Sains Malaysiana 43(4)(2014): 643–648

 

Comparing Groups Using Robust H Statistic with Adaptive Trimmed Mean

(Perbandingan Kumpulan Menggunakan H Statistik Tegar dan Min Terpangkas Suai)

 

 

NUR FARAIDAH MUHAMMAD DI1*, SHARIPAH SOAAD SYED YAHAYA2& SUHAIDA ABDULLAH2

 

139. JBC, Taman Bukit Cermin, 28400 Mentakab, Pahang Darul Makmur, Malaysia

 

2School of Quantitative Science, College of Arts and Sciences

University Utara Malaysia, 06010 UUM Sintok, Kedah Darul Aman, Malaysia

 

Received: 23 July 2012/Accepted: 14 August 2013

 

ABSTRACT

An alternative robust method for testing the equality of central tendency measures was developed by integrating H Statistic with adaptive trimmed mean using hinge estimator, HQ. H Statistic is known for its ability to control Type I error rates and HQ is a robust location estimator. This robust estimator used asymmetric trimming technique, where it trims the tail of the distribution based on the characteristic of that particular distribution. To investigate on the performance (i.e. robustness) of the procedure, some variables were manipulated to create conditions which are known to highlight its strengths and weaknesses. Bootstrap method was used to test the hypothesis. The integration seemed to produce promising robust procedure that is capable of addressing the problem of violations to the assumptions. About 20% trimming is the appropriate amount of trimming for the procedure, where this amount is found to be robust in most conditions. This procedure was also proven to be robust as compared to the parametric (ANOVA) and non-parametric (Kruskal-Wallis) methods.

 

Keywords: Asymmetric trimmed mean; bootstrap; H Statistic; hinge estimator; robust statistics; Type I error rates

ABSTRAK

Kaedah alternatif yang teguh bagi menguji persamaan sukatan kecenderungan memusat telah dibentuk dengan mengintegrasikan H Statistik dengan min terpangkas suai menggunakan penganggar engsel, HQ. H Statistik dikenali kerana kebolehannya untuk mengawal ralat jenis I dan HQ adalah penganggar lokasi yang teguh. Penganggar teguh ini menggunakan teknik pemangkasan asimetri, dengan memangkas hujung taburan berdasarkan ciri-ciri taburan tersebut. Bagi menguji prestasi (iaitu keteguhan) prosedur, beberapa pemboleh ubah dimanipulasi untuk melihat kekuatan dan kelemahan prosedur. Kaedah Butstrap digunakan untuk menguji hipotesis. Integrasi ini menghasilkan prosedur teguh yang mampu menangani masalah pelanggaran andaian. Nilai pemangkas yang sesuai bagi prosedur ini ialah 20% dan didapati tegar dalam kebanyakan keadaan yang dikaji. Prosedur ini juga telah terbukti teguh berbanding kaedah parametrik (ANOVA) dan kaedah tidak berparametrik (Kruskal-Wallis).

 

Kata kunci: Butstrap; H statistik; min terpangkas asimetri; penganggar engsel; ralat jenis I; statistik teguh

REFERENCES

Baguio, C.B. 2008. Trimmed mean as an adaptive robust estimator of a 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.

Hogg, R.V. 1974. Adaptive robust procedures: A partial review and some suggestions for future applications and theory. Journal of the American Statistical Association 69: 909-923.

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., Algina, J. & Fradette, K. 2005. Robust confidence intervals for effect size in the two-group case. Journal of Modern Applied Statistical Methods 4(2): 353-371.

Luh, W.M. & Guo, J.H. 1999. A powerful transformation trimmed mean method for one-way fixed effects ANOVA model under non-normality and inequality of variances. British Journal of Mathematical and Statistical Pscycology 52(2): 303-320.

Othman, A.R., Keselman, H.J., Padmanabhan, A.R., Wilcox, R.R & Fradette, K. 2004. Comparing measures of the  'typical' score across treatment groups. British Journal of Mathematical and Statistical Psychology 57(2): 215-234.

Reed, J.F. & Stark, D.B. 1996. Hinge estimators of location: Robust to asymmetry. Computer Methods and Programs in Biomedicine 49(1): 11-17.

Schrader, R.M. & Hettmansperger, T.P. 1980. Robust analysis of variance based upon a likelihood ratio criterion. Biometrika 67(1): 93-101.

Syed Yahya, S.S. 2005. Robust statistical procedures for testing the equality of central tendency parameters under skewed distribution. PhD thesis. Universiti Sains Malaysia, Penang (Unpublished).

Wilcox, R.R. 2005. Trimmed Means. Encyclopedia of Statistics in Behavioral Science 4: 2066-2067.

Wilcox, R.R. 2012. Introduction to Robust Estimation and Hypothesis Testing. 3rd ed. San Diego, CA: Academic Press.

Wu, P.C. 2007. Modern one-way ANOVA F methods: Trimmed means, one step M-estimators and bootstrap methods. Journal of Quantitative Research 1: 155-172.

Yu, C.H. 2010. Parametric Tests. Creative Wisdom: http://www. creative-wisdom.com/teaching/WBI/parametric_test.shtml. Accessed on January 10, 2010.

Zar, J.H. 1996. ANOVA Assumptions. Biostatistical Analysis. 3rd ed. New Jersey: Prentice Hall Inc. p. 128.

 

*Corresponding author; email: nurfaraidah@gmail.com