Robust bootstrapped Mandel's h and k statistics for outlier detection in interlaboratory studies

Abstract

This study proposes the use of the bootstrap methodology to estimate the distribution of the Mandel's h and k statistics, commonly applied to identify laboratories that supply inconsistent results, in the framework of Interlaboratory Studies (ILS). These statistics are usually used to detect those outlier laboratories by testing the hypothesis of reproducibility and repeatability (R&R). The statistical tests involved in the ILS have been currently developed assuming that the measured variables are Gaussian distributed. Thus, the results of the application of these statistical techniques, such is the case of Mandel's h and k statistics, will be more valid the more plausible is the Gaussian distribution hypothesis. If the variable measured by the laboratories is far from be assumed normal distributed, the application of nonparametric techniques based on bootstrap procedures could be very useful to estimate more accurately the distribution of these statistics and, consequently, the critical values of the tests. Thus, in this case, the laboratories that provide inconsistent results should be identified in a more reliable way.For the validation of the proposed algorithm, a simulation study has been proposed, where normal, skew normal, and Laplace distributions were simulated, assuming different sample sizes and number of laboratories. The most scenarios the bootstrap approach for the h and k tests provides better results than those obtained using the parametric classical methodology. Additionally, the proposed bootstrap procedure has been applied to real case studies, such as the ILS corresponding to hematic biometry, on the one hand, and the measure of serum glucose, on the other hand.