Data Transformation Technique to Improve the Outlier Detection Power of Grubbs’ Test for Data Expected to Follow Linear Relation
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 x1≤x2≤x3≤⋯≤xn (i=1,2,3,…,n). However, ranking of data eliminates the actual sequence of a data series, which is an important fa...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2015/708948 |
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| author | K. K. L. B. Adikaram M. A. Hussein M. Effenberger T. Becker |
| author_facet | K. K. L. B. Adikaram M. A. Hussein M. Effenberger T. Becker |
| author_sort | K. K. L. B. Adikaram |
| collection | DOAJ |
| description | 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 x1≤x2≤x3≤⋯≤xn (i=1,2,3,…,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. |
| format | Article |
| id | doaj-art-47d7b36b271346409db7025fbb82600f |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-47d7b36b271346409db7025fbb82600f2025-02-03T06:08:32ZengWileyJournal of Applied Mathematics1110-757X1687-00422015-01-01201510.1155/2015/708948708948Data Transformation Technique to Improve the Outlier Detection Power of Grubbs’ Test for Data Expected to Follow Linear RelationK. K. L. B. Adikaram0M. A. Hussein1M. Effenberger2T. Becker3Group Bio-Process Analysis Technology, Technische Universität München, Weihenstephaner Steig 20, 85354 Freising, GermanyGroup Bio-Process Analysis Technology, Technische Universität München, Weihenstephaner Steig 20, 85354 Freising, GermanyInstitut für Landtechnik und Tierhaltung, Vöttinger Straße 36, 85354 Freising, GermanyGroup Bio-Process Analysis Technology, Technische Universität München, Weihenstephaner Steig 20, 85354 Freising, GermanyGrubbs 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 x1≤x2≤x3≤⋯≤xn (i=1,2,3,…,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.http://dx.doi.org/10.1155/2015/708948 |
| spellingShingle | K. K. L. B. Adikaram M. A. Hussein M. Effenberger T. Becker Data Transformation Technique to Improve the Outlier Detection Power of Grubbs’ Test for Data Expected to Follow Linear Relation Journal of Applied Mathematics |
| title | Data Transformation Technique to Improve the Outlier Detection Power of Grubbs’ Test for Data Expected to Follow Linear Relation |
| title_full | Data Transformation Technique to Improve the Outlier Detection Power of Grubbs’ Test for Data Expected to Follow Linear Relation |
| title_fullStr | Data Transformation Technique to Improve the Outlier Detection Power of Grubbs’ Test for Data Expected to Follow Linear Relation |
| title_full_unstemmed | Data Transformation Technique to Improve the Outlier Detection Power of Grubbs’ Test for Data Expected to Follow Linear Relation |
| title_short | Data Transformation Technique to Improve the Outlier Detection Power of Grubbs’ Test for Data Expected to Follow Linear Relation |
| title_sort | data transformation technique to improve the outlier detection power of grubbs test for data expected to follow linear relation |
| url | http://dx.doi.org/10.1155/2015/708948 |
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