Data Transformation Technique to Improve the Outlier Detection Power of Grubbs’ Test for Data Expected to Follow Linear Relation

Abstract

Grubbs test (extreme studentized deviate test, maximum normed residual test) is used in various fields to identify outliers in a data set, which are ranked in the order of $x_1\le x_2\le x_3\le \cdots \le x_n\hspace{0.17em}\hspace{0.17em}(i=\mathrm{1,2},3,\dots ,n)$. However, ranking of data eliminates the actual sequence of a data series, which is an important factor for determining outliers in some cases (e.g., time series). Thus in such a data set, Grubbs test will not identify outliers correctly. This paper introduces a technique for transforming data from sequence bound linear form to sequence unbound form $(y=c)$. Applying Grubbs test to the new transformed data set detects outliers more accurately. In addition, the new technique improves the outlier detection capability of Grubbs test. Results show that, Grubbs test was capable of identifing outliers at significance level 0.01 after transformation, while it was unable to identify those prior to transforming at significance level 0.05.