Model Adequacy Checking in Homogeneity and Stability Studies

Abstract

The production of reference materials necessitates, among other factors, evaluations of homogeneity and stability. The aim of the homogeneity study is to ensure uniformity in property values across all samples. On the other hand, stability pertains to a sample’s ability to retain its property value over time. ISO Guide 35 dictates that homogeneity, between and within samples, is appraised using a one-way random effects analysis of variance, while stability is gauged by a univariate linear regression model. Both these statistical techniques presuppose the normality and homoscedasticity of the residuals. Notably, the ISO Guide 35 standard omits any reference to the assumption of homoscedasticity in its prescribed statistical methods. This communication introduces the Shapiro–Wilk and Koenker–Bassett tests as tools to verify the assumptions of normality and homoscedasticity, respectively. Moreover, it advances the feasible generalized least squares method as a remedy for instances where these assumptions are breached. Initial findings suggest that, in certain scenarios, breaches in statistical model assumptions might influence evaluations of homogeneity and/or stability.