An Alternative Robust Measure of Outlier Detection in Univariate Data Sets

Md. Siraj- Ud- Doulah; Md. Hafizul Islam

Abstract

A univariate outlier is a data point that consists of an extreme value on one variable. Here we applied two types of outlier detection methods: one is graphical and another is analytical. This paper presents graphical methods for different statistical outlier detection such as scatter diagram, box plot and normal probability plot. Furthermore, the quantitative methods for outlier detection in this paper are the IQR method, SD method, Z-score method, the modified Z-score method, Tukey’s method, adjusted box plot method, MADe method, Hampel method, Carling’s modification method, MAD-Median rule, Grubb’s test and our proposed HM- method. The performance of these outlier detection methods was observed based on different types of data sets. The analysis has shown that graphically we have suspected that the data sets contain outlier(s). But when we applied our analytical tests, only two methods including our proposed HM-method out of 12 methods were able to detect, in an appropriate and satisfactory way, as outlier. The main reasons for this can be found in the violation of normal distribution assumptions and in masking as well as swamping. Keywords: Real data sets, outlier detection methods, proposed HM- method, statistical methodCite this ArticleMd. Siraj-Ud-Doulah, Md. Hafizul Islam. An Alternative Robust Measure of Outlier Detection in Univariate Data Sets. Research & Reviews: Journal of Statistics. 2019; 8(1): 1–11p.