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

Diserahkan: 23 Julai 2012/Diterima: 14 Ogos 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 parameteric (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 mengintegrasikanH 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

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*Pengarang untuk surat-menyurat; email: nurfaraidah@gmail.com