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Year 2021, Volume: 42 Issue: 1, 191 - 200, 29.03.2021

Hasan Hüseyin Gül , Hülya Bayrak

https://doi.org/10.17776/csj.762235
Cited By: 1

Abstract

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.
  • [10] Gokpinar E., Gul H.H., Gokpinar F., Bayrak H., Ozonur D., Permutation Test Approach for Ordered Alternatives in Randomized Complete Block Design: A Comparative Study, Gazi University Journal of Science, 27(1) (2014) 645-651.
  • [11] Akdur H.T.K., Ozonur D., Gul H.H., Bayrak H., Comparison of Rank-Based Tests for Ordered Alternative Hypotheses in Randomized Complete Block Designs, Gazi University Journal of Science, 32(2) (2019) 705-716.
  • [12] Wilcoxon F., Individual Comparisons by Ranking Methods, Biometrics Bulletin, 1 (1945) 80-83.
  • [13] Dubnicka S.R., Blair R.C., Hettmansperger T.P., Rank-Based Procedures for Mixed Pire and Two Sample Designs, Journal of Modern Applied Statistical Methods, 1(1) (2002) 32-41.
  • [14] Magel R., Terpstra J., Canonizado K., Park J.I., Nonparametric Tests for Mixed Designs, Communications in Statistics-Simulation and Computation, 39 (2010) 1228-1250.
  • [15] Magel R., Fu R., Proposed Nonparametric Test for the Mixed Two-Sample Desig., Journal of Statistical Theory and Practice, 8(2) (2014) 221-237.
  • [16] Olet S., Magel R., A Comparison of Nonparametric Tests in a Mixed Design for the Simple Tree Alternative, International Journal for Research in Business Management and Accounting, 3(3) (2017) 1-23.
  • [17] Magel R., Terpstra J., Wen J., Proposed Tests for the Nondecreasing Alternative in a Mixed Design, Journal of Statistics and Management Systems, 12 (2014) 963-977.

Proposed nonparametric tests for the ordered alternative in a completely randomized and randomized block mixed design

Year 2021, Volume: 42 Issue: 1, 191 - 200, 29.03.2021

Hasan Hüseyin Gül , Hülya Bayrak

https://doi.org/10.17776/csj.762235
Cited By: 1

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

Randomized complete block design Completely randomized design Page’s test Hollander test

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.
  • [10] Gokpinar E., Gul H.H., Gokpinar F., Bayrak H., Ozonur D., Permutation Test Approach for Ordered Alternatives in Randomized Complete Block Design: A Comparative Study, Gazi University Journal of Science, 27(1) (2014) 645-651.
  • [11] Akdur H.T.K., Ozonur D., Gul H.H., Bayrak H., Comparison of Rank-Based Tests for Ordered Alternative Hypotheses in Randomized Complete Block Designs, Gazi University Journal of Science, 32(2) (2019) 705-716.
  • [12] Wilcoxon F., Individual Comparisons by Ranking Methods, Biometrics Bulletin, 1 (1945) 80-83.
  • [13] Dubnicka S.R., Blair R.C., Hettmansperger T.P., Rank-Based Procedures for Mixed Pire and Two Sample Designs, Journal of Modern Applied Statistical Methods, 1(1) (2002) 32-41.
  • [14] Magel R., Terpstra J., Canonizado K., Park J.I., Nonparametric Tests for Mixed Designs, Communications in Statistics-Simulation and Computation, 39 (2010) 1228-1250.
  • [15] Magel R., Fu R., Proposed Nonparametric Test for the Mixed Two-Sample Desig., Journal of Statistical Theory and Practice, 8(2) (2014) 221-237.
  • [16] Olet S., Magel R., A Comparison of Nonparametric Tests in a Mixed Design for the Simple Tree Alternative, International Journal for Research in Business Management and Accounting, 3(3) (2017) 1-23.
  • [17] Magel R., Terpstra J., Wen J., Proposed Tests for the Nondecreasing Alternative in a Mixed Design, Journal of Statistics and Management Systems, 12 (2014) 963-977.
There are 16 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Natural Sciences
Authors

Hasan Hüseyin Gül 0000-0003-4280-4800

Hülya Bayrak 0000-0001-5666-4250

Publication Date March 29, 2021
Submission Date July 1, 2020
Acceptance Date January 12, 2021
Published in Issue Year 2021Volume: 42 Issue: 1

Cite

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

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