EN
Proposed nonparametric tests for the ordered alternative in a completely randomized and randomized block mixed design
Abstract
Two nonparametric tests are proposed for the mixed design consisting of a randomized complete block and a completely randomized design to test for k nondecreasing treatment effects. The Hollander test and the Page test are used in randomized complete block design and completely randomized design, respectively. We compared the performance of the proposed tests against the Z_CombI, Z_CombII Page and Hollander tests. A Monte Carlo simulation study was conducted comparing the estimated powers of the tests 3, 4 and 5 treatments under various treatment effects and three different underlying distributions. In conclusion, the two proposed tests have higher powers than the Page, Hollander, Z_CombI and Z_CombII tests.
Keywords
References
- [1] Magel R., Ndungu A., Nonparametric Tests for Ordering in Completely Randomized and Randomized Block Mixed Designs, Journal of Biometrics & Biostatistics, 4 (2013) 170-4 . [2] Hollander M., Rank Tests for Randomized Blocks When the Alternatives Have a Priori Ordering, Annals of Mathematical Statistics, 38 (1967) 867-877.
- [3] Jonckheere A.R., A Distribution-Free k-Sample Test Against Ordered Alternatives, Biometrika, 41 (1954) 133-145.
- [4] Terpstra T.J., The Asymptotic Normality and Consistency of Kendall’s Test against Trend. When Ties Are Present in One Ranking, Indigationes Mathematicae, 14 (1952) 327-333.
- [5] Kruskal W.H., Wallis W.A., Use of Ranks in One-Criterion Variance Analysis, Journal of the American Statistical Association, 47(260) (1952) 583-621.
- [6] Mann H.B., Whitney D.R., On a Test of Whether One of Two Random Variables is Stochastically Larger Than The Other, Annals of Mathematical Statistics, 18 (1954) 50-60.
- [7] Akdur H.T.K., Gokpinar F., Bayrak H., Gokpinar E., A Modified Jonckheere Test Statistic for Ordered Alternatives in Repeated Measures Design, Suleyman Demirel University Journal of Natural and Applied Sciences, 20(3) (2016) 391-398.
- [8] Hollander M., Wolfe D.A., Nonparametric Statistical Methods., 2nd ed., New York: Wiley, (1999).
- [9] Page E.B., Ordered Hypotheses for Multiple Treatments: A Significance Test for Linear Ranks, Journal of the American Statistical Association, 58 (1963) 216-230.
Details
Primary Language
English
Subjects
Statistics
Journal Section
Research Article
Publication Date
March 29, 2021
Submission Date
July 1, 2020
Acceptance Date
January 12, 2021
Published in Issue
Year 2021 Volume: 42 Number: 1
APA
Gül, H. H., & Bayrak, H. (2021). Proposed nonparametric tests for the ordered alternative in a completely randomized and randomized block mixed design. Cumhuriyet Science Journal, 42(1), 191-200. https://doi.org/10.17776/csj.762235
AMA
1.Gül HH, Bayrak H. Proposed nonparametric tests for the ordered alternative in a completely randomized and randomized block mixed design. CSJ. 2021;42(1):191-200. doi:10.17776/csj.762235
Chicago
Gül, Hasan Hüseyin, and Hülya Bayrak. 2021. “Proposed Nonparametric Tests for the Ordered Alternative in a Completely Randomized and Randomized Block Mixed Design”. Cumhuriyet Science Journal 42 (1): 191-200. https://doi.org/10.17776/csj.762235.
EndNote
Gül HH, Bayrak H (March 1, 2021) Proposed nonparametric tests for the ordered alternative in a completely randomized and randomized block mixed design. Cumhuriyet Science Journal 42 1 191–200.
IEEE
[1]H. H. Gül and H. Bayrak, “Proposed nonparametric tests for the ordered alternative in a completely randomized and randomized block mixed design”, CSJ, vol. 42, no. 1, pp. 191–200, Mar. 2021, doi: 10.17776/csj.762235.
ISNAD
Gül, Hasan Hüseyin - Bayrak, Hülya. “Proposed Nonparametric Tests for the Ordered Alternative in a Completely Randomized and Randomized Block Mixed Design”. Cumhuriyet Science Journal 42/1 (March 1, 2021): 191-200. https://doi.org/10.17776/csj.762235.
JAMA
1.Gül HH, Bayrak H. Proposed nonparametric tests for the ordered alternative in a completely randomized and randomized block mixed design. CSJ. 2021;42:191–200.
MLA
Gül, Hasan Hüseyin, and Hülya Bayrak. “Proposed Nonparametric Tests for the Ordered Alternative in a Completely Randomized and Randomized Block Mixed Design”. Cumhuriyet Science Journal, vol. 42, no. 1, Mar. 2021, pp. 191-00, doi:10.17776/csj.762235.
Vancouver
1.Hasan Hüseyin Gül, Hülya Bayrak. Proposed nonparametric tests for the ordered alternative in a completely randomized and randomized block mixed design. CSJ. 2021 Mar. 1;42(1):191-200. doi:10.17776/csj.762235
Cited By
Tamamlanmış Blok ve Tamamen Rasgele Tasarımdan Oluşan Bir Karma Tasarımda Genel Alternatif için Önerilen Testler
Afyon Kocatepe University Journal of Sciences and Engineering
https://doi.org/10.35414/akufemubid.1107460