Jonckheere Trend Test under Indeterminacy with Applications

Article Sidebar

PDF
DOI: https://doi.org/10.28924/2291-8639-22-2024-130
Published: Aug 5, 2024
Cite as:
Abdulrahman AlAita, Muhammad Aslam, Florentin Smarandache, Jonckheere Trend Test under Indeterminacy with Applications, Int. J. Anal. Appl., 22 (2024), 130.

Main Article Content

Abdulrahman AlAita, Muhammad Aslam, Florentin Smarandache

Abstract

The classical Jonckheere trend test is a non-parametric statistical tool usually employed to compare the medians of multiple independent groups, especially when there is a natural ordering or trend among the groups. This paper aims to develop a more comprehensive and adaptable version of the Jonckheere trend test, called the neutrosophic Jonckheere trend test (NJT), which can be used to analyze different types of uncertainty data. This paper discusses neutrosophic hypotheses and decision rules pertaining to the NJT test. Furthermore, the practical uses of the NJT test have been discussed in the context of real-world applications with COVID-19 data. Lastly, a simulation study is carried out to evaluate the effectiveness of the proposed test in terms of Type I error and test power. The results validate that the proposed test is more effective and adaptable than the existing test in uncertain environments.

Article Details

References

  1. A.R. Jonckheere, a Distribution-Free K-Sample Test Against Ordered Alternatives, Biometrika 41 (1954), 133–145. https://doi.org/10.1093/biomet/41.1-2.133.
  2. T.J. Terpstra, The Asymptotic Normality and Consistency of Kendall’s Test Against Trend, When Ties Are Present in One Ranking, Indag. Math. 55 (1952), 327–333. https://doi.org/10.1016/s1385-7258(52)50043-x.
  3. M. Vock, N. Balakrishnan, A Connection Between Two Nonparametric Tests for Perfect Ranking in Balanced Ranked Set Sampling, Commun. Stat. - Theory Meth. 42 (2013), 191–193. https://doi.org/10.1080/03610926.2011.575515.
  4. A. Ali, A. Rasheed, A.A. Siddiqui, M. Naseer, S. Wasim, W. Akhtar, Non-Parametric Test for Ordered Medians: The Jonckheere Terpstra Test, Int. J. Stat. Med. Res. 4 (2015), 203–207. https://doi.org/10.6000/1929-6029.2015.04.02.6.
  5. H. Murakami, S.K. Lee, Unbiasedness and Biasedness of the Jonckheere-Terpstra and the Kruskal-wallis Tests, J. Korean Stat. Soc. 44 (2015), 342–351. https://doi.org/10.1016/j.jkss.2014.10.001.
  6. C. Joutard, Large Deviation Approximations for the Mann-Whitney Statistic and the Jonckheere-Terpstra Statistic, J. Nonparametric Stat. 25 (2013), 873–888. https://doi.org/10.1080/10485252.2013.816701.
  7. R.C. Magel, An Extension of the Jonckheere-Terpstra Test for Ranked-Set Samples Data, Biometrical J. 36 (1994), 701–707. https://doi.org/10.1002/bimj.4710360608.
  8. M. Hollander, D.A. Wolfe, Nonparametric Statistical Methods, Wiley, 2013.
  9. E.L. Lehmann, H.J. D’Abrera, Nonparametrics: Statistical Methods Based on Ranks, Holden-Day, 1975.
  10. T.P. Hettmansperger, J.W. McKean, Robust Nonparametric Statistical Methods, CRC Press, 2010.
  11. E. Jonckheere, S. Schirmer, F. Langbein, Jonckheere-terpstra Test for Nonclassical Error Versus Log-sensitivity Relationship of Quantum Spin Network Controllers, Int. J. Robust Nonlinear Control. 28 (2018), 2383–2403. https://doi.org/10.1002/rnc.4022.
