Testing the equality of central tendency measures using T1 statistic with different trimming strategies

• Main Authors: Md Yusof, Zahayu, Abdullah, Suhaida, Syed Yahaya, Sharipah Soaad
• Format: Monograph
• Language: English
• Published: Universiti Utara Malaysia 2011
• Subjects: QA Mathematics
• Online Access: http://repo.uum.edu.my/8212/1/sHA.pdf; http://repo.uum.edu.my/8212/; http://lintas.uum.edu.my:8080/elmu/index.jsp?module=webopac-l&action=fullDisplayRetriever.jsp&szMaterialNo=0000780154

When the assumptions of normality and homoscedasticity are met, researchers should have no doubt in using classical test such as t-test and ANOVA to test for the equality of central tendency measures for two and more than two groups respectively.However, in real life we do not often encounter with this perfect situation.T1 statistic was proposed as an alternative robust method that could handle the problem of nonnormality when using trimmed mean with 15% symmetric trimming as the central tendency measures, but their study only focused on the condition of homogeneous variances.Motivated by the good performance of the method, in this study we propose using T1 statistic with three different trimming strategies, namely, i) predetermined 15% symmetric trimming ii) predetermined asymmetric trimming based upon hinge estimators and iii) empirically determined asymmetric trimming based on robust scale estimators, MADn, Tn and LMSn to handle simultaneously the problem of nonnormality and heteroscedasticity.To test for the robustness of the procedures towards the violation of the assumptions, several variables will be manipulated.The variables are types of distributions, heterogeneity of variances, sample sizes, nature of pairings of group sample sizes and group variances, and number of groups.Type I error for each procedures will then be calculated.This study will be based on simulated data with each procedure will be simulated 5000 times and each set of data will be bootstrapped 599 times.The proposed procedures, generally, generated good Type I error control.The combination of T1 statistic with HQ1 produced promising procedures that are capable of addressing the problem of testing the equality of central tendency measures especially for skewed distributions.