A statistical test and metric for matrix effects in non-linear calibration curves

Matrix effects in chemical analysis cause sample-dependent response changes that compromise quantification. Their systematic assessment is therefore an essential component of method validation. Currently, matrix effects are evaluated by comparing slopes between calibration curves, but this approach fails for non-linear response profiles common in modern methods. An L 2 norm-based statistical framework is presented that quantifies matrix effects through the integrated squared difference between calibration curves; a strategy not restricted to any specific calibration curve shape. The framework, which introduces a hypothesis test and generalized matrix-effect coefficient, is demonstrated for quadratic polynomial models, in which closed-form solutions are available, and four-parameter logistic models, necessitating numerical methods. For simple linear calibrations, both the proposed test and matrix-effect coefficient reduce to their classical counterparts, the slope t -test and slope ratio, thereby providing a unified framework for effect detection and magnitude. Monte Carlo simulations demonstrate near-nominal Type I error rates and high power for detecting matrix effects under typical analytical conditions. Experimental validation using LC-MS showed increased sensitivity to matrix effects by identifying statistically significant response distortions undetected by conventional slope comparison, while UV protein quantification assays demonstrated specificity by correctly discriminating true matrix interference from baseline-related artifacts. An open-source R implementation provides an immediately applicable tool for validating non-linear calibrations in analytical method validation workflows. • Novel method for detecting matrix effects. • Works for linear and non-linear models. • Introducing a generalized matrix effect coefficient to indicate effect magnitude.