A New Approach for Multivariate Data Analysis in Interlaboratory Comparisons Based on Multidimensional Scaling and Robust Confidence Ellipse

Abstract

Interlaboratory comparisons (IC) present a challenge related to multivariate data analysis. ISO 13528:2015 is a reference document for interlaboratory comparisons. This standard does not provide descriptions of statistical methods for multivariate analysis and, according to our best knowledge, there is no practical guidance for the organizing and evaluation of multivariate data analysis for interlaboratory comparisons available. Due to this reason, some researchers have made efforts to develop methodologies that make it possible to analyze multivariate data in IC. Generally, these approaches are based dimensionality-reduction methods like principal component analysis. This paper proposes a new approach to reduce the dimensionality of large data set and check the performance of laboratories based on multidimensional scaling (MDS) and robust confidence ellipse/ellipsoid (RCE). MDS is a multivariate analysis technique that allows grouping laboratories according to their similarity in a Euclidean space. On the other hand, RCE is a statistical method for outlier detection in a multivariate data set. In this work, it is proposed combine MDS and RCE to evaluate laboratory proficiency in interlaboratory comparison. This methodology was compared with the multivariate z-score and both methodologies identified the same outlying laboratories. This preliminary result indicates that MDS/RCE is promising for classifying IC results.