Examining the reliability of interval level data using root mean square differences and concordance correlation coefficients

Abstract

This article introduces new statistics for evaluating score consistency. Psychologists usually use correlations to measure the degree of linear relationship between 2 sets of scores, ignoring differences in means and standard deviations. In medicine, biology, chemistry, and physics, a more stringent criterion is often used: the extent to which scores are identically equal. For each test taker (or other unit of measurement), the difference between the 2 scores is calculated. The root mean square difference (RMSD) represents the average change from 1 set of scores to the other, and the concordance correlation coefficient (CCC) rescales this coefficient to have a maximum value of 1. This article shows the relationship of the RMSD and CCC to the intraclass correlation coefficients, product-moment correlation, and standard error of measurement. Finally, this article adapts the RMSD and the CCC for linear, consistency, and absolute definitions of agreement.