Comparing the Performance of Test Statistics for More Than Two Population Means under Symmertric Distribution
Abstract
The purpose of this study is to compare the performance of three test statistics which are F– test, Kruskal – Wallis test and permutation test. Three symmetric distributions of data, logistic, Laplace and uniform distribution are considered. These data sets have standard deviations 1 and 2. The sample sizes are 5, 10, 15 and 20. The mean is 0 and the mean differences are 0.0, 0.5 and 1.5. Significance level will be set at 0.05. The considered criterions are type I error rates and power of the tests. A Monte Carlo simulation is performed with repeated 10,000 times. The number of permutation is 2,000. The results show that three test statistics control the nominal level well. Considering the power of a test, the permutation test has the highest power when the data are chosen from logistic distribution. For Laplace distribution, Kruskal – Wallis test test has the highest power except for the case sample size 5 which the permutation test performs well. For uniform distribution, F-test statistic test has the highest power. Keywords : permutation test, F-test, Kruskal – Wallis test, power of a test, type I errorReferences
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Kruskal, W.H. & Wallis, W.A. (1952). Use of ranks in one-criterion variance analysis. Journal of the American
Statistical Association, 47, 583-621.
Mathematics Education, 2(2), 20-29.
Casella, G. & Berger, R.L. (2001). Statistical Inference. United States of America: Duxbury.
Efron, B. and Tibshirani, R. J. (1993). An introduction to the Bootstrap. New York: Chapman & Hall.
Ernst, M.D. (2004). Permutation methods: A basis for exact inference. Statistical Science, 19(4), 676-685.
Fisher, R.A. (1971). The Design of Experiments. New York: Hafner Publishing Company.
Gleason, J.H. (2013). Comparative power of The Anova, Randomization Anova, and Kruskal-Wallis test. Doctoral Dissertation, Evaluation and Research, Graduate School, Wayne State University.
Kruskal, W.H. & Wallis, W.A. (1952). Use of ranks in one-criterion variance analysis. Journal of the American
Statistical Association, 47, 583-621.
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Published
2018-03-16
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Research Article
