Robustness of the Pearson Correlation against Violations of Assumptions

Abstract

The purpose of this study was to determine empirically effects of the violation of assumptions of normality and of measurement scales on the Pearson product-moment correlation coefficient. The effects of such violations were studied separately and in combination for samples of varying size from 5 to 60. Monte Carlo procedures were used to generate populations of scores for four basic distributions: normal, positively skewed, negatively skewed, and leptokurtic. Samples of varying sizes were then randomly selected from specific populations. Results of the study were based on distributions of rs which were calculated on 5,000 sets of samples of n = 5 or n = 15 and 3,000 sets of samples of n = 30 and n = 60. Results indicated that the Pearson r is insensitive to rather extreme violations of the basic assumptions of normality and type of measurement scale. Failure to meet the basic assumptions separately or in combinations had little effect upon the obtained distributions of rs.