A Brief Note on the Standard Error of the Pearson Correlation

The product-moment correlation is a central statistic in psychological research including meta-analysis. Unfortunately, it has a rather complex sampling distribution which leads to sample correlations that are biased indicators of the respective population correlations. Moreover, there seems to be s...

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Bibliographic Details
Published in:Collabra. Psychology 2023-09, Vol.9 (1)
Main Author: Gnambs, Timo
Format: Article
Language:English
Subjects:
Correlation (Statistics)
Meta-analysis
Methods
Psychological research
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Summary:The product-moment correlation is a central statistic in psychological research including meta-analysis. Unfortunately, it has a rather complex sampling distribution which leads to sample correlations that are biased indicators of the respective population correlations. Moreover, there seems to be some uncertainty on how to properly calculate the standard error of these correlations. Because no simple analytical solution exists, several approximations have been previously introduced. This note aims to briefly summarize 10 different ways to calculate the standard error of the Pearson correlation. Moreover, a simulation study on the accuracy of these estimators compared their relative percentage biases for different population correlations and sample sizes. The results showed that all estimators were largely unbiased for sample sizes of at least 40. For smaller samples, a simple approximation by Bonett (2008) led to the least biased results. Based on these results, it is recommended to use the expression (1−r2)/N−3 for the calculation of the standard error of the Pearson correlation.
ISSN:2474-7394
2474-7394
DOI:10.1525/collabra.87615