Comparative Study on Synchronized Permutation Tests in Balanced IXJ Designs in Case of Non-Normally Distributed Error Terms
Abstract
ANOVA methodology is one of the important models in the experimental design theory. Synchronized permutation provides exact solution in factorial designs within a nonparametric framework. Synchronized permutation tests have quadratic form test statistics. In this paper we studied synchronized permutation tests with absolute value form in the test statistics for main factors and interaction for IXJ balanced factorial designs in case of nonnormal distributed error terms. Then we investigate the behavior of synchronized permutation tests with absolute value form and quadratic form in the test statistics in a comparative simulation study with the parametric ANOVA is reported in 3X2 design when error terms normal and non-normal distributed.
References
- Arnold, H. J., 1964. Permutation support for multivariate techniques. Biometrika 51: 65–70.
- Mansouri, H., Chang, G. H., 1995. A comparative study of some rank tests for interaction.Computat. Statistics Data Anal. 9: 85–96.
- Fisher, R., 1935. The design of experiments. Oliver & Boyd Edinburgh, Scotland.
- Anderson, MJ., Legendre, P., 1999. An empirical comparison of permutation methods for tests of partial regression coefficients in a linear model. J Stat Comput Simul, 62: 271-303.
- Manly, B., 1997. Randomization, Bootstrap and Monte Carlo Methods in Biology. Chapman and Hall, Landon.
- Good, P., 1994. Author Permutation Tests: A Practical Guide to Resampling Methods for Testing Hypotheses. Springer.
- Edgington, E.S., 1995. Randomization Tests. 3rd ed. New York: Marcel Dekker.
- Salmaso, L., 2003. Synchronized permutation tests in factorial designs. Comm. Statist. Theory Methods 32: 1419–1437.
- Basso, D., Chiarandini, M., Salmaso, L., 2006. Synchronized permutation tests in IXJ designs. J. Statist. Plann. Infer. 137(8): 2564–2578.
- Corain, L., Salmaso, L., 2007. A Critical Review and a Comparative Communications in StatisticsSimulation and Computation, 36(4): 791-805.
- Hahn S., Konietschke F., Salmaso L., 2014. A Comparison of Efficient Permutation Tests for Unbalanced ANOVA in Two by Two Designs and Their Behavior Under Heteroscedasticity. In: Melas V., Mignani S., Monari P., Salmaso L. (eds) Topics in Statistical Simulation. Springer Proceedings in Mathematics & Statistics, vol 114. Springer, New York, NY.
Hata Terimleri Normal Dağılıma Sahip Olmadığı Durumlarda IXJ Dengeli Tasarımlarda Senkronize Permütasyon Testleri Üzerinde Karşılaştırmalı Bir Çalışma
Abstract
ANOVA metodolojisi, deney tasarım teorisindeki önemli modellerden biridir. Senkronize permütasyon testleri faktöriyel tasarımlarında parametrik olmayan bir çerçevede kesin bir çözüm sunmaktadırlar. Senkronize permütasyon testleri karesel formda test istatistiklerine sahiptir. Bu çalışmada IXJ dengeli faktöriyel tasarımlar için hata terimlerinin normal dağılma sahip olmadığı durumlarda, ana faktörlerin etkisi ve etkileşim etkisi için önerilen test istatistiklerinin sahip olduğu karesel formun mutlak değer ile değiştirilerek senkronize permütasyon testinin davranışı incelenmiştir. Daha sonra, 3X2 dengeli tasarımı için hataların normal dağılmadığı durumlarda senkronize permütasyon testlerinin mutlak değer formda ve karesel formda test istatistiklerinin davranışını araştırıp, parametrik ANOVA ile karşılaştırmalı bir simülasyon çalışması sunuldu.
References
- Arnold, H. J., 1964. Permutation support for multivariate techniques. Biometrika 51: 65–70.
- Mansouri, H., Chang, G. H., 1995. A comparative study of some rank tests for interaction.Computat. Statistics Data Anal. 9: 85–96.
- Fisher, R., 1935. The design of experiments. Oliver & Boyd Edinburgh, Scotland.
- Anderson, MJ., Legendre, P., 1999. An empirical comparison of permutation methods for tests of partial regression coefficients in a linear model. J Stat Comput Simul, 62: 271-303.
- Manly, B., 1997. Randomization, Bootstrap and Monte Carlo Methods in Biology. Chapman and Hall, Landon.
- Good, P., 1994. Author Permutation Tests: A Practical Guide to Resampling Methods for Testing Hypotheses. Springer.
- Edgington, E.S., 1995. Randomization Tests. 3rd ed. New York: Marcel Dekker.
- Salmaso, L., 2003. Synchronized permutation tests in factorial designs. Comm. Statist. Theory Methods 32: 1419–1437.
- Basso, D., Chiarandini, M., Salmaso, L., 2006. Synchronized permutation tests in IXJ designs. J. Statist. Plann. Infer. 137(8): 2564–2578.
- Corain, L., Salmaso, L., 2007. A Critical Review and a Comparative Communications in StatisticsSimulation and Computation, 36(4): 791-805.
- Hahn S., Konietschke F., Salmaso L., 2014. A Comparison of Efficient Permutation Tests for Unbalanced ANOVA in Two by Two Designs and Their Behavior Under Heteroscedasticity. In: Melas V., Mignani S., Monari P., Salmaso L. (eds) Topics in Statistical Simulation. Springer Proceedings in Mathematics & Statistics, vol 114. Springer, New York, NY.
Details
| Primary Language | English |
|---|---|
| Journal Section | Research Articles |
| Authors | |
| Publication Date | December 18, 2020 |
| Submission Date | October 31, 2019 |
| Published in Issue | Year 2020 Volume: 5 Issue: 2 |
