Comparison of product moment and rank correlation coefficients in the assessment of laboratory method-comparison data

Abstract

The authors have studied the effects of range and distribution of data on product moment and rank correlation coefficients when deviation from a linear relationship was due solely to experimentally produced random error. All correlation coefficients (Pearson r, Spearman rho, and Kendall tau) were markedly influenced by the range of the data, and, for the rank correlation coefficients, the effect of range varied for different data distributions. While correlation coefficients may be useful in assessing whether an association exists between two variables, they are not useful in assessing the degree of random error about the regression line when a strong linear association is presumed to exist between the two variables. Thus, neither product moment nor rank correlation coefficients are of value in analysis of laboratory method-comparison data. The standard deviation of the residual error of regression should be calculated as a measure of the random error about the regression line.