title: 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 (rp) and the Spearman rank correlation coefficient (rs) are widely used in psychological research. We comparerpandrson 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,rpandrshave similar expected values butrsis more variable, especially when the correlation is strong. However, when the variables have high kurtosis,rpis more variable thanrs. 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,rphad lower variability thanrsin the psychometric dataset. In the survey datasets with heavy-tailed variables in particular,rshad lower variability thanrp, and often corresponded more accurately to the population Pearson correlation coefficient (Rp) thanrpdid. The simulations and the sampling studies showed that variability in terms of standard deviations can be reduced by about 20% by choosingrsinstead ofrp. In comparison, increasing the sample size by a factor of 2 results in a 41% reduction of the standard deviations ofrsandrp. In conclusion,rpis suitable for light-tailed distributions, whereasrsis preferable when variables feature heavy-tailed distributions or when outliers are present, as is often the case in psychological research.
authors.affiliation: Department of BioMechanical Engineering, Faculty of Mechanical, Maritime and Materials Engineering.
authors.forename: Joost C F
authors.initials: JC
authors.lastname: de Winter
authors.affiliation: Department of Psychology, University of Texas.
authors.forename: Samuel D
authors.initials: SD
authors.lastname: Gosling
authors.affiliation: Atof Inc.
authors.forename: Jeff
authors.initials: J
authors.lastname: Potter
mesh_terms: D003198:Computer Simulation; D006801:Humans; D011594:Psychometrics; D018401:Sample Size; D012494:Sampling Studies; D018709:Statistics, Nonparametric; D011795:Surveys and Questionnaires