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Robustness of S1 statistic with Hodges-Lehmann for skewed distributions


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.

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Abstract

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.

Item Type: Conference or Workshop Item (Paper)
Additional Information: ISBN: 978-0-7354-1444-0
Subjects: Q Science > QA Mathematics
Divisions: School of Quantitative Sciences
Depositing User: Mrs. Nor Aishah Ahad
Date Deposited: 04 Dec 2016 06:55
Last Modified: 04 Dec 2016 06:55
URI: http://repo.uum.edu.my/id/eprint/20177

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