Robustness of S1 statistic with Hodges-Lehmann for skewed distributions
Analysis of variance (ANOVA) is a common use parametric method to test the differences in means for more than two groups when the populations are normally distributed. ANOVA is highly inefficient under the influence of non- normal and heteroscedastic settings.When the assumptions are violated, resea...
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| Format: | Conference or Workshop Item |
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2016
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| _version_ | 1825804321069989888 |
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| author | Ahad, Nor Aishah Syed Yahaya, Sharipah Soaad Lee, Ping Yin |
| author_facet | Ahad, Nor Aishah Syed Yahaya, Sharipah Soaad Lee, Ping Yin |
| author_sort | Ahad, Nor Aishah |
| collection | UUM |
| description | Analysis of variance (ANOVA) is a common use parametric method to test the differences in means for more than two groups when the populations are normally distributed. ANOVA is highly inefficient under the influence of non- normal and heteroscedastic settings.When the assumptions are violated, researchers are looking for alternative such as Kruskal-Wallis under nonparametric or robust method.This study focused on flexible method, S 1 statistic for comparing groups using median as the location estimator.S 1 statistic was modified by substituting the median with Hodges-Lehmann and the default scale estimator with the variance of Hodges-Lehmann and MAD n to produce two different test statistics for comparing groups. Bootstrap method was used for testing the hypotheses since the sampling distributions of these modified S 1 statistics are unknown. The performance of the proposed statistic in terms of Type I error was measured and compared against the original S 1 statistic, ANOVA and Kruskal-Wallis. The propose procedures show improvement compared to the original statistic especially under extremely skewed distribution. |
| first_indexed | 2024-07-04T06:12:39Z |
| format | Conference or Workshop Item |
| id | uum-20177 |
| institution | Universiti Utara Malaysia |
| last_indexed | 2024-07-04T06:12:39Z |
| publishDate | 2016 |
| record_format | eprints |
| spelling | uum-201772016-12-04T06:55:07Z https://repo.uum.edu.my/id/eprint/20177/ Robustness of S1 statistic with Hodges-Lehmann for skewed distributions Ahad, Nor Aishah Syed Yahaya, Sharipah Soaad Lee, Ping Yin QA Mathematics Analysis of variance (ANOVA) is a common use parametric method to test the differences in means for more than two groups when the populations are normally distributed. ANOVA is highly inefficient under the influence of non- normal and heteroscedastic settings.When the assumptions are violated, researchers are looking for alternative such as Kruskal-Wallis under nonparametric or robust method.This study focused on flexible method, S 1 statistic for comparing groups using median as the location estimator.S 1 statistic was modified by substituting the median with Hodges-Lehmann and the default scale estimator with the variance of Hodges-Lehmann and MAD n to produce two different test statistics for comparing groups. Bootstrap method was used for testing the hypotheses since the sampling distributions of these modified S 1 statistics are unknown. The performance of the proposed statistic in terms of Type I error was measured and compared against the original S 1 statistic, ANOVA and Kruskal-Wallis. The propose procedures show improvement compared to the original statistic especially under extremely skewed distribution. 2016-08-16 Conference or Workshop Item PeerReviewed Ahad, Nor Aishah and Syed Yahaya, Sharipah Soaad and Lee, Ping Yin (2016) Robustness of S1 statistic with Hodges-Lehmann for skewed distributions. In: 4th International Conference on Quantitative Sciences and Its Applications (ICOQSIA 2016), 16–18 August 2016, Bangi, Selangor, Malaysia. http://doi.org/10.1063/1.4966092 doi:10.1063/1.4966092 doi:10.1063/1.4966092 |
| spellingShingle | QA Mathematics Ahad, Nor Aishah Syed Yahaya, Sharipah Soaad Lee, Ping Yin Robustness of S1 statistic with Hodges-Lehmann for skewed distributions |
| title | Robustness of S1 statistic with Hodges-Lehmann for skewed distributions |
| title_full | Robustness of S1 statistic with Hodges-Lehmann for skewed distributions |
| title_fullStr | Robustness of S1 statistic with Hodges-Lehmann for skewed distributions |
| title_full_unstemmed | Robustness of S1 statistic with Hodges-Lehmann for skewed distributions |
| title_short | Robustness of S1 statistic with Hodges-Lehmann for skewed distributions |
| title_sort | robustness of s1 statistic with hodges lehmann for skewed distributions |
| topic | QA Mathematics |
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