Kaedah Alexander-Govern Menggunakan Penganggar Teguh Dengan Pendekatan Pangkasan Data: Kajian Simulasi

Kaedah Alexander-Govern Menggunakan Penganggar Teguh Dengan Pendekatan Pangkasan Data: Kajian Simulasi

Alexander-Govern method enables equality test of central tendency measures when the problem of heterogeneous variances arises. However, this method distorts under non-normal data. This shortcoming is caused by the use of mean as the central tendency measure, which is non robust to the non-normal da...

Full description

Saved in:
Bibliographic Details
Main Author: Suhaida, Abdullah
Format: Thesis
Language:eng
eng
Published: 2011
Subjects:
QA273-280 Probabilities
Mathematical statistics
Online Access:https://etd.uum.edu.my/2959/1/Suhaida_Abdullah.pdf
https://etd.uum.edu.my/2959/2/1.Suhaida_Abdullah.pdf
Tags: Add Tag
No Tags, Be the first to tag this record!
id my-uum-etd.2959
record_format uketd_dc
institution Universiti Utara Malaysia
collection UUM ETD
language eng
eng
advisor Syed Yahaya, Sharipah Soaad
Othman, Abdul Rahman
topic QA273-280 Probabilities
Mathematical statistics
spellingShingle QA273-280 Probabilities
Mathematical statistics
Suhaida, Abdullah
Kaedah Alexander-Govern Menggunakan Penganggar Teguh Dengan Pendekatan Pangkasan Data: Kajian Simulasi
description Alexander-Govern method enables equality test of central tendency measures when the problem of heterogeneous variances arises. However, this method distorts under non-normal data. This shortcoming is caused by the use of mean as the central tendency measure, which is non robust to the non-normal data. Under this condition, substituting the usual mean with robust estimators, namely adaptive trimmed mean and modified one step M estimator (MOM) apparently contribute to good control of Type I Error rates and improve the power of Alexander-Govern test. Both of these robust estimators used the technique of data trimming, yet with different approaches. Adaptive trimmed mean removes data based on a predetermined percentage of trimming and the trimming is done after the distributional shape of the data has been identified. The percentages of trimming used in this study encompassed the 10%, 15%, 20% and 25%. In contrast, the MOM estimator uses the technique of trimming data empirically. Empirical data trimming in this study emphasized on the trimming mechanism using three scale estimators, namely MADn, Sn and Tn. The new Alexander-Govern method is categorized as AH (Alexander-Govern method with adaptive trimmed mean) and AM (Alexander-Govern method with MOM estimator). AH method consists of AH10, AH15, AH20 and AH25 which are AH with trimming percentage of 10%, 15%, 20% and 25% respectively. While AM method comprises of AMM, AMS and AMT which denotes the integration of each of the scale estimators, MADn, Sn and Tn respectively in Alexander-Govern method. These new methods were assessed at certain conditions ranging from ideal to extreme. Evidently, the method of AH with 15% trimming is robust for all the conditions, with most of them are robust under liberal criterion. However, this method has low power in regards to heavy-tailed distribution. The performances of all the AM methods are however comparable to each other based on their ability to control Type I Error rates and the power of the tests which are almost the same for all the scale estimators used. Even though AM methods failed to control Type I error rates under heavy tailed distribution, nonetheless, the AM methods are very robust under skewed distribution where in most cases these methods meet the stringent robust criteria and high in power. All the new Alexander-Govern methods also show comparable performances with the original Alexander-Govern and the classical method under ideal conditions.
format Thesis
qualification_name Ph.D.
