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Year 2019, Volume: 32 Issue: 2, 705 - 716, 01.06.2019

Abstract

References

  • [1] Jonckheere AR. A distribution-free k-sample test against ordered alternatives. Biometrika 1954:41(1/2):133-145.[2] Terpstra TJ. The asymptotic normality and consistency of Kendall's test against trend, when ties are present in one ranking. Indagations Math 1952:14:327-33.[3] Page EB. Ordered hypotheses for multiple treatments: a significance test for linear ranks. J Amer Math Soc 1963:58(301):216-230.[4] Hollander M. Rank tests for randomized blocks when the alternatives have an a priori ordering. Ann Inst Statist Math 1967:1:867-877.[5] Skillings JH, Wolfe DA. Distribution-free tests for ordered alternatives in a randomized block design. J Amer Math Soc 1978:73(362):427-431.[6] Alvo M, Cabilio P. Testing ordered alternatives in the presence of incomplete data. J Amer Math Soc 1995:90(431):1015-1024.[7] Rayner JCW, Best DJ. Modelling ties in the sign test. Biometrics 1999:55(2):663-665.[8] Terpstra TJ, Magel R. A new nonparametric test for the ordered alternative problem. J Nonparametr Stat 2003:15(3):289-301.[9] Thas O, Best DJ, Rayner, JCW. Using orthogonal trend contrasts for testing ranked data with ordered alternatives. Statist Neerlandica 2012:66(4):452-471.[10] Zhang Y, Cabilio P. A generalized Jonckheere test against ordered alternatives for repeated measures in randomized blocks. Stat Med 2013:32(10):1635-1645.[11] Akdur, HTK, Gokpinar, F, Bayrak, H, Gokpinar, E. A Modified Jonckheere Test Statistic for Ordered Alternatives in Repeated Measures Design. SDÜ Fen Bil Enst Der 2016: 20(3), 391-398.[12] Dogan I., Dogan N. Örüntülü Seçenek Hipotezler İçin Bağımsız-Örneklem Testleri/Independent-Sample Tests for Patterned Alternatives. Turkiye Klinikleri J Biostat 2016: 8(1), 94.[13] Akilen R, Tsiami A, Devendra D, Robinson N. Glycated haemoglobin and blood pressure‐lowering effect of cinnamon in multi‐ethnic Type 2 diabetic patients in the UK: a randomized, placebo‐controlled, double‐blind clinical trial. Diabet Med 2010: 27(10), 1159-1167.[14] Heffner, TG, Drawbaugh, RB, Zigmond, MJ. Amphetamine and operant behavior in rats: relationship between drug effect and control response rate. J Comp Physiol Psychol 1974:86(6):1031.[15] Nams VO, Folkard NF, Smith JN. Nitrogen fertilization stimulates herbivory by snowshoe hares in the boreal forest. Can J Zool 1996:74(1):196-199.[16] Shan G, Young D, Kang L. A new powerful nonparametric rank test for ordered alternative problem. PloS one 2014:9(11):e112924.[17] Best DJ, Rayner JCW. An Alternative to Page’s Test Permitting Both Tied and Missing Data. J Stat Theory Prac 2015:9(3):524-536.[18] Jones JM, Wentzell, LA, Toews, DP. Posterior lymph heart pressure and rate and lymph flow in the toad Bufo marinus in response to hydrated and dehydrated conditions. J Exp Biol 1992:169(1): 207-220.[19] Cabilio P, Peng J. Multiple rank-based testing for ordered alternatives with incomplete data. Statist Probab Lett 2008:78(16): 2609-2613.

Comparison of Rank-Based Tests for Ordered Alternative Hypotheses in Randomized Complete Block Designs

Year 2019, Volume: 32 Issue: 2, 705 - 716, 01.06.2019

Abstract

Nonparametric tests are useful when underlying distribution of a population is unknown or sample size is quiet small to satisfy assumptions of a traditional F test. Nonparametric tests have a good usage in a sample which consists of observations from various populations, as well. Randomized block designs are purposive when experimental subjects vary in natural heterogeneity. Nonparametric tests which are suitable for two-way ANOVA designs where the blocks containing observations which follow an increasing or a decreasing trend are main focus of this study. A recently proposed nonparametric test which was developed as an alternative to Jonckheere test is modified for ordered alternative hypotheses in randomized complete block designs. This modification test and several nonparametric tests for detecting ordered alternative hypotheses in randomized complete block designs are compared empirically in a broad set of Monte Carlo simulations under different conditions. A numerical example is provided to illustrate test procedures. The modified test provides better performance than Jonckheere test in terms of type I error and power values whereas Hollander test provides slightly better power values among the other test statistics. In terms of type I error values, it can be stated that the most conservative test is Jonckheere test whereas, estimated type 1 error values of the other test statistics are usually closer to nominal level of alpha.

