Performance measures of color-difference equations: correlation coefficient versus standardized residual sum of squares

Abstract

For evaluating the performance of color-difference equations, several goodness-of-fit measures were proposed in the past, such as Pearson’s correlation coefficient (r), the performance factor PF/3, and the recently proposed standardized residual sum of squares (STRESS) measure. The STRESS shares its main advantage, which is the possibility to statistically test performance differences, with the correlation coefficient. We show, by mathematical analysis supported by instructive numerical examples, that the STRESS has no meaningful interpretation in this regression analysis context. In addition, we present objections to the use of the STRESS for evaluating color-difference equations. Therefore, we recommend using the correlation coefficient in combination with a graphical and diagnostics analysis to ensure proper application as with any statistical technique.