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Power and Robustness in Product-Moment Correlation

University of South Florida

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 deter mining theoretical power under conditions of bivariate normality are presented for the Pearson (r_P), Spearman (r_s), point-biserial (r_pb), and phi (r_fp) coefficients. A monte carlo study supported previous conclusions that t as a test of H ₀: p = 0, with r_P estimating p, is robust over a wide range of non-normality; however, frequent use of r_s leads to greater power under identical distri butional 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.

Applied Psychological Measurement, Vol. 11, No. 4, 419-428 (1987)
DOI: 10.1177/014662168701100407


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