qualification_level Doctorate
author Suhaida, Abdullah
author_facet Suhaida, Abdullah
author_sort Suhaida, Abdullah
title Kaedah Alexander-Govern Menggunakan Penganggar Teguh Dengan Pendekatan Pangkasan Data: Kajian Simulasi
title_short Kaedah Alexander-Govern Menggunakan Penganggar Teguh Dengan Pendekatan Pangkasan Data: Kajian Simulasi
title_full Kaedah Alexander-Govern Menggunakan Penganggar Teguh Dengan Pendekatan Pangkasan Data: Kajian Simulasi
title_fullStr Kaedah Alexander-Govern Menggunakan Penganggar Teguh Dengan Pendekatan Pangkasan Data: Kajian Simulasi
title_full_unstemmed Kaedah Alexander-Govern Menggunakan Penganggar Teguh Dengan Pendekatan Pangkasan Data: Kajian Simulasi
title_sort kaedah alexander-govern menggunakan penganggar teguh dengan pendekatan pangkasan data: kajian simulasi
granting_institution Universiti Utara Malaysia
granting_department Awang Had Salleh Graduate School of Arts & Sciences
publishDate 2011
url https://etd.uum.edu.my/2959/1/Suhaida_Abdullah.pdf
https://etd.uum.edu.my/2959/2/1.Suhaida_Abdullah.pdf
_version_ 1747827470921367552
spelling my-uum-etd.29592016-04-28T00:36:55Z Kaedah Alexander-Govern Menggunakan Penganggar Teguh Dengan Pendekatan Pangkasan Data: Kajian Simulasi 2011 Suhaida, Abdullah Syed Yahaya, Sharipah Soaad Othman, Abdul Rahman Awang Had Salleh Graduate School of Arts & Sciences Awang Had Salleh Graduate School of Sciences QA273-280 Probabilities. Mathematical statistics Alexander-Govern method enables equality test of central tendency measures when the problem of heterogeneous variances arises. However, this method distorts under non-normal data. This shortcoming is caused by the use of mean as the central tendency measure, which is non robust to the non-normal data. Under this condition, substituting the usual mean with robust estimators, namely adaptive trimmed mean and modified one step M estimator (MOM) apparently contribute to good control of Type I Error rates and improve the power of Alexander-Govern test. Both of these robust estimators used the technique of data trimming, yet with different approaches. Adaptive trimmed mean removes data based on a predetermined percentage of trimming and the trimming is done after the distributional shape of the data has been identified. The percentages of trimming used in this study encompassed the 10%, 15%, 20% and 25%. In contrast, the MOM estimator uses the technique of trimming data empirically. Empirical data trimming in this study emphasized on the trimming mechanism using three scale estimators, namely MADn, Sn and Tn. The new Alexander-Govern method is categorized as AH (Alexander-Govern method with adaptive trimmed mean) and AM (Alexander-Govern method with MOM estimator). AH method consists of AH10, AH15, AH20 and AH25 which are AH with trimming percentage of 10%, 15%, 20% and 25% respectively. While AM method comprises of AMM, AMS and AMT which denotes the integration of each of the scale estimators, MADn, Sn and Tn respectively in Alexander-Govern method. These new methods were assessed at certain conditions ranging from ideal to extreme. Evidently, the method of AH with 15% trimming is robust for all the conditions, with most of them are robust under liberal criterion. However, this method has low power in regards to heavy-tailed distribution. The performances of all the AM methods are however comparable to each other based on their ability to control Type I Error rates and the power of the tests which are almost the same for all the scale estimators used. Even though AM methods failed to control Type I error rates under heavy tailed distribution, nonetheless, the AM methods are very robust under skewed distribution where in most cases these methods meet the stringent robust criteria and high in power. All the new Alexander-Govern methods also show comparable performances with the original Alexander-Govern and the classical method under ideal conditions. 2011 Thesis https://etd.uum.edu.my/2959/ https://etd.uum.edu.my/2959/1/Suhaida_Abdullah.pdf application/pdf eng validuser https://etd.uum.edu.my/2959/2/1.Suhaida_Abdullah.pdf application/pdf eng public Ph.D. doctoral Universiti Utara Malaysia Abdullah, S., Syed Yahaya, S. S., & Othman, A. R. (2008, 5-8 December). A power investigation of Alexander-Govern test using modified one step M estimator as a central tendency measure. Paper presented at the Joint Meeting of 4th World Conference of the IASC and 6th Conference of the Asian Regional Section of the IASC on Computational Statistics & Data Analysis, Yokohama, Japan. Abdullah, S., Syed Yahaya S. S., & Othman, A. R. (2007, 12-14 December). Modified one step M estimator as a central tendency measure for Alexander Govern test. Paper presented at the 9th Islamic Countries Conference On Statistical Sciences 2007, Shah Alam, Selangor, Malaysia. Alexander, R. A., & Govern, D. M. (1994). A new and simpler approximation for ANOVA under variance heterogeneity. Journal of Educational Statistics, 19(2), 91-101. Algina, J., & Lin, W.