Sains Malaysiana 45(3)(2016): 499–506

Comparison of Outlier Detection Methods in Standard 2 × 2 Crossover Design

(Perbandingan Kaedah Pengesanan Titik Terpencil dalam Piawai 2 × 2 Reka Bentuk Pindah Silang)

FONG PENG LIM¹, IBRAHIM MOHAMED¹*, NOORIZAM DAUD² & SIEW LI GOH³

¹Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Federal Territory

Malaysia

²Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, 40450 Shah Alam, Selangor Darul Ehsan, Malaysia

³Sport Medicine Clinic, University of Malaya Hospital, 50603 Kuala Lumpur, Federal Territory

Malaysia

Diserahkan: 19 Januari 2015/Diterima: 21 September 2015

ABSTRACT

This paper discussed methods for outlier detection in standard 2 × 2 crossover studies. Two outlier detection procedures were carried out based on residuals. Under a simplified model of 2 × 2 crossover design, we present the classical calculation of studentized residual (SR1) and propose a new studentized residual using median absolute deviation (SR2) to identify possible outlying subjects. The performances of both procedures in detecting subject outliers were compared. We show via simulation that a proposed procedure using SR2 is more powerful than that using SR1 for outlier detection. As an illustration, these procedures were applied to two real data sets from studies of bioavailability and kinesiology, respectively.

Keywords: Crossover design; median absolute deviation; outlier; residual

ABSTRAK

Kertas kerja ini membincangkan kaedah untuk mengesan titik terpencil dalam piawai 2 × 2 kajian pindah silang. Dua prosedur mengesan titik terpencil telah dijalankan berdasarkan sisa. Berdasarkan satu model 2 × 2 kajian pindah silang yang diringkaskan, kami menunjukkan pengiraan studentized sisa klasik (SR1) dan mencadangkan satu studentized sisa baharu yang menggunakan sisihan mutlak median (SR2) untuk mengesan subjek terpencil yang mungkin wujud. Prestasi kedua-dua prosedur dalam pengesanan subjek terpencil dibandingkan. Melalui simulasi, kami mendapati prosedur menggunakan SR2 yang dicadangkan memberikan prestasi yang lebih baik daripada prosedur menggunakan SR1 untuk pengesanan titik terpencil. Sebagai ilustrasi, prosedur tersebut digunakan untuk dua set data kajian sebenar dalam bidang bioketersediaan dan kinesiologi.

Kata kunci: Reka bentuk pindah silang; sisa; sisihan mutlak median; titik terpencil

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*Pengarang untuk surat-menyurat; email: imohamed@um.edu.my