Sains Malaysiana 43(7)(2014): 1095–1100

Sensitivity Analysis of the Refinement to the Mann-Whitney Test

(Analisis Kepekaan Penghalusan kepada Ujian Mann-Whitney)

ABDUL RAHMAN BIN OTHMAN & LAI CHOO HENG*

Robust Statistics Computational Laboratory, Pusat Pengajian Pendidikan Jarak Jauh

Universiti Sains Malaysia, 11800 USM, Pulau Pinang, Malaysia

Diserahkan: 5 Februari 2013/Diterima: 2 Oktober 2013

ABSTRACT

The aim of researchers when comparing two independent groups is to collect large normally distributed samples unless they lack the resources to access them. In these situations, there are a myriad of non-parametric tests to select, of which the Mann Whitney U test is the most commonly used. In spite of its great advantages of usage, the U test is capable of producing inflated Type I error when applied in situation of heterogeneity or distinct variances. This current study will present a viable alternative called the refined Mann-Whitney test (RMW). A Monte Carlo evaluation test is conducted on RMW using artificial data of various combinations of extreme test conditions. This study reviews that the RMW test justified its development by enhancing the performance of the U test. The RMW test is able to control well its Type I error rates even though it has a lower power.

Keywords: Mann-Whitney test; Monte Carlo; power; refined Mann-Whitney test; Type I error

ABSTRAK

Semasa membuat perbandingan dua kumpulan tak bersandar, matlamat penyelidik ialah untuk mengumpul sampel taburan normal yang besar. Jika menghadapi kekurangan sumber untuk mencapai matlamat tersebut, terdapat pelbagai pilihan ujian tak-berparameter dengan ujian U Mann-Whitney paling sering dipilih. Sungguhpun ujian Mann-Whitney mempunyai banyak kelebihan daripada segi kegunaan, tetapi ia berkemungkinan menghasilkan ralat jenis I yang tinggi semasa digunakan dalam situasi beza varians yang ketara. Kajian ini akan memperkenalkan satu ujian alternatif yang dikenali sebagai ujian pengubahsuaian Mann-Whitney (RMW). Satu ujian penilaian Monte Carlo dijalankan dengan menggunakan data tiruan daripada pelbagai gabungan situasi pengujian yang ekstrem. Kajian ini mendapati ujian RMW menepati langkah pengubahsuaian demi penambahbaikan prestasi ujian Mann-Whitney. Ujian RMW dapat mengawal ralat jenis I dengan baik sungguhpun kuasanya rendah.

Kata kunci: Kuasa; Monte Carlo; ralat jenis I; ujian Mann-Whitney; ujian pengubahsuaian Mann-Whitney

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*Pengarang untuk surat-menyurat; email: lchooheng@yahoo.com