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Estimation of the biserial correlation and its sampling variance for use in meta‐analysis
Author(s) -
Jacobs Perke,
Viechtbauer Wolfgang
Publication year - 2017
Publication title -
research synthesis methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.376
H-Index - 35
eISSN - 1759-2887
pISSN - 1759-2879
DOI - 10.1002/jrsm.1218
Subject(s) - statistics , variance (accounting) , correlation coefficient , correlation , mathematics , sampling (signal processing) , pearson product moment correlation coefficient , range (aeronautics) , fisher transformation , meta analysis , moment (physics) , econometrics , computer science , accounting , medicine , geometry , physics , filter (signal processing) , classical mechanics , business , composite material , computer vision , materials science
Meta‐analyses are often used to synthesize the findings of studies examining the correlational relationship between two continuous variables. When only dichotomous measurements are available for one of the two variables, the biserial correlation coefficient can be used to estimate the product–moment correlation between the two underlying continuous variables. Unlike the point‐biserial correlation coefficient, biserial correlation coefficients can therefore be integrated with product–moment correlation coefficients in the same meta‐analysis. The present article describes the estimation of the biserial correlation coefficient for meta‐analytic purposes and reports simulation results comparing different methods for estimating the coefficient's sampling variance. The findings indicate that commonly employed methods yield inconsistent estimates of the sampling variance across a broad range of research situations. In contrast, consistent estimates can be obtained using two methods that appear to be unknown in the meta‐analytic literature. A variance‐stabilizing transformation for the biserial correlation coefficient is described that allows for the construction of confidence intervals for individual coefficients with close to nominal coverage probabilities in most of the examined conditions. Copyright © 2016 John Wiley & Sons, Ltd.