ROBUSTNESS OF TRIMMED F STATISTIC WHEN HANDLING NONNORMAL DATA - Md Yusof, Zahayu; Othman, 2Abdul Rahman; Syed Yahaya, Sharipah Soaad (Malaysian Journal of Science, 2013)
When the assumptions of normality and homoscedasticity are met, researchers should have no doubt in using classical test such as t-test, to test for the equality of central tendency measures for two groups. However, in real life this perfect situation is rarely encountered. When the problem of nonnormality and variance heterogeneity simultaneously arise, rates of Type I error are usually inflated resulting in spurious rejection of null hypotheses. In addition, the classical least squares estimators can be highly inefficient when assumptions of normality are not fulfilled. The effect of non-normality on the trimmed F statistic was demonstrated in this study. We propose the modifications of the trimmed F statistic mentioned by using (1) a priori determined 15% symmetric trimming and (2) empirically determined trimming using robust scale estimators such as MADn, Tn and LMSn. The later trimming method will trim extreme values without prior trimming percentage. Based on the rates of Type I error, the procedures were then compared. Data from g- and h- distributions were considered in this study. We found the trimmed F statistic using robust scale estimator LMSn as trimming criterion provided good control of Type I error compared to the other methods. ABSTRAK Apabila andaian normal dan homokedastik dipenuhi, penyelidik tidak perlu ragu untuk menggunakan ujian klasik seperti ujian-t bagi menguji kesamaan sukatan kecenderungan memusat untuk dua kumpulan. Walau bagaimanapun, dalam kehidupan sebenar situasi yang sempurna ini jarang dijumpai. Apabila masalah ketaknormalan dan varians heterogen berlaku serentak, ini akan memberi kesan kepada kadar ralat Jenis I dan seterusnya menyebabkan berlakunya penolakan terhadap hipotesis nol. Di samping itu, penganggar kuasa dua terkecil boleh menjadi sangat tidak cekap apabila andaian kenormalan tidak dipenuhi. Kesan ketidaknormalan pada statistik F terpangkas telah dibuktikan dalam kajian ini. Kami mencadangkan pengubahsuaian statistik F terpangkas menggunakan (1) penentuan awal 15% pemangkasan secara simetri dan (2) pemangkasan secara empirikal menggunakan penganggar skala teguh seperti MADn, Tn dan LMSn. Kaedah pemangkasan yang terkemudian, akan memangkas nilai ekstrem tanpa penentuan awal peratusan pemangkasan. Berdasarkan kadar ralat Jenis I, prosedur-prosedur ini dibandingkan. Data dari taburan g- dan h- dipertimbangkan dalam kajian ini. Kami mendapati statistik F terpangkas menggunakan penganggar skala kukuh LMSn sebagai kriteria pemangkasan mempunyai kawalan ralat Jenis I yang baik berbanding dengan kaedah lain. (Keywords: Trimming criterion, robust scale estimators, Type I error)