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A Brief Note on the Standard Error of the Pearson Correlation
[journal article]
Abstract 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... view more
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.... view less
Classification
Methods and Techniques of Data Collection and Data Analysis, Statistical Methods, Computer Methods
Free Keywords
correlation; sampling distribution; standard error; Pearson correlation
Document language
English
Publication Year
2023
Journal
Collabra: Psychology, 9 (2023) 1
ISSN
2474-7394
Status
Published Version; peer reviewed
Licence
Creative Commons - Attribution 4.0
FundingThe publication was supported by the Leibniz Association's Open Access Publishing Fund for articles in open access journals.