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Journal of Applied Mathematics
Volume 2015, Article ID 708948, 9 pages
Research Article

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

1Group Bio-Process Analysis Technology, Technische Universität München, Weihenstephaner Steig 20, 85354 Freising, Germany
2Institut für Landtechnik und Tierhaltung, Vöttinger Straße 36, 85354 Freising, Germany
3Computer Unit, Faculty of Agriculture, University of Ruhuna, Mapalana, 81100 Kamburupitiya, Sri Lanka

Received 9 September 2014; Revised 9 December 2014; Accepted 10 December 2014

Academic Editor: Carlos Conca

Copyright © 2015 K. K. L. B. Adikaram et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 . 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 . 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.