Robust multiple pairwise comparison procedure for adaptive trimmed mean via P-Method

Robust multiple pairwise comparison procedure for adaptive trimmed mean via P-Method

Robust omnibus tests which are widely available are commonly used as alternatives to the classical Analysis of Variance (ANOVA) when the assumptions are violated. Like ANOVA, each of these omnibus tests needs a post hoc (pairwise multiple comparison) procedure when the test turns out to be signific...

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Main Author: Low, Joon Khim
Format: Thesis
Language:eng
eng
Published: 2016
Subjects:
QA273-280 Probabilities
Mathematical statistics
QA299.6-433 Analysis
Online Access:https://etd.uum.edu.my/6059/1/s810421_01.pdf
https://etd.uum.edu.my/6059/2/s810421_02.pdf
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id my-uum-etd.6059
record_format uketd_dc
institution Universiti Utara Malaysia
collection UUM ETD
language eng
eng
advisor Syed Yahya, Sharipah Soaad
topic QA273-280 Probabilities
Mathematical statistics
QA299.6-433 Analysis
spellingShingle QA273-280 Probabilities
Mathematical statistics
QA299.6-433 Analysis
Low, Joon Khim
Robust multiple pairwise comparison procedure for adaptive trimmed mean via P-Method
description Robust omnibus tests which are widely available are commonly used as alternatives to the classical Analysis of Variance (ANOVA) when the assumptions are violated. Like ANOVA, each of these omnibus tests needs a post hoc (pairwise multiple comparison) procedure when the test turns out to be significant. However, works on post hoc procedures for the existing robust omnibus tests are not given much attention. Most of the robust omnibus tests are left without the post hoc procedures and the tests are deemed incomplete. In this study, we have taken the initiative to develop the post hoc test known as P-Method for HQ and HQ1, the two robust estimators priori used in testing the equality of groups. Apart from the two robust estimators, this study also looked into the effectiveness of the classical mean using P-Method. P-Method is a bootstrap based method. Respectively denoted as P-HQ, P-HQ1 and P-Mean, computer programs for the procedures were developed and their effectiveness in controlling Type I error (robustness) was evaluated. A simulation study was conducted to investigate on the strength and weakness of the procedures. For such, five variables were manipulated to create various conditions that often occur in real life. These variables are the shape of the distributions, number of groups, sample sizes, degree of variance heterogeneity and pairing of sample sizes and variances. A total of 2000 datasets were simulated using SAS/IML Version 9.2. Bradley’s liberal criterion of robustness was adopted to benchmark each procedure. Finally, the proposed methods (P-HQ and P-HQ1) and P-Mean were compared with the existing LSD-Bonferroni correction. The finding revealed that P-HQ and P-HQ1 could effectively control Type I error and thus could be used as the post hoc procedure for significant omnibus test using HQ and HQ1 estimators. In addition, this study also observed that P-Mean is robust even under severe violation of assumptions. In general, this study managed to develop a reliable post hoc test for HQ dan HQ1 estimators.
format Thesis
qualification_name masters
qualification_level Master's degree
author Low, Joon Khim
author_facet Low, Joon Khim
author_sort Low, Joon Khim
title Robust multiple pairwise comparison procedure for adaptive trimmed mean via P-Method
title_short Robust multiple pairwise comparison procedure for adaptive trimmed mean via P-Method
title_full Robust multiple pairwise comparison procedure for adaptive trimmed mean via P-Method
title_fullStr Robust multiple pairwise comparison procedure for adaptive trimmed mean via P-Method
title_full_unstemmed Robust multiple pairwise comparison procedure for adaptive trimmed mean via P-Method
title_sort robust multiple pairwise comparison procedure for adaptive trimmed mean via p-method
granting_institution Universiti Utara Malaysia
granting_department Awang Had Salleh Graduate School of Arts & Sciences
publishDate 2016
url https://etd.uum.edu.my/6059/1/s810421_01.pdf
https://etd.uum.edu.my/6059/2/s810421_02.pdf
_version_ 1747828016557326336
spelling my-uum-etd.60592021-04-05T03:18:55Z Robust multiple pairwise comparison procedure for adaptive trimmed mean via P-Method 2016 Low, Joon Khim Syed Yahya, Sharipah Soaad Awang Had Salleh Graduate School of Arts & Sciences Awang Had Salleh Graduate School of Arts and Sciences QA273-280 Probabilities. Mathematical statistics QA299.6-433 Analysis Robust omnibus tests which are widely available are commonly used as alternatives to the classical Analysis of Variance (ANOVA) when the assumptions are violated. Like ANOVA, each of these omnibus tests needs a post hoc (pairwise multiple comparison) procedure when the test turns out to be significant. However, works on post hoc procedures for the existing robust omnibus tests are not given much attention. Most of the robust omnibus tests are left without the post hoc procedures and the tests are deemed incomplete. In this study, we have taken the initiative to develop the post hoc test known as P-Method for HQ and HQ1, the two robust estimators priori used in testing the equality of groups. Apart from the two robust estimators, this