Percentage Points for a Generalized ESD Many-Outlier Procedure

TLDR

A generalized extreme Studentized deviate (ESD) many‑outlier procedure is introduced to detect from one to k outliers in a dataset. The method approximates required percentiles using the t distribution and provides implementation tables for sample sizes 25–500 and k up to 10 at α = .05, .01, .005. Compared to Rosner’s original ESD, the new procedure controls type I error under both null and alternative hypotheses and, as shown by Monte Carlo simulation, accurately detects up to ten outliers even in samples as small as 25.

Abstract

A generalized (extreme Studentized deviate) ESD many-outlier procedure is given for detecting from 1 to k outliers in a data set. This procedure has an advantage over the original ESD many-outlier procedure (Rosner 1975) in that it controls the type I error both under the hypothesis of no outliers and under the alternative hypotheses of 1, 2, …. k-l outliers. A method is given for approximating percentiles for this procedure based on the t distribution. This method is shown to be adequately accurate using Monte Carlo simulation, for detecting up to 10 outliers in samples as small as 25. Tables are given for implementing this method for n = 25(1)50(10)100(50)500; k = 10, α = .05, .Ol, .005.