Proposed Nonparametric Tests Using Moses Test For Location and Scale Testing
Three nonparametric tests are proposed for the simple tree alternative to test for differences in location and/or scale. These tests are combinations of the Fligner-Wolfe test and a modified Moses test. A simulation study is conducted to determine how well the proposed tests maintain their significance levels. Powers are also estimated for the proposed tests under a variety of conditions for three and four populations. Three different types of variable parameters vectors are considered with each vector containing a location and a scale parameter. The first type of parameter vectors considered include different location parameters and equal scale parameters. The second type include different scale parameters and equal location parameters, and the third type include both different location parameters and different scale parameters. Results are given as far as which test does better under certain conditions.
2. Ansari, A. R., & Bradley R. A. (1960). Rank-Sum Tests for Dispersion. Annals of Mathematical statistics 31, 1174-1189.
3. Bailer, A.J. (2010). Statistical programming in SAS, Cary, NC: SAS Institute Inc.
4. Conroy, D. (2011). Proposed Nonparametric Test for The Simple Tree Alternative When Variances Are Unequal. Doctoral Dissertation for North Dakota State University. Statistics Department.
5. Fligner, M., & Wolfe, D. (1982). Distribution-free tests for comparing several treatments with a control. Statistica Neerlandica 36, 119-127
6. Hollander, M., & Wolfe, D. (1999). Nonparametric Statistical Methods. 2nd Edition. New York: Wiley.
7. Karpatkin, M., Porges, R. F., & Karpatkin, S. (1981). Platelet counts in infants of women with autoimmune thrombocytopenia: effects of steroid administration to the mother. New England Journal of Medicine 305, 936–939.
8. Lepage, Y. (1971). A combination of Wilcoxon’s and Ansari-Bradley’s statistics. Biometrika 58, 213-217.
9. Mann, H. B., & Whitney, D. R. (1947). On a Test of Whether One of Two Random Variables is Stochastically Larger than the Other. Annals of Mathematical statistics 18, 50-60.
10. Marozzi, M. (2013). Nonparametric Simultaneous Tests for Location and Scale Testing: A Comparison of several Methods. Communication in Statistics - Simulation and Computation, 42, 1298–1317.
11. Moses, L. E. (1963). Rank Tests of Dispersion. Annals of Mathematical statistics 34, 973-983.
12. Olet, Susan and Magel, Rhonda (2017). A Comparison of Nonparametric Tests in a Mixed Design for the Simple Tree Alternative. International Journal for Research in Business Management and Accounting, Volume3, Issue 3, 1-23.
13. Wang, Z. (2011). A Proposed Nonparametric Test for Simple Tree Alternative in A BIBD Design. Master’s Thesies for North Dakota State University. Statistics Department.
Copyright (c) 2020 Journal of Progressive Research in Mathematics
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
TRANSFER OF COPYRIGHT
JPRM is pleased to undertake the publication of your contribution to Journal of Progressive Research in Mathematics.
The copyright to this article is transferred to JPRM(including without limitation, the right to publish the work in whole or in part in any and all forms of media, now or hereafter known) effective if and when the article is accepted for publication thus granting JPRM all rights for the work so that both parties may be protected from the consequences of unauthorized use.