Spearman Correlation Coefficients, Differences between

Abstract

Testing the equality of two population correlation coefficients when the data are bivariate normal and Pearson correlation coefficients are used as estimates of the population parameters is a straightforward procedure covered in many introductory statistics courses. The coefficients are converted using Fisher's z ‐transformation with standard errors ( N − 3) −1/2 . The two transformed values are then compared using a standard normal procedure. When data are not bivariate normal, Spearman's correlation coefficient rho is often used as the index of correlation. Comparison of two Spearman rho's is not as well documented. Three approaches were investigated using Monte Carlo simulations. Treating the Spearman coefficients as though they were Pearson coefficients and using the standard Fisher's z ‐transformation and subsequent comparison was more robust with respect to Type I error than either ignoring the nonnormality and computing Pearson coefficients or converting the Spearman coefficients to Pearson equivalents prior to transformation.