-Y. (1993). Type I error rate for Welch's test and James's second-order test under nonnormality and inequality of variance when there are two groups. . Paper presented at the The Annual Meeting of American Educational Research Association. Baguio, C. B. (2008). Trimmed mean as an adaptive robust estimator of location parameter for Weibull distribution. World Academy of Science, Engineering and Technology, 42, 681-686. Bradley, J. V. (1978). Robustness? British Journal of Mathematical and Statistical Psychology(31), 144-152. Cohen, J. (1988). Statistical power analysis for the behavioral sciences. New York: Academic Press, Inc. Efron, B., & Tibshirani, R. J. (1993). An introduction to the bootstrap. New York: Chapman & Hall, Inc. Elamir, E. A. H., & Seheult, A. H. (2003). Trimmed L-moments. Computational Statistics & Data analysis, 43, 299-314. Garthwaite, P. H., Jolliffe, I. T., & Jones, B. (2002). Statistical inference (Second ed.). New York: Oxford University Press. Guo, J.-H., & Luh, W.-M. (2000). Testing methods for the one-way fixed effects ANOVA models of log-normal samples. Journal of Applied Statistics, 27(6), 731-738. Hampel, F. R. (1974). The influence curve and its role in robust estimation. Journal of American Statisical Association, 69(346), 383-393. Hayes, A. F. (2005). Statistical methods for communication science (Vol. 1). New Jersey: Lawrence Erlbaum Associates, Inc. Hess, B., Olejnik, S., & Huberty, C. J. (2001). The efficacy of two improvement-over-chance effect sizes for two-group univariate comparisons under variance heterogeneity and nonnormality. Educational and Psychological Measurement, 61(909), 909-936. Hill, G. W. (1970). Algorithm 395. Student's t-distribution. Cummunications of the ACM, 13(10), 617-619. Hoaglin, D. C., Mosteller, F., & Tukey, J. W. (1983). Understanding robust and exploratory data analysis: John Wiley & Sons, Inc. Hogg, R. V. (1967). Some observations on robust estimation. Journal of American Statisical Association, 62(320), 1179-1186. Hogg, R. V. (1974). Adaptive robust prosedures: A partial review and some suggestion for future applications and theory Journal of American Statisical Association, 69(348), 909-923. Hosking, J. R. M. (2007). Some theory and practical uses of trimmed L-moments. Journal of Statistical Planning and Inference, 137, 3024-3039. Huber, P. J. (2004). Robust statistics. New Jersey: John Wiley & Sons, Inc. James, G. S. (1951). The comparison of several groups of observations when the ratios of the population variances are unknown. Biometrika, 38, 324-329. Keselman, H. J., Othman, A. R., Wilcox, R. R., & Fradette, K. (2004). The new and improved two-sample t test. Psychological Science, 15(1), 47-51. 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. Keselman, H. J., Wilcox, R. R., Othman, A. R., & Fradette, K. (2002). Trimming, transforming statistics, and bootstrapping: Circumvanting the biasing effect of heteroscedasticityand nonnormality. Journal of Modern Applied Statistical Methods, 1(2), 288-309. Leonowicz, Z., Karvanen, J., & Shishkin, S. L. (2005). Trimmed estimators for robust averaging of event-related potentials. Journal of Neuroscience Methods, 142(1), 17-26. Lix, L. M., & Keselman, H. J. (1998). To trim or not to trim: Tests of location equality under heteroscedasticity and nonnormality. Educational and Psychological Measurement, 58(3), 409-429. Luh, W.-M. (1999). Developing trimmed mean test statistics for two-way fixed-effects ANOVA models under variance heterogeneity and nonnormality. Journal of Experimental Education, 67(3), 243-265. Luh, W.-M., & Guo, J.-H. (2001). Transformation Works For Non-normality? On One-sample Transformation Trimmed t Methods. British Journal of Mathematical and Statistical Psychology, 54, 227-236. Luh, W.-M., & Guo, J.