Sains Malaysiana 51(11)(2022): 3829-3841
http://doi.org/10.17576/jsm-2022-5111-26
A
Comparison of Efficiency of Test Statistics for Detecting Outliers in Normal
Population
(Suatu Perbandingan Kecekapan Ujian Statistik untuk Mengesan Maklumat Tepian dalam Populasi Normal)
KULLAPHAT PROMTEP1,2 PHONTITA THIUTHAD1,2,* & NATCHITA INTARAMO2
1Statistics and
Applications Research Unit, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla,
90110 Thailand
2Division of Computational
Science, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla,
90110 Thailand
Diserahkan: 20 Oktober 2021/Diterima: 24 Jun 2022
Abstract
The objective of this research was to compare the efficiency among the test statistics which are used to detect outliers by testing hypothesis methods. The test statistics considered were Dixon’s test, Ferguson’s test, Grubbs’ test, Tw-test,
and Tietjen-Moore’s test. The outliers were divided, by how far
they are, into two groups: mild and extreme outliers. The efficiency of the test statistics was measured by the probability of type I error and the power of the test. The results showed that Tietjen-Moore’s test can control the probability of type I error according to Cochran and Bradley criteria in every situation. Tw-test has highest sensitivity in detecting one outlier when the sample size is small or moderate but, if the sample size is large, Grubbs’ test performs better. In the case of detecting one extreme outlier, the power
of four tests tend to increase as the sample size increases at the significance level 0.01. Given that k outliers are detected, Tietjen-Moore’s test provides higher power than Tw-test when k equals 10% of sample size when the outliers are both mild and extreme, contrary to the case when k make up for 20%.
Keywords: Detection of outliers; normal distribution; power of the test; Tietjen-Moore’s test; type I error
Abstrak
Objektif kajian ini adalah untuk membandingkan kecekapan antara statistik ujian yang digunakan untuk mengesan maklumat tepian dengan menguji kaedah hipotesis. Statistik ujian yang dipertimbangkan ialah ujian Dixon, ujian Ferguson, ujian Grubbs, ujian Tw dan ujian Tietjen-Moore.
Maklumat tepian dibahagikan mengikut jarak kepada dua kumpulan: maklumat tepian ringan dan maklumat tepian ekstrem. Kecekapan ujian statistik diukur dengan kebarangkalian ralat jenis I dan kuasa ujian. Keputusan menunjukkan bahawa ujian Tietjen-Moore boleh mengawal kebarangkalian ralat jenis I mengikut kriteria Cochran dan Bradley dalam setiap situasi. Ujian Tw mempunyai kepekaan tertinggi dalam mengesan satu maklumat tepian apabila saiz sampel kecil atau sederhana tetapi jika saiz sampel besar, ujian Grubbs menunjukkan prestasi yang lebih baik. Dalam kes mengesan satu maklumat tepian melampau, kuasa empat ujian cenderung meningkat apabila saiz sampel meningkat pada tahap keertian 0.01. Memandangkan k maklumat tepian dikesan, ujian Tietjen-Moore memberikan kuasa yang lebih tinggi daripada ujian Tw apabila k bersamaan dengan 10% saiz sampel apabila maklumat tepian adalah ringan dan melampau, bertentangan dengan kes apabila k membentuk 20%.
Kata kunci: Kuasa ujian; pengesan maklumat tepian; ralat jenis I; taburan normal; ujian Tietjen-Moore
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*Pengarang untuk surat-menyurat; email: phontita.t@psu.ac.th