Alexander-Govern test using Winsorized means

Classical tests for testing the equality of independent groups which are based on arithmetic mean can produce invalid results especially when dealing with non-normal data and heterogeneous variances (heteroscedasticity). In alleviating the problem, researchers are working on methods that are more a...

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主要作者:	Faridzah, Jamaluddin
格式:	Thesis
语言:	eng eng
出版:	2015
主题:	QA299.6-433 Analysis
在线阅读:	https://etd.uum.edu.my/5339/1/s812426.pdf https://etd.uum.edu.my/5339/2/s812426_abstract.pdf
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id	my-uum-etd.5339
record_format	uketd_dc
institution	Universiti Utara Malaysia
collection	UUM ETD
language	eng eng
advisor	Abdullah, Suhaida
topic	QA299.6-433 Analysis
spellingShingle	QA299.6-433 Analysis Faridzah, Jamaluddin Alexander-Govern test using Winsorized means
description	Classical tests for testing the equality of independent groups which are based on arithmetic mean can produce invalid results especially when dealing with non-normal data and heterogeneous variances (heteroscedasticity). In alleviating the problem, researchers are working on methods that are more adapt to the aforementioned conditions which include a procedure known as Alexander-Govern test. This procedure is insensitive in the presence of heteroscedasticity under normal distribution. However, the test which employs the arithmetic mean as the central tendency measure is sensitive to non-normal data. This is due to the fact that the arithmetic mean is easily influenced by the shape of distribution. In this study, the arithmetic mean is replaced by robust estimators, namely the Winsorized mean or adaptive Winsorized mean. The proposed Alexander-Govern test with Winsorized mean and with adaptive Winsorized mean are denoted as AGW and AGAW, respectively. For the purpose of comparison, different Winsorization percentages of 5%, 10%, 15% and 20% are considered. A simulation study was conducted to investigate on the performance of the tests which is based on rate of Type I error and power. Four variables; shape of distribution, sample size, level of variance heterogeneity and nature of pairings are manipulated to create the conditions which could highlight the strengths and weaknesses of each test. The performance of the proposed tests is compared with their parametric counterparts, the t-test and ANOVA. The proposed tests show improvement in terms of controlling Type I Error and increasing power under the influence of heteroscedasticity and non-normality. The AGAW test performed best with 10% Winsorization while AGW test performed best with 5% Winsorization. Under most conditions (74%), AGAW tests outperform AGW tests. Therefore, the Winsorized mean and the adaptive Winsorized mean can significantly improve the performance of the original Alexander-Govern test. These proposed procedures are beneficial to statistical practitioners in testing the equality of independent groups even under the influence of non-normality and variance heterogeneity.
format	Thesis
qualification_name	masters
qualification_level	Master's degree
author	Faridzah, Jamaluddin
author_facet	Faridzah, Jamaluddin
author_sort	Faridzah, Jamaluddin
title	Alexander-Govern test using Winsorized means
title_short	Alexander-Govern test using Winsorized means
title_full	Alexander-Govern test using Winsorized means
title_fullStr	Alexander-Govern test using Winsorized means
title_full_unstemmed	Alexander-Govern test using Winsorized means
title_sort	alexander-govern test using winsorized means
granting_institution	Universiti Utara Malaysia
granting_department	Awang Had Salleh Graduate School of Arts & Sciences
publishDate	2015
url	https://etd.uum.edu.my/5339/1/s812426.pdf https://etd.uum.edu.my/5339/2/s812426_abstract.pdf
_version_	1747827911971307520
spelling	my-uum-etd.53392021-03-18T06:55:44Z Alexander-Govern test using Winsorized means 2015 Faridzah, Jamaluddin Abdullah, Suhaida Awang Had Salleh Graduate School of Arts & Sciences Awang Had Salleh Graduate School of Arts and Sciences QA299.6-433 Analysis Classical tests for testing the equality of independent groups which are based on arithmetic mean can produce invalid results especially when dealing with non-normal data and heterogeneous variances (heteroscedasticity). In alleviating the problem, researchers are working on methods that are more adapt to the aforementioned conditions which include a procedure known as Alexander-Govern test. This procedure is insensitive in the presence of heteroscedasticity under normal distribution. However, the test which employs the arithmetic mean as the central tendency measure is sensitive to non-normal data. This is due to the fact that the arithmetic mean is easily influenced by the shape of distribution. In this study, the arithmetic mean is replaced by robust estimators, namely the Winsorized mean or adaptive Winsorized mean. The proposed Alexander-Govern test with Winsorized mean and with adaptive Winsorized mean are denoted as AGW and AGAW, respectively. For the purpose of comparison, different Winsorization percentages of 5%, 10%, 15% and 20% are considered. A simulation study was conducted to investigate on the performance of the tests which is based on rate of Type I error and power. Four variables; shape of distribution, sample size, level of variance heterogeneity and nature of pairings are manipulated to create the conditions which could highlight the strengths and weaknesses of each test. The performance of the proposed tests is compared with their parametric counterparts, the t-test and ANOVA. The proposed tests show improvement in terms of controlling Type I Error and increasing power under the influence of heteroscedasticity and non-normality. The AGAW test performed best with 10% Winsorization while AGW test performed best with 5% Winsorization. Under most conditions (74%), AGAW tests outperform AGW tests. Therefore, the Winsorized mean and the adaptive Winsorized mean can significantly improve the performance of the original Alexander-Govern test. These proposed procedures are beneficial to statistical practitioners in testing the equality of independent groups even under the influence of non-normality and variance heterogeneity. 2015 Thesis https://etd.uum.edu.my/5339/ https://etd.uum.edu.my/5339/1/s812426.pdf text eng public https://etd.uum.edu.my/5339/2/s812426_abstract.pdf text eng public masters masters Universiti Utara Malaysia Abdullah, S. (2011). Kaedah Alexander-Govern Menggunakan Penganggar Teguh Dengan Pendekatan Pangkasan Data: Satu Kajian Simulasi. Unpublished Ph.D thesis, UniversitiUtara Malaysia. Aberson, C. L. (2010). Applied power analysis for the behavioral sciences. New York, NY: Taylor & Francis Group. 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Alexander-Govern test using Winsorized means

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