H-statistic with winsorized modified one-step M-estimator as central tendency measure

Two-sample independent t-test and ANOVA are classical procedures which are widely used to test the equality of two groups and more than two groups respectively. However, these parametric procedures are easily affected by non-normality, becoming more obvious when heterogeneity of variances and unbala...

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Main Author:	Ong, Gie Xao
Format:	Thesis
Language:	eng eng
Published:	2017
Subjects:	QA273-280 Probabilities Mathematical statistics
Online Access:	https://etd.uum.edu.my/6993/1/s811088_01.pdf https://etd.uum.edu.my/6993/2/s811088_02.pdf
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id	my-uum-etd.6993
record_format	uketd_dc
institution	Universiti Utara Malaysia
collection	UUM ETD
language	eng eng
advisor	Syed Yahaya, Sharipah Soaad Abdullah, Suhaida
topic	QA273-280 Probabilities Mathematical statistics
spellingShingle	QA273-280 Probabilities Mathematical statistics Ong, Gie Xao H-statistic with winsorized modified one-step M-estimator as central tendency measure
description	Two-sample independent t-test and ANOVA are classical procedures which are widely used to test the equality of two groups and more than two groups respectively. However, these parametric procedures are easily affected by non-normality, becoming more obvious when heterogeneity of variances and unbalanced group sizes exist. It is well known that the violation in the assumption of the tests will lead to inflation in Type I error rate and decreasing in the power of test. Nonparametric procedures like Mann-Whitney and Kruskal-Wallis may be the alternative to the parametric procedures, however, loss of information occur due to the ranking data. In mitigating these problems, robust procedures can be used as the other alternative. One of the procedures is H-statistic. When used with modified one-step M-estimator (MOM), the test statistic (MOM-H) produces good control of Type I error rate even under small sample size but inconsistent under certain conditions investigated. Furthermore, power of test is low which might be due to the trimming process. In this study, MOM was winsorized (WMOM) to retain the original sample size. The Hstatistic when combines with WMOM as the central tendency measure (WMOM-H) shows better control of Type I error rate as compared to MOM-H especially under balanced design regardless of the shape of distributions. It also performs well under highly skewed and heavy tailed distribution for unbalanced design. On top of that, WMOM-H also generates better power value, as compared to MOM-H and ANOVA under most of the conditions investigated. WMOM-H also has better control of Type I error rates with no liberal value (>0.075) compared to the parametric (t-test and ANOVA) and nonparametric (Mann-Whitney and Kruskal-Wallis) procedures. In general, this study demonstrates that winsorization process (WMOM) is able to improve the performance of H-statistic in terms of controlling Type I error rate and increasing power of test.
format	Thesis
qualification_name	masters
qualification_level	Master's degree
author	Ong, Gie Xao
author_facet	Ong, Gie Xao
author_sort	Ong, Gie Xao
title	H-statistic with winsorized modified one-step M-estimator as central tendency measure
title_short	H-statistic with winsorized modified one-step M-estimator as central tendency measure
title_full	H-statistic with winsorized modified one-step M-estimator as central tendency measure
title_fullStr	H-statistic with winsorized modified one-step M-estimator as central tendency measure
title_full_unstemmed	H-statistic with winsorized modified one-step M-estimator as central tendency measure
title_sort	h-statistic with winsorized modified one-step m-estimator as central tendency measure
granting_institution	Universiti Utara Malaysia
granting_department	Awang Had Salleh Graduate School of Arts & Sciences
publishDate	2017
url	https://etd.uum.edu.my/6993/1/s811088_01.pdf https://etd.uum.edu.my/6993/2/s811088_02.pdf
_version_	1747828142215528448
spelling	my-uum-etd.69932021-08-18T05:36:30Z H-statistic with winsorized modified one-step M-estimator as central tendency measure 2017 Ong, Gie Xao Syed Yahaya, Sharipah Soaad Abdullah, Suhaida Awang Had Salleh Graduate School of Arts & Sciences Awang Had Salleh Graduate School of Arts and Sciences QA273-280 Probabilities. Mathematical statistics Two-sample independent t-test and ANOVA are classical procedures which are widely used to test the equality of two groups and more than two groups respectively. However, these parametric procedures are easily affected by non-normality, becoming more obvious when heterogeneity of variances and unbalanced group sizes exist. It is well known that the violation in the assumption of the tests will lead to inflation in Type I error rate and decreasing in the power of test. Nonparametric procedures like Mann-Whitney and Kruskal-Wallis may be the alternative to the parametric procedures, however, loss of information occur due to the ranking data. In mitigating these problems, robust procedures can be used as the other alternative. One of the procedures is H-statistic. When used with modified one-step M-estimator (MOM), the test statistic (MOM-H) produces good control of Type I error rate even under small sample size but inconsistent under certain conditions investigated. Furthermore, power of test is low which might be due to the trimming process. In this study, MOM was winsorized (WMOM) to retain the original sample size. The Hstatistic when combines with WMOM as the central tendency measure (WMOM-H) shows better control of Type I error rate as compared to MOM-H especially under balanced design regardless of the shape of distributions. It also performs well under highly skewed and heavy tailed distribution for unbalanced design. On top of that, WMOM-H also generates better power value, as compared to MOM-H and ANOVA under most of the conditions investigated. WMOM-H also has better control of Type I error rates with no liberal value (>0.075) compared to the parametric (t-test and ANOVA) and nonparametric (Mann-Whitney and Kruskal-Wallis) procedures. In general, this study demonstrates that winsorization process (WMOM) is able to improve the performance of H-statistic in terms of controlling Type I error rate and increasing power of test. 2017 Thesis https://etd.uum.edu.my/6993/ https://etd.uum.edu.my/6993/1/s811088_01.pdf text eng public https://etd.uum.edu.my/6993/2/s811088_02.pdf text eng public masters masters Universiti Utara Malaysia Abdullah, S., Syed Yahaya, S. S., & Othman, A. R. (2011). Modified Alexander- Govern test as alternative to t-test and ANOVA F test. Sains Malaysiana, 40(10), 1187-1192. Ahmad Mahir, R.., & Al-Khazaleh, A. M. H. (2009). New method to estimate missing data by using the asymmetrical winsorized mean in a time series. Applied Mathematical Sciences, 3(35), 1715–1726. Alan, O., Phyllis, S., & John, Q. (2008). 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H-statistic with winsorized modified one-step M-estimator as central tendency measure

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