The Fault in R-squared: Better Metrics for Calibration Evaluation

Ensuring Reliable Data
Oral Presentation

Prepared by J. Hoisington
Restek Corporation, 110 Benner Circle, Bellefonte, PA, 16823, United States


Contact Information: [email protected]; 1-814-353-1300

ABSTRACT

The coefficient of determination r-squared has long been used to measure the goodness of fit of calibration curves in chemical analysis. However, due to the fact that this metric measures total error rather than relative error it is not always appropriate for use in calibrations that span multiple orders of magnitude, especially when low-level accuracy is needed. While newer EPA methods sometimes include more appropriate metrics such as relative standard error (RSE), the use of r-squared persists in some newer and legacy methods. In addition, this calculation is usually offloaded on to instrument software, and newer chemists may not understand what r-squared is telling them or be able to verify the calculations.
This presentation will give a summary of the math behind r-squared and RSE to show how they measure goodness of fit and show why RSE can be better for assessing low-level accuracy. A comparison of r-squared values from different software packages will also be given, showing that when weighted and force through zero calibrations are used r-squared is not calculated the same by different software packages.