A Comparison of the Performance of Tukey's Multiple Comparison Test and Step-Down Bootstrap Min P Procedure
Abstract
The purpose of this research is to compare the performance of three test statistics for multiple comparison test which are Tukey’s test, Step-down independent bootstrap min P and Step-down dependent bootstrap min P. Five distributions of data sets, Normal, Laplace, Logistic, log-normal and Gamma distributions are considered. A Monte Carlo simulation is performed with repeated 5,000 times. The number of bootstrap resampling is 1,000 times. The number of treatments are 3 and 4 with equal sample sizes and equal variance. The sample sizes are 5, 7, 10 and 15. The variance of all data sets are 0.5 and 1.0. The significance level will be set at 0.05. The results show that the familywise error rate of three test statistics can be controlled for all cases. Most power of the test of both step-down bootstrap min P procedures are higher than that of Tukey’s test for all distributions. Keywords : multiple comparison test, Tukey’s test, Step-down bootstrap min P procedureReferences
Budsaba, K. & Phetcharat, A. (2011). Robustness study of step-down bootstrap min P for comparing several means with a control. Journal of Science and Technology Thammasat University, 19(3), 29-39. (in Thai)
Efron, B. and Tibshirani, R. J. (1993). An introduction to the Bootstrap. New York: Chapman & Hall.
Haidous, N N., and Sawilowsky. S. S. (2013) "Robustness and Power of the Kornbrot Rank Difference, Signed Ranks, and Dependent Samples T-test." American Journal of Applied Mathematics and Statistics, 1(5), 99-102.
Horn, M. & Dunnett, C.W. (2004). Power and sample size comparisons of stepwise FEW and FDR controlling test procedures in the normal many-one case. Lecture Notes Monograph Series, 47, 48-64.
Komonniramit, Y. (2008). Step-down dependent bootstrap min p for comparison several means with a control. Master’s thesis, Faculty of Science and Technology, Thammasat University. (In Thai)
Montgomery D.C. (2009). Design and analysis of experiments. (7th edition). Asia: John Wiley & Sons.
Richter, S. J., & McCann, M. H. (2013). Simultaneous multiple comparisons with a control using median
differences and permutation tests. Statistics & Probability Letters, 83(4), 1167-1173
Efron, B. and Tibshirani, R. J. (1993). An introduction to the Bootstrap. New York: Chapman & Hall.
Haidous, N N., and Sawilowsky. S. S. (2013) "Robustness and Power of the Kornbrot Rank Difference, Signed Ranks, and Dependent Samples T-test." American Journal of Applied Mathematics and Statistics, 1(5), 99-102.
Horn, M. & Dunnett, C.W. (2004). Power and sample size comparisons of stepwise FEW and FDR controlling test procedures in the normal many-one case. Lecture Notes Monograph Series, 47, 48-64.
Komonniramit, Y. (2008). Step-down dependent bootstrap min p for comparison several means with a control. Master’s thesis, Faculty of Science and Technology, Thammasat University. (In Thai)
Montgomery D.C. (2009). Design and analysis of experiments. (7th edition). Asia: John Wiley & Sons.
Richter, S. J., & McCann, M. H. (2013). Simultaneous multiple comparisons with a control using median
differences and permutation tests. Statistics & Probability Letters, 83(4), 1167-1173
Downloads
Published
2019-02-01
Issue
Section
Research Article
