Using the coefficient of correlation in method-comparison studies

Abstract

The coefficient of correlation (R) is one of the most commonly computed statistics in method-comparison studies. Usually, it is simply quoted without interpretation. In this paper, we show how R may be used to detect interference, nonlinearity, and misuse of the imprecision components. Specifically, one may precisely predict what R should be considering the imprecisions of the two methods being compared, even before the comparison is performed. When the actual R disagrees with the predicted R, then one of the mentioned effects is present. We also describe a statistical test to detect these effects at the P = 0.05 level, then evaluate this test by using computer simulation and present two examples of its use. We also present the theory underlying the usage of R, including how R is affected by the distribution and range of the data, by the joint imprecisions of the methods being compared, by the sample size, and by the randomness of the specimen-selection process.