Power and robustness in product-moment correlation

Abstract

The power of statistical tests based on four popular product-moment correlation coefficients was examined when relatively small samples (10 ≤ N ≤ 100) are drawn from bivariate populations of several different distributional shapes. Analytical procedures for determining theoretical power under conditions of bivariate normality are presented for the Pearson (r[subscript p]), Spearman (r[subscript s]), point-biserial (r[subscript pb]), and phi (r[subscript fp]) coefficients. A monte carlo study supported previous conclusions that t as a test of H[subscript 0]: ρ=0, with r[subscript p] estimating ρ, is robust over a wide range of non-normality; however, frequent use of r[subscript s] leads to greater power under identical distributional assumption violations. The proportion of power due to Type III errors was also specified both analytically and empirically, and revealed the relative invulnerability of most statistical tests to directional misinterpretation.