Goodness-of-Fit Tests in Calibration: Are They Any Good for Selecting Least-Squares Weighting Formulas?

Area of Science:

• Analytical Chemistry
• Calibration and Measurement Uncertainty

Background:

• Goodness-of-fit (GOF) tests are commonly used to select weighting schemes in calibration models.
• Existing GOF tests often exhibit bias, favoring constant or inverse-square weighting regardless of the true data characteristics.

Purpose of the Study:

• To quantify the flaws in conventional goodness-of-fit tests for calibration weighting.
• To introduce and validate variance function (VF) estimation as a robust method for determining optimal calibration weighting.

Main Methods:

• Monte Carlo simulations were employed to assess the performance of different GOF tests and weighting strategies.
• Variance function (VF) estimation was performed using replicate calibration data.
• Comparison of parameter precision and estimation of detection/quantification limits under different weighting schemes.

Main Results:

• Conventional GOF tests falsely prefer constant or inverse-square weighting, leading to suboptimal precision.
• Inverse-square weighting, when incorrect, can yield falsely optimistic detection and quantification limits, especially at low signal levels.
• VF estimation, even with limited replicate data, provides accurate weighting and improves precision without significant loss of calibration parameter accuracy.

Conclusions:

• Variance function estimation is the correct approach to solve the calibration weighting problem, separating it from response function selection.
• Accurate weighting via VF estimation is crucial for reliable estimates of unknowns and for avoiding biased detection and quantification limits.
• VF estimation is practical and data-efficient, debunking claims of excessive data requirements.