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

The Pearson product-moment correlation coefficient (r_p) and the Spearman rank correlation coefficient (r_s) are widely used in psychological research. We compare r_p and r_s 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, r_p and r_s have similar expected values but r_s is more variable, especially when the correlation is strong. However, when the variables have high kurtosis, r_p is more variable than r_s. 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, r_p had lower variability than rs in the psychometric dataset. In the survey datasets with heavy-tailed variables in particular, r_s had lower variability than r_p, and often corresponded more accurately to the population Pearson correlation coefficient (R_p) than r_p did. The simulations and the sampling studies showed that variability in terms of standard deviations can be reduced by about 20% by choosing r_s instead of r_p. In comparison, increasing the sample size by a factor of 2 results in a 41% reduction of the standard deviations of r_s and r_p. In conclusion, r_p is suitable for light-tailed distributions, whereas r_s is preferable when variables feature heavy-tailed distributions or when outliers are present, as is often the case in psychological research.