Power and Robustness in Product-Moment Correlation

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 condi...

Full description

Saved in:
Bibliographic Details
Published in:Applied psychological measurement 1987-12, Vol.11 (4), p.419-428
Main Author: Fowler, Robert L.
Format: Article
Language:English
Subjects:
Biological and medical sciences
Fundamental and applied biological sciences. Psychology
Psychology. Psychoanalysis. Psychiatry
Psychology. Psychophysiology
Psychometrics. Statistics. Methodology
Statistics. Mathematics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0146-6216
1552-3497
DOI:10.1177/014662168701100407