Winsorized modified one of step M-estimator in Alexander-govern test

Winsorized modified one of step M-estimator in Alexander-govern test

This research centres on independent group test of comparing two or more means by using the parametric method, namely the Alexander-Govern (AG) test. It uses mean as its central tendency measure and is considered as a better alternative to the ANOVA, the Welch test and the James test. Although the...

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محفوظ في:
التفاصيل البيبلوغرافية
المؤلف الرئيسي: Ochuko, Tobi Kingsley
التنسيق: أطروحة
اللغة:eng
eng
منشور في: 2016
الموضوعات:
QA273-280 Probabilities
Mathematical statistics
الوصول للمادة أونلاين:https://etd.uum.edu.my/6065/1/s813614_01.pdf
https://etd.uum.edu.my/6065/2/s813614_02.pdf
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id my-uum-etd.6065
record_format uketd_dc
institution Universiti Utara Malaysia
collection UUM ETD
language eng
eng
advisor Abdullah, Suhaida
Zain, Zakiyah
topic QA273-280 Probabilities
Mathematical statistics
spellingShingle QA273-280 Probabilities
Mathematical statistics
Ochuko, Tobi Kingsley
Winsorized modified one of step M-estimator in Alexander-govern test
description This research centres on independent group test of comparing two or more means by using the parametric method, namely the Alexander-Govern (AG) test. It uses mean as its central tendency measure and is considered as a better alternative to the ANOVA, the Welch test and the James test. Although the AG test has a good control of Type I error rate and produces a high power under variance heterogeneity, it is not robust to non-normal data. Thus, trimmed mean was proposed in the test to handle the problem of non-normality and later, a more robust estimator called modified one step M (MOM) estimator was introduced. These estimators are not influenced by the number of groups, but failed to give a good control of Type I error rate, under extreme conditions of skewness and kurtosis. This research proposes the Winsorized MOM (FFWOM) estimator as a measure of central tendency in attempt to robustify the AG test. This enhanced AG test, AGWMOM is able to remove the appearance of outliers from the data distribution. A simulation study of 5,000 data sets was conducted to compare the performance of the tests: AG, AGMOM (AG test using MOM estimator), AGPMOM, t-test and ANOVA. The results show that the AGWMOM test has improved the number of robust conditions under skewed normal tailed and skewed heavy tailed distributions compared to the other tests. Additionally, the test produced high power in most conditions under four groups with unbalanced sample size. It leads that this test is convenient specifically when the data distribution is heavy tailed.
format Thesis
qualification_name other
qualification_level Master's degree
author Ochuko, Tobi Kingsley
author_facet Ochuko, Tobi Kingsley
author_sort Ochuko, Tobi Kingsley
title Winsorized modified one of step M-estimator in Alexander-govern test
title_short Winsorized modified one of step M-estimator in Alexander-govern test
title_full Winsorized modified one of step M-estimator in Alexander-govern test
title_fullStr Winsorized modified one of step M-estimator in Alexander-govern test
title_full_unstemmed Winsorized modified one of step M-estimator in Alexander-govern test
title_sort winsorized modified one of step m-estimator in alexander-govern test
granting_institution Universiti Utara Malaysia
granting_department Awang Had Salleh Graduate School of Arts & Sciences
publishDate 2016
url https://etd.uum.edu.my/6065/1/s813614_01.pdf
https://etd.uum.edu.my/6065/2/s813614_02.pdf
_version_ 1747828017088954368
spelling my-uum-etd.60652021-04-19T06:14:47Z Winsorized modified one of step M-estimator in Alexander-govern test 2016 Ochuko, Tobi Kingsley Abdullah, Suhaida Zain, Zakiyah Awang Had Salleh Graduate School of Arts & Sciences Awang Had Salleh Graduate School of Arts and Sciences QA273-280 Probabilities. Mathematical statistics This research centres on independent group test of comparing two or more means by using the parametric method, namely the Alexander-Govern (AG) test. It uses mean as its central tendency measure and is considered as a better alternative to the ANOVA, the Welch test and the James test. Although the AG test has a good control of Type I error rate and produces a high power under variance heterogeneity, it is not robust to non-normal data. Thus, trimmed mean was proposed in the test to handle the problem of non-normality and later, a more robust estimator called modified one step M (MOM) estimator was introduced. These estimators are not influenced by the number of groups, but failed to give a good control of Type I error rate, under extreme conditions of skewness and kurtosis. This research proposes the Winsorized MOM (FFWOM) estimator as a measure of central tendency in attempt to robustify the AG test. This enhanced AG test, AGWMOM is able to remove the appearance of outliers from the data distribution. A simulation study of 5,000 data sets was conducted to compare the performance of the tests: AG, AGMOM (AG test using MOM estimator), AGPMOM, t-test and ANOVA. The results show that the AGWMOM test has improved the number of robust conditions under skewed normal tailed and skewed heavy tailed distributions compared to the other tests. Additionally, the test produced high power in most conditions under four groups with unbalanced sample size. It leads that this test is convenient specifically when the data distribution is heavy tailed. 2016 Thesis https://etd.uum.edu.my/6065/ https://etd.uum.edu.my/6065/1/s813614_01.pdf text eng public https://etd.uum.edu.my/6065/2/s813614_02.pdf text eng public other masters Universiti Utara Malaysia Abdullah, S., Yahaya, S. S. S., & Othman, A. R. (2007). Proceedings of The 9th Islamic Countries Conference on Statistical Sciences 2007. In Modified One Step M Estimator as a Central Tendency Measure for Alexander-Govern Test P. 834-842. Abdullah, S, Syed Yahaya, & Othman, A. R. (2008). A Power Investifation of Alexander-Govern Test Using Modified One Step M-Estimator as the Central Tendency Measure. IASC 2008: December 5-8, Yokohama, Japan. Alexander, R A,, & Govern, D. M. (1994). A New and Simpler Approximation for ANOVA Under Variance Heterogeneity. Journal Educational Statistics, 19(2), 91-101. Algina, J., Oshirna, T. C., & Lin, W.-Y. (1994). 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