Comparing the Effectiveness of Robust Statistical Estimators of Proficiency Testing Schemes in Outlier Detection

This study investigates the effectiveness of robust estimators of location and dispersion, used in proficiency testing and listed in ISO 13528:2015, in outlier detection. The models utilize (a) kernel density plots, (b) Z-factors, (c) Monte Carlo simulations, and (d) distributions derived from at most two contaminating distributions and one main Gaussian. The simulation parameters cover a wide range of those commonly encountered in proficiency testing (PT) schemes, so the results presented are of fairly general application. We chose a functional sub-optimal solution by grouping and classifying the model settings, resulting in five matrices readily usable for selecting the best robust estimator. Whenever at most half of the distribution of each contaminating population is outside the central distribution, there is only one optimal estimator. For all other cases, the five matrices provide the appropriate robust statistic. The proposed method applies to 95.1% of 144 results for an existing PT for cement. These actual datasets indicate that the Hampel estimator for the mean and the Q-method for the standard deviation provide the most appropriate performance statistic in 86.1% of the cases.