Robust Parametric Bootstrap Test with MOM Estimator: An Alternative to Independent Sample t-Test

• Main Authors: Harun, Nurul Hanis, Md Yusof, Zahayu
• Format: Conference or Workshop Item
• Language: English
• Published: 2014
• Subjects: QA Mathematics
• Online Access: https://repo.uum.edu.my/id/eprint/30926/1/ICOQSIA%201635%2001%202014%20755-761.pdf; https://repo.uum.edu.my/id/eprint/30926/; http://dx.doi.org/10.1063/1.4903667
• Institution: Universiti Utara Malaysia

Normality and homogeneity are two major assumptions that need to be fulfilled when using independent sample t-test. However, not all data encompassed with these assumptions. Consequently, the result produced by independent sample t-test becomes invalid. Therefore, the alternative is to use robust statistical procedure in handling the problems of nonnormality and variances heterogeneity. This study proposed to use Parametric Bootstrap test with popular robust estimators, MADn and Tn which empirically determines the amount of trimming. The Type I error rates produced by each procedure were examined and compared with classical parametric test and nonparametric test namely independent sample t-test and Mann Whitney test, respectively. 5000 simulated data sets are used in this study in order to generate the Type I error for each procedure. The findings of this study indicate that the Parametric Bootstrap test with MADn and Tn produces the best Type I error control compared to the independent sample t-test and the Mann Whitney test under nonnormal distribution, heterogeneous variances and unbalanced design. Then, the performance of each procedure was demonstrated using real data