A new methodology for proficiency testing scheme interpretation based on residual analysis

Proficiency testing schemes by interlaboratory comparisons are used to determine the performance of individual laboratories for specific tests or measurements. The international standard ISO 13528:2015 provides a description of statistical methods used for achieving this goal; one of these methods is the z score. The standard allows each participant to choose a measurement method and this can lead to inhomogeneity between participant variance known as heteroscedasticity. The ISO 13528:2015 standard does not mention heteroscedasticity in its statistical procedures. This paper describes a new approach, based on residuals analysis, to assess the performance of an interlaboratory comparison for determining the presence of benzoic acid in orange juice. The results indicate that the conclusions (using z scores) and the proposed approach are different for some laboratories. This occurs due to violation of the homoscedasticity assumption. The z score procedure does not consider this assumption violation while residual analysis can provide such information. Feasible generalized least squares allow one to deal with non-homoscedasticity.