Permutation Test Approach for Ordered Alternatives in Randomized Complete Block Design: A Comparative Study

Abstract

Randomized complete block design is one of the most used experimental designs in statistical analysis. For testing ordered alternatives in randomized complete block design, parametric tests are used if random sample are drawn from Normal distribution. If normality assumption is not provide, nonparametric methods are used. In this study, we are interested nonparametric tests and we introduce briefly the nonparametric tests, such as Page, Modified Page and Hollander tests. We also give Permutation Version of Page test. We compare the performance of these tests in terms of the empirical type I error rates and powers of tests.

Key words: Permutation test, Page test, Hollander test, Modified Page test, Simulation study

Keywords

• Permutation test, Page test, Hollander test, Modified Page test, Simulation study

A Comparative Study

Abstract

References

1. Jonckheree G.R., “A distribution-free k-sample test against ordered alternatives”, Biometrika, 41, 133-145 (1954).
2. Terpstra, T.J., “The asymptotic normality and consistency of Kendall’s test against trend”, when ties are present in one ranking, Indagationes Mathematicae, 14, 327-333 (1952).
3. Page, E.B., “Ordered hypotheses for multiple treatments: a significance tests for linear ranks”, Journal of the American Statistical Association, 58, 216-230 (1963).
4. Hollander, M., “Rank tests for randomized blocks when the alternatives have a priori ordering”, Annals of Mathematical Statistics, 38, 867-877 (1967).
5. Skillings, J.H., Wolfe, D.A., “Distribution-free tests for ordered alternatives in a randomized block design”, Journal of the American Statistical Association, 73, 427-431 (1978).
6. Alvo, M., Cabilio, P., “Testing ordered alternatives in the presence of incomplete data”, Journal of the American Statistical Association, 90, 1015-1024 (1995).
7. Gökpınar, E.Y., Gökpınar, F., Bayrak, H., “Permutation approach for adjusted Durbin rank test used in balanced incomplete block designs for tied data”, Iranian Journal of Science & Technology, A3, 305-310 (2012).
8. Bi, J., “Computer-intensive methods for sensory data analysis, exemplified by Durbin’s rank test”, Food Quality and Preference, 20(3): 195-202 (2009).

9. Best, D.J., Brockhoff, P.B., Rayner, J.C.W., “Tests for balanced incomplete block ranked data with ties”, Statistica Nerlandica, 60(1): 3-11 (2006).
10. Hollander, M., Wolfe, D.A., “Nonparametric Statistical Methods”, 2nd ed., Wiley (1999).