References

  • [1] Jonckheere AR. A distribution-free k-sample test against ordered alternatives. Biometrika 1954:41(1/2):133-145.[2] Terpstra TJ. The asymptotic normality and consistency of Kendall's test against trend, when ties are present in one ranking. Indagations Math 1952:14:327-33.[3] Page EB. Ordered hypotheses for multiple treatments: a significance test for linear ranks. J Amer Math Soc 1963:58(301):216-230.[4] Hollander M. Rank tests for randomized blocks when the alternatives have an a priori ordering. Ann Inst Statist Math 1967:1:867-877.[5] Skillings JH, Wolfe DA. Distribution-free tests for ordered alternatives in a randomized block design. J Amer Math Soc 1978:73(362):427-431.[6] Alvo M, Cabilio P. Testing ordered alternatives in the presence of incomplete data. J Amer Math Soc 1995:90(431):1015-1024.[7] Rayner JCW, Best DJ. Modelling ties in the sign test. Biometrics 1999:55(2):663-665.[8] Terpstra TJ, Magel R. A new nonparametric test for the ordered alternative problem. J Nonparametr Stat 2003:15(3):289-301.[9] Thas O, Best DJ, Rayner, JCW. Using orthogonal trend contrasts for testing ranked data with ordered alternatives. Statist Neerlandica 2012:66(4):452-471.[10] Zhang Y, Cabilio P. A generalized Jonckheere test against ordered alternatives for repeated measures in randomized blocks. Stat Med 2013:32(10):1635-1645.[11] Akdur, HTK, Gokpinar, F, Bayrak, H, Gokpinar, E. A Modified Jonckheere Test Statistic for Ordered Alternatives in Repeated Measures Design. SDÜ Fen Bil Enst Der 2016: 20(3), 391-398.[12] Dogan I., Dogan N. Örüntülü Seçenek Hipotezler İçin Bağımsız-Örneklem Testleri/Independent-Sample Tests for Patterned Alternatives. Turkiye Klinikleri J Biostat 2016: 8(1), 94.[13] Akilen R, Tsiami A, Devendra D, Robinson N. Glycated haemoglobin and blood pressure‐lowering effect of cinnamon in multi‐ethnic Type 2 diabetic patients in the UK: a randomized, placebo‐controlled, double‐blind clinical trial. Diabet Med 2010: 27(10), 1159-1167.[14] Heffner, TG, Drawbaugh, RB, Zigmond, MJ. Amphetamine and operant behavior in rats: relationship between drug effect and control response rate. J Comp Physiol Psychol 1974:86(6):1031.[15] Nams VO, Folkard NF, Smith JN. Nitrogen fertilization stimulates herbivory by snowshoe hares in the boreal forest. Can J Zool 1996:74(1):196-199.[16] Shan G, Young D, Kang L. A new powerful nonparametric rank test for ordered alternative problem. PloS one 2014:9(11):e112924.[17] Best DJ, Rayner JCW. An Alternative to Page’s Test Permitting Both Tied and Missing Data. J Stat Theory Prac 2015:9(3):524-536.[18] Jones JM, Wentzell, LA, Toews, DP. Posterior lymph heart pressure and rate and lymph flow in the toad Bufo marinus in response to hydrated and dehydrated conditions. J Exp Biol 1992:169(1): 207-220.[19] Cabilio P, Peng J. Multiple rank-based testing for ordered alternatives with incomplete data. Statist Probab Lett 2008:78(16): 2609-2613.
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Details

Primary Language English
Subjects Engineering
Journal Section Statistics
Authors

Hatice Tul Kubra Akdur 0000-0003-2144-0518

Deniz Ozonur 0000-0002-7622-1008

Hasan Huseyin Gul This is me 0000-0003-4280-4800

Hulya Bayrak 0000-0001-5666-4250

Publication Date June 1, 2019
Published in Issue Year 2019 Volume: 32 Issue: 2

Cite

APA Akdur, H. T. K., Ozonur, D., Gul, H. H., Bayrak, H. (2019). Comparison of Rank-Based Tests for Ordered Alternative Hypotheses in Randomized Complete Block Designs. Gazi University Journal of Science, 32(2), 705-716.
AMA Akdur HTK, Ozonur D, Gul HH, Bayrak H. Comparison of Rank-Based Tests for Ordered Alternative Hypotheses in Randomized Complete Block Designs. Gazi University Journal of Science. June 2019;32(2):705-716.
Chicago Akdur, Hatice Tul Kubra, Deniz Ozonur, Hasan Huseyin Gul, and Hulya Bayrak. “Comparison of Rank-Based Tests for Ordered Alternative Hypotheses in Randomized Complete Block Designs”. Gazi University Journal of Science 32, no. 2 (June 2019): 705-16.
EndNote Akdur HTK, Ozonur D, Gul HH, Bayrak H (June 1, 2019) Comparison of Rank-Based Tests for Ordered Alternative Hypotheses in Randomized Complete Block Designs. Gazi University Journal of Science 32 2 705–716.
IEEE H. T. K. Akdur, D. Ozonur, H. H. Gul, and H. Bayrak, “Comparison of Rank-Based Tests for Ordered Alternative Hypotheses in Randomized Complete Block Designs”, Gazi University Journal of Science, vol. 32, no. 2, pp. 705–716, 2019.
ISNAD Akdur, Hatice Tul Kubra et al. “Comparison of Rank-Based Tests for Ordered Alternative Hypotheses in Randomized Complete Block Designs”. Gazi University Journal of Science 32/2 (June 2019), 705-716.
JAMA Akdur HTK, Ozonur D, Gul HH, Bayrak H. Comparison of Rank-Based Tests for Ordered Alternative Hypotheses in Randomized Complete Block Designs. Gazi University Journal of Science. 2019;32:705–716.
MLA Akdur, Hatice Tul Kubra et al. “Comparison of Rank-Based Tests for Ordered Alternative Hypotheses in Randomized Complete Block Designs”. Gazi University Journal of Science, vol. 32, no. 2, 2019, pp. 705-16.
Vancouver Akdur HTK, Ozonur D, Gul HH, Bayrak H. Comparison of Rank-Based Tests for Ordered Alternative Hypotheses in Randomized Complete Block Designs. Gazi University Journal of Science. 2019;32(2):705-16.