Comparative performance of thirteen single outlier discordancy tests from Monte Carlo simulations

Abstract

We evaluated the performance of thirteen single extreme outlier statistical discordancy tests (Grubbs-type N1, N2, N4; Dixon-type N7, N8, N9, N10; and high-order moment statistics skewness N14 and kurtosis N15) using highly precise and accurate Monte Carlo simulations for 20,000,000 replications and 102 independent simulation experiments. Our simulation errors and total uncertainties were extremely low for normal samples of sizes 5 to 20 involving a simple statistical contamination of one datum resulting from a parameter called δ from ±0.1 up to ±20 for modeling the slippage of central tendency or another parameterε from ±1.1 up to ±200 for the slippage of dispersion. Both criteria - Power of Test proposed by Hayes and Kinsella [1] and Test Performance Criterion of Barnett and Lewis [2] were used. Our results indicate that the Dixon tests perform less well than the Grubbs-type, skewness, and kurtosis tests.