A Modified Jonckheere Test Statistic for Ordered Alternatives in Repeated Measures Design
Öz
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
Kaynakça
- [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.
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- [7] Kendall, M. G. 1955.Rank correlation methods. Second edition, revised and enlarged. Hafner Publishing Co, Newyork, 196pp.
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Ayrıntılar
Birincil Dil
Türkçe
Konular
-
Bölüm
-
Yayımlanma Tarihi
8 Eylül 2016
Gönderilme Tarihi
6 Eylül 2015
Kabul Tarihi
-
Yayımlandığı Sayı
Yıl 2016 Cilt: 20 Sayı: 3
APA
Akdur, H. T. K., Gökpınar, F., Bayrak, H., & Gökpınar, E. (2016). A Modified Jonckheere Test Statistic for Ordered Alternatives in Repeated Measures Design. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 20(3), 391-398. https://doi.org/10.19113/sdufbed.73024
AMA
1.Akdur HTK, Gökpınar F, Bayrak H, Gökpınar E. A Modified Jonckheere Test Statistic for Ordered Alternatives in Repeated Measures Design. Süleyman Demirel Üniv. Fen Bilim. Enst. Derg. 2016;20(3):391-398. doi:10.19113/sdufbed.73024
Chicago
Akdur, Hatice Tül Kübra, Fikri Gökpınar, Hülya Bayrak, ve Esra Gökpınar. 2016. “A Modified Jonckheere Test Statistic for Ordered Alternatives in Repeated Measures Design”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20 (3): 391-98. https://doi.org/10.19113/sdufbed.73024.
EndNote
Akdur HTK, Gökpınar F, Bayrak H, Gökpınar E (01 Aralık 2016) A Modified Jonckheere Test Statistic for Ordered Alternatives in Repeated Measures Design. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20 3 391–398.
IEEE
[1]H. T. K. Akdur, F. Gökpınar, H. Bayrak, ve E. Gökpınar, “A Modified Jonckheere Test Statistic for Ordered Alternatives in Repeated Measures Design”, Süleyman Demirel Üniv. Fen Bilim. Enst. Derg., c. 20, sy 3, ss. 391–398, Ara. 2016, doi: 10.19113/sdufbed.73024.
ISNAD
Akdur, Hatice Tül Kübra - Gökpınar, Fikri - Bayrak, Hülya - Gökpınar, Esra. “A Modified Jonckheere Test Statistic for Ordered Alternatives in Repeated Measures Design”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 20/3 (01 Aralık 2016): 391-398. https://doi.org/10.19113/sdufbed.73024.
JAMA
1.Akdur HTK, Gökpınar F, Bayrak H, Gökpınar E. A Modified Jonckheere Test Statistic for Ordered Alternatives in Repeated Measures Design. Süleyman Demirel Üniv. Fen Bilim. Enst. Derg. 2016;20:391–398.
MLA
Akdur, Hatice Tül Kübra, vd. “A Modified Jonckheere Test Statistic for Ordered Alternatives in Repeated Measures Design”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 20, sy 3, Aralık 2016, ss. 391-8, doi:10.19113/sdufbed.73024.
Vancouver
1.Hatice Tül Kübra Akdur, Fikri Gökpınar, Hülya Bayrak, Esra Gökpınar. A Modified Jonckheere Test Statistic for Ordered Alternatives in Repeated Measures Design. Süleyman Demirel Üniv. Fen Bilim. Enst. Derg. 01 Aralık 2016;20(3):391-8. doi:10.19113/sdufbed.73024