COMPARING CORRELATED BUT NONOVERLAPPING CORRELATIONS

A common situation in psychological research involves the comparison o f two correlations on the same sample of subjects, in which the correl ations are nonoverlapping in the sense of having a variable in common (e.g., r(14) and r(23) rather than r(13) and r(12)). The classic stati stic for this situation is the Pearson-Filon statistic, (PF) which is based on the difference of rs. A much more accurate statistic is the v ersion of this statistic based on the difference of Fisher r-to-Z tran sformed rs, (ZPF). Both PF and ZPF involve an easily computed but visu ally unattractive expression for the large-N sampling correlation betw een the correlations and thus may not be especially easy to motivate o r teach. We develop a simple approximation that is simple to calculate and teach and therefore has pedagogical value. We also provide simula tion evidence to support the superiority of ZPF of PF with respect to both alpha level and power.