study also looked into the effectiveness of the classical mean using P-Method. P-Method is a bootstrap based method. Respectively denoted as P-HQ, P-HQ1 and P-Mean, computer programs for the procedures were developed and their effectiveness in controlling Type I error (robustness) was evaluated. A simulation study was conducted to investigate on the strength and weakness of the procedures. For such, five variables were manipulated to create various conditions that often occur in real life. These variables are the shape of the distributions, number of groups, sample sizes, degree of variance heterogeneity and pairing of sample sizes and variances. A total of 2000 datasets were simulated using SAS/IML Version 9.2. Bradley’s liberal criterion of robustness was adopted to benchmark each procedure. Finally, the proposed methods (P-HQ and P-HQ1) and P-Mean were compared with the existing LSD-Bonferroni correction. The finding revealed that P-HQ and P-HQ1 could effectively control Type I error and thus could be used as the post hoc procedure for significant omnibus test using HQ and HQ1 estimators. In addition, this study also observed that P-Mean is robust even under severe violation of assumptions. In general, this study managed to develop a reliable post hoc test for HQ dan HQ1 estimators. 2016 Thesis https://etd.uum.edu.my/6059/ https://etd.uum.edu.my/6059/1/s810421_01.pdf text eng public https://etd.uum.edu.my/6059/2/s810421_02.pdf text eng public masters masters Universiti Utara Malaysia Abdullah, S. (2011). Kaedah Alexander – Govern dengan pendekatan pangkasan data: satu kajian simulasi. (Unpublished doctoral dissertation). Universiti Utara Malaysia. Abdullah, S., Syed Yahaya, S. 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Pairwise multiple comparison tests when data are nonnormal. Educational and Psychological Measurement, 62, 420-434. Keselman, H. J., Othman, A. R., Wilcox, R. R. & Fradette, K. (2004). The new and improved two-sample t test. Psychological Science, 15(1), 47. Keselman, H. J., Wilcox, R. R., Algina, J. & Othman, A. R. (2004). A power comparison of robust test statistics based on adaptive estimators. Journal of Modern Applied Statistical Methods, 3(1), 27–38. Keselman, H. J., Wilcox, R. R., Lix, L. M., Algina, J. & Fradette, K. (2007). Adaptive robust estimation and testing. British Journal of Mathematical and Statistical Psychology, 60, 267–293. Kowalchuk, R. K., Keselman, H. J., Wilcox, R. R. & Algina, J. (2006). Multiple comparison procedures, trimmed means and transformed statistics. Journal of Modern Applied Statistical Methods, 5, 43 – 64. McClave, Benson & Sincich (2007). Statistics for business and economics (9th ed.). Singapore: Pearson Education South Asia Pte Ltd. McHugh, M. L. (2011). Multiple comparison analysis testing in ANOVA. Biochemia Medica, 21(3), 2011, 203 – 209. Md. Yusof, Z., Othman, A. R. & Syed Yahaya, S. S. (2010). Comparison of Type I errorrates between T1 and Ft statistics for unequal population variance using variable trimming. Malaysian Journal of Mathematical Sciences, 4(2), 2010, 195 – 207. Muhammad Di, N. F. (2013). The robustness of H Statistic with Hinge estimators as the location measures. (Unpublished doctoral dissertation). Universiti Utara Malaysia. Muhammad Di, N. F., Syed Yahaya, S. S. & Abdullah, S. (2014). Comparing groups using robust H statistics with adaptive trimmed mean. Sains Malaysiana, 43(4), 643 – 648. Multiple-Comparison Procedures. Retrieved from http://www2.hawaii.edu/~taylor/z631/multcomp.pdf/ Newsom (2006). Post hoc tests. USP 534 Data Analysis I Spring. Retrieved from www.strath.ac.uklaer/materials/4dataanalysisin educationalresearch/unit6/posthoctests/ Newsom (2012). Post hoc tests. USP 634 Data Analysis I Spring. Retrieved from http://web.pdx.edu/~g3jn/da1/ho_post%20hoc.pdf Reed, J.F. & Stark, D. B. (1996). Hinge estimators of location: robust to asymmetry. Computer Methods and Programs in Biomedicine, 49, 11 – 17. Rousseeuw, P. J. & Leroy, A. M. (2003). Robust regression and outlier detection. United States of America. Singh, K. (1998). Breakdown theory for bootstrap quantiles. Annals of Statistics, 26, 1719 – 1732. Spinella, S. (2011). Using the descriptive bootstrap to evaluate result replicability (because statistical significance doesn’t). Texas A&M University. Staudte, R. G. & Sheather, S. J. (1990). Robust Estimation and Testing. John Wiley & Sons Inc., New York. Stuart, J. P., Nancy, L. G. & Anastasios, A. T. (1987). The analysis of multiple endpoints in clinical trials. Biometrics, 43(3), 487 – 498. Wilcox, R. R. (1997). Introduction to Robust Estimation and Hypothesis Testing. Academic Press, New York. Wilcox, R. R. (2001). Pairwise comparisons of trimmed means for two or more groups. Psychometrika, 66(3), 343 – 356. Wilcox, R. R. & Keselman, H. J. (2002). Power analyses when comparing trimmed means. Journal of Modern Applied Statistical Methods, 1(1): 24 – 31. Wilcox, R. R. (2003). Multiple comparisons based on a modified one-step Mestimator. Journal of Applied Statistics, 30(10), 1231 – 1241. Williams, L. J. & Abdi, H. (2010). Fisher’s least significant difference (LSD) test. Encyclopedia of Research Design. Zachary, R. S. & Craig, S. W. (2006). Central limit theorem and sample size. Retrieved from http://www.umass.edu/remp/Papers/Smith&Wells_NERA06.pdf

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