Comparing the Pearson and Spearman correlation coefficients across distributions and sample sizes: A tutorial using simulations and empirical data.

Abstract

The Pearson product–moment correlation coefficient () and the Spearman rank correlation coefficient () are widely used in psychological research. We compare and on 3 criteria: variability, bias with respect to the population value, and robustness to an outlier. Using simulations across low (N = 5) to high (N = 1,000) sample sizes we show that, for normally distributed variables, and have similar expected values but is more variable, especially when the correlation is strong. However, when the variables have high kurtosis, is more variable than . Next, we conducted a sampling study of a psychometric dataset featuring symmetrically distributed data with light tails, and of 2 Likert-type survey datasets, 1 with light-tailed and the other with heavy-tailed distributions. Consistent with the simulations, had lower variability than in the psychometric dataset. In the survey datasets with heavy-tailed variables in particular, had lower variability than , and often corresponded more accurately to the population Pearson correlation coefficient () than did. The simulations and the sampling studies showed that variability in terms of standard deviations can be reduced by about 20% by choosing instead of . In comparison, increasing the sample size by a factor of 2 results in a 41% reduction of the standard deviations of and . In conclusion, is suitable for light-tailed distributions, whereas is preferable when variables feature heavy-tailed distributions or when outliers are present, as is often the case in psychological research.

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