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Zakiyah Zain
Universiti Utara Malaysia
Computer Science & IT Decision Sciences, Operations Research & Management Engineering Environmental Science Industrial & Manufacturing Engineering Mathematics Transportation

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Journal : ComTech: Computer, Mathematics and Engineering Applications

 1 
Winsorized Modified One Step M-Estimator As a Measure of the Central Tendency in the Alexander-Govern Test Tobi Kingsley Ochuko; Suhaida Abdullah; Zakiyah Zain; Sharipah Syed Soaad Yahaya
ComTech: Computer, Mathematics and Engineering Applications Vol. 7 No. 3 (2016): ComTech
Publisher : Bina Nusantara University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21512/comtech.v7i3.2505

Abstract

This research dealt with making comparison of the independent group tests with the use of parametric technique. This test used mean as its central tendency measure. It was a better alternative to the ANOVA, the Welch test and the James test, because it gave a good control of Type I error rates and high power with ease in its calculation, for variance heterogeneity under a normal data. But the test was found not to be robust to non-normal data. Trimmed mean was used on the test as its central tendency measure under non-normality for two group condition, but as the number of groups increased above two, the test failed to give a good control of Type I error rates. As a result of this, the MOM estimator was applied on the test as its central tendency measure and is not influenced by the number of groups. However, under extreme condition of skewness and kurtosis, the MOM estimator could no longer control the Type I error rates. In this study, the Winsorized MOM estimator was used in the AG test, as a measure of its central tendency under non-normality. 5,000 data sets were simulated and analysed for each of the test in the research design with the use of Statistical Analysis Software (SAS) package. The results of the analysis shows that the Winsorized modified one step M-estimator in the Alexander-Govern (AGWMOM) test, gave the best control of Type I error rates under non-normality compared to the AG test, the AGMOM test, and the ANOVA, with the highest number of conditions for both lenient and stringent criteria of robustness. 
The Power of the Test for the Winsorized Modified Alexander-Govern Test Tobi Kingsley Ochuko; Suhaida Abdullah; Zakiyah Zain; Sharipah Syed Soaad Yahaya
ComTech: Computer, Mathematics and Engineering Applications Vol. 7 No. 4 (2016): ComTech
Publisher : Bina Nusantara University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21512/comtech.v7i4.3764

Abstract

This research examined the usage of the parametric method in comparing two or more means as independent group test, for instance, the Alexander-Govern (AG) test. The utilization of mean as the determinant for the center of distribution of variance diversity takes place in testing, and the test provides excellence in maintaining the amount of Type I error and giving immense sensitivity for a regular data. Unfortunately, it isineffective on irregular data, leading to the application of trimmed mean upon testing as the determinant for the center of distribution under irregular data for two group condition. However, as the group quantity is more than two, the estimator unsuccessfully provides excellence in maintaining the amount of Type I error. Therefore, an estimator high in effectiveness called the MOM estimator was introduced for the testing as the determinant for the center of distribution. Group quantity in a test does not affect the estimator, but it unsuccessfully providesexcellence in maintaining the amount of Type I error under intense asymmetry and unevenness. The application of Winsorized modified one-step M-estimator (WMOM) upon the Alexander-Govern testing takes place so that it can prevail against its drawbacks under irregular data in the presence of variance diversity, can eliminate the presence of the outside observation and can provide effectiveness for the testing on irregular data. Statistical Analysis Software (SAS) was used for the analysis of the tests. The results show that the AGWMOM test gave the most intense sensitivity under g = 0,5 and h = 0,5, for four group case and g = 0 and h = 0, under six group case, differing from three remaining tests and the sensitivity of the AG testing is said suffices and intense enough.
Co-Authors Mohd Kamal Mohd Nawawi Sharipah Syed Soaad Yahaya Siti Mariam Man Suhaida Abdullah Tobi Kingsley Ochuko