Estimation of the simple correlation coefficient

Gwowen Shieh*

*Corresponding author for this work

Research output: Contribution to journalArticle

16 Scopus citations

Abstract

This article investigates some unfamiliar properties of the Pearson product-moment correlation coefficient for the estimation of simple correlation coefficient. Although Pearson's r is biased, except for limited situations, and the minimum variance unbiased estimator has been proposed in the literature, researchers routinely employ the sample correlation coefficient in their practical applications, because of its simplicity and popularity. In order to support such practice, this study examines the mean squared errors of r and several prominent formulas. The results reveal specific situations in which the sample correlation coefficient performs better than the unbiased and nearly unbiased estimators, facilitating recommendation of r as an effect size index for the strength of linear association between two variables. In addition, related issues of estimating the squared simple correlation coefficient are also considered.

Original languageEnglish
Pages (from-to)906-917
Number of pages12
JournalBehavior Research Methods
Volume42
Issue number4
DOIs
StatePublished - 1 Nov 2010

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