A Modified Jonckheere Test Statistic for Ordered Alternatives in Repeated Measures Design

Hatice Tül Kübra AKDUR, Fikri GÖKPINAR, Hülya BAYRAK, Esra GÖKPINAR
2.150 354


In this article, a new test based on Jonckheere test [1] for  randomized blocks which have dependent observations within block is presented. A weighted sum for each block statistic rather than the unweighted sum proposed by Jonckheereis included. For Jonckheere type statistics, the main assumption is independency of observations within block. In the case of repeated measures design, the assumption of independence is violated. The weighted Jonckheere type statistic for the situation of dependence for different variance-covariance structure and the situation based on ordered alternative hypothesis structure of each block on the design is used. Also, the proposed statistic is compared to the existing test based on Jonckheere in terms of type I error rates by performing Monte Carlo simulation. For the strong correlations, circular bootstrap version of the proposed Jonckheere test provides lower rates of type I error.

Anahtar kelimeler

Repeated measures; Jonckheere test; Circular bootstrap; Type 1 error

Tam metin:


DOI: http://dx.doi.org/10.19113/sdufbed.73024


[1] Jonckheere, A. R. 1954. A test of significance for the relation between m rankings and k ranked categories, British Journal of Statistical Psychology, 7(1954), 93-100.

[2] Page, E. B. 1963. Ordered hypotheses for multiple treatments: a significance test for linear ranks. Journal of the American Statistical Association, 58(301), 216-230.

[3] Zhang, Y., Cabilio, P. 2013. A generalized Jonckheere test against ordered alternatives for repeated measures in randomized blocks. Statistics in medicine, 32(10), 1635-1645.

[4] Agresti, A., Pendergast, J. 1986. Comparing mean ranks for repeated measures data. Communications in Statistics-Theory and Methods, 15(5), 1417-1433.

[5] Conover, W. J., Iman, R. L. 1981. Rank transformations as a bridge between parametric and nonparametric statistics. The American Statistician,35(3), 124-129.

[6] Pellegrini, A. D., Long, J. D. 2002. A longitudinal study of bullying, dominance, and victimization during the transition from primary school through secondary school. British journal of developmental psychology,20(2), 259-280.

[7] Kendall, M. G. 1955.Rank correlation methods. Second edition, revised and enlarged. Hafner Publishing Co, Newyork, 196pp.

[8] Von Storch, H. 1999. Misuses of statistical analysis in climate research. pp 11-26. Von Storch, H., Navarra, A. 1999. Analysis of climate variability: applications of statistical techniques. Springer Science & Business Media, 337p.

[9] Hamed, K. H., Rao, A. R. 1998. A modified Mann-Kendall trend test for autocorrelated data. Journal of Hydrology, 204(1), 182-196.

[10] Skillings, J. H., Wolfe, D. A. 1978. Distribution-free tests for ordered alternatives in a randomized block design. Journal of the American Statistical Association, 73(362), 427-431.

[11] Kunsch, H. R. 1989. The jackknife and the bootstrap for general stationary observations. The Annals of Statistics, 1217-1241.

[12] Politis, D. N., Romano, J. P. 1992. A circular block-resampling procedure for stationary data.pp. 263-270. Lepage, R., Billard, L. 1992. Exploring the limits of bootstrap (Vol. 270). John Wiley & Sons, New York, 437p.

[13] Dehling, H., Wendler, M. 2010. Central limit theorem and the bootstrap for U-statistics of strongly mixing data. Journal of Multivariate Analysis,101(1), 126-137

[14] Önöz, B., & Bayazit, M. 2012. Block bootstrap for Mann–Kendall trend test of serially dependent data. Hydrological Processes, 26(23), 3552-3560.

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.

e-ISSN: 1308-6529