop a simple approximation that is simple to calculate and teach and therefore has pedagogical value. We also provide simulation evidence to support the superiority of ZPF of PF with respect to both alpha level and power.