-H. (2005). Heteroscedastic Test Statistics for One-Way Analysis of Variance: The Trimmed Means and Hall's Transformation Conjunction. The Journal of Experimental Education, 74(1), 75-100. Md Yusof, Z. (2010). Type I error and power rates of robust methods with variable trimmed mean. Unpublished PhD thesis, Universiti Sains Malaysia. Morgenthaler, S. (2007). Resistence to outliers vs heavy-talied error distributions. Paper presented at the 9th Islamic Countries Conference on Statistical Sciences. Murphy, K. R., & Myors, B. (1998). Statistical Power Analysis: A Simple and General Model for Traditional and Modern Hypothesis Tests: Lawrence Erlbaum Associates. Myers, L. (1998). Comparability of the James' second-order approximation test and the Alexander and Govern A statistic for non-normal heteroscedastic data. Journal of Statistical Computational Simulation, 60, 207-222. Othman, A. R., Keselman, H. J., Padmanabhan, A. R., Wilcox, R. R., & Fredette, K. (2004). Comparing Measures of The 'Typical' Score Across Treatment Groups. British Journal of Mathematical and Statistical Psychology, 57, 215-234. Reed III, J. F., & Stark, D. B. (1996). Hinge estimator of location: Robust to asymmetry. Computer methods and programming in biomedicine, 49, 11-17. Rosenberger, J. L., & Gasko, M. (1983). Comparing Location Estimators: Trimmed Means, Medians and Trimean. In D. C. Hoaglin, F. Mosteller & J. W. Tukey (Eds.), Understanding robust and exploratory data analysis (pp. 297-338). New York: John Wiley & Sons, Inc. Rousseeuw, P. J., & Croux, C. (1993). Alternatives to the Median Absolute Deviation. Journal of American Statisical Association, 88(424), 1273-1283. Rousseeuw, P. J., & Verboven, S. (2002). Robust estimation in very small samples. Computational Statistics & Data analysis, 40, 741-758. SAS Institute Inc. (2009). SAS/IML 9.2 User's guide. SAS Institute Inc, Cary, NC Schneider, P. J., & Penfield, D. A. (1997). Alexander and Govern's approximation: Providing an alternative to ANOVA under variance heterogeneity. Journal of Experimental Education, 65(3), 271-287. Staudte, R.G. and Sheather, S.J. (1990). Robust Estimation and Testing. John Wiley & Sons Inc., New York. Stevens, J. P. (2007). Intermediate statistics: A modern approach (Third edition ed.). Lawrence Erlbaum Associates. New York. Syed Yahaya, S. S. (2005). Robust statistical procedures for testing the equality of central tendency parameters under skewed distributions. Unpublished Ph.D thesis. Universiti Sains Malaysia. Syed Yahaya, S. S., Othman, A. R., & Keselman, H. J. (2006). Comparing the “typical score” across independent groups based on different criteria for trimming. Metodološki zvezki, 3(1), 49-62. Syed Yahaya, S. S., Othman, A. R., & Keselman, H. J. (2004). Testing the equality of location parameters for skewed distributions using S1 with high breakdown robust scale estimators. Statistics for Industry and Technology, 319-328. Tiku, M. L., Tan, W. Y., & Balakrishnan, N. (1986). Robust inference. New York, USA: Marcel Dekker Inc. Weerahandi, S. (1995). ANOVA under unequal error variances. Biometrics, 51(2), 589-599. Welch, B. L. (1947). The generalization of Student's problem when several different population variances are involved. Biometrika, 34, 29-35. Welch, B. L. (1951). On the comparison of several mean values: An alternative approach. Biometrika, 38, 330-336. Wilcox, R. R. (2005a). Introduction to robust estimation and hypothesis testing (Second ed.): California: Academic Press. Wilcox, R. R. (2005b). Comparing Medians: An overview plus new results on dealing with heavy-tailed distributions. The Journal of Experimental Education, 73(3), 249-263. Wilcox, R. R. (2005c). New methods for comparing groups: Strategies for incresing the probability of detecting true differences. Psychological Science, 14(5), 272-275. Wilcox, R. R. (2003). Multiple comparisons based on a modified one-step M-estimator. Journal of Applied Statistics, 30(10), 1231-1241. Wilcox, R. R. (2002). Understanding the practical advantages of modern ANOVA methods. Journal of Clinical Child and Adolescent Psychology, 31(3), 399-412. Wilcox, R. R. (1997) A Bootstrap modification of the Alexander-Govern ANOVA method, plus comments on comparing trimmed means. Educational and Psychological Measurement, 57(4), 655-665. Wilcox, R. R. (1992). Why can methods for comparing means have relatively low power, and what can you do to correct the problem? Current Directions in Psychological Science, 1(3), 101-105. Wilcox, R. R., Charlin, V. L., & Thompson, K. L. (1986). New monte carlo results on the robustness of the ANOVA F, W and F* statistics. Communications in Statistics-Simulations, 15(4), 933-943. Wilcox, R. R., & Keselman, H. J. (2003). Repeated measures one-way ANOVA based on a modified one-step m-estimator. British Journal of Mathematical and Statistical Psychology, 56(15-25). Wu, M. (2006). Trimmed and winsorized estimators. Unpublished Ph.D thesis, Michigan State University. Yuen, K. K. (1974). The two-sample trimmed t for unequal population variances. Biometrika, 61(1), 165-171.

Similar Items