  12. F. Smarandache, Introduction to Neutrosophic Statistics, Romania-Educational Publisher, Columbus, Ohio, USA, 2014.
  13. M. Aslam, A New Attribute Sampling Plan Using Neutrosophic Statistical Interval Method, Complex Intell. Syst. 5 (2019), 365–370. https://doi.org/10.1007/s40747-018-0088-6.
  14. F. Smarandache, Neutrosophic Statistics Is an Extension of Interval Statistics, While Plithogenic Statistics Is the Most General Form of Statistics, Int. J. Neutrosophic Sci. 19 (2022), 148–165. https://doi.org/10.54216/ijns.190111.
  15. R.A.K. Sherwani, H. Shakeel, M. Saleem, W.B. Awan, M. Aslam, M. Farooq, A New Neutrosophic Sign Test: An Application to COVID-19 Data, PLoS ONE 16 (2021), e0255671. https://doi.org/10.1371/journal.pone.0255671.
  16. R.A.K. Sherwani, H. Shakeel, W.B. Awan, M. Faheem, M. Aslam, Analysis of COVID-19 Data Using Neutrosophic Kruskal Wallis H Test, BMC Med. Res. Methodol. 21 (2021), 215. https://doi.org/10.1186/s12874-021-01410-x.
  17. M. Aslam, M. Sattam Aldosari, ANalyzing Alloy Melting Points Data Using a New Mann-Whitney Test Under Indeterminacy, J. King Saud Univ. - Sci. 32 (2020), 2831–2834. https://doi.org/10.1016/j.jksus.2020.07.005.
  18. M. B. Zeina, M. Miari and M. T. Anan, Single Valued Neutrosophic Kruskal-Wallis and Mann Whitney Tests, Neutrosophic Sets Syst. 51 (2022), 948–957.
  19. M. Aslam, Neutrosophic Analysis of Variance: Application to University Students, Complex Intell. Syst. 5 (2019), 403–407. https://doi.org/10.1007/s40747-019-0107-2.
  20. S. Ullah, M. Kashif, M. Aslam, G. Haider, A. AlAita, M. Saleem, A Generalized Approach to Compute Neutrosophic k-Factor Analysis of Variance, J. Intell. Fuzzy Syst. 45 (2023), 6005–6017. https://doi.org/10.3233/jifs-223636.
  21. A. AlAita, H. Talebi, Exact Neutrosophic Analysis of Missing Value in Augmented Randomized Complete Block Design, Complex Intell. Syst. 10 (2023), 509–523. https://doi.org/10.1007/s40747-023-01182-5.
  22. A. AlAita, M. Aslam, Analysis of Covariance Under Neutrosophic Statistics, J. Stat. Comput. Simul. 93 (2022), 397–415. https://doi.org/10.1080/00949655.2022.2108423.
  23. A. AlAita, H. Talebi, M. Aslam, K. Al Sultan, Neutrosophic Statistical Analysis of Split-Plot Designs, Soft Comput. 27 (2023), 7801–7811. https://doi.org/10.1007/s00500-023-08025-y.
  24. M. Aslam, M. Albassam, Presenting Post Hoc Multiple Comparison Tests Under Neutrosophic Statistics, J. King Saud Univ. - Sci. 32 (2020), 2728–2732. https://doi.org/10.1016/j.jksus.2020.06.008.
  25. A.A. Salama, O.M. Khaled, K.M. Mahfouz, Neutrosophic Correlation and Simple Linear Regression, Neutrosophic Sets Syst. 5 (2014), 3–8.
  26. D. Nagarajan, S. Broumi, F. Smarandache, J. Kavikumar, Analysis of Neutrosophic Multiple Regression, Neutrosophic Sets Syst. 43 (2021), 44–53.
  27. A.M. Alomair, U. Shahzad, Neutrosophic Mean Estimation of Sensitive and Non-Sensitive Variables with Robust Hartley-Ross-Type Estimators, Axioms 12 (2023), 578. https://doi.org/10.3390/axioms12060578.
  28. M. Aslam, M. Saleem, Neutrosophic Test of Linearity With Application, AIMS Math. 8 (2023), 7981–7989. https://doi.org/10.3934/math.2023402.
  29. M. Aslam, Analyzing Wind Power Data Using Analysis of Means Under Neutrosophic Statistics, Soft Comput. 25 (2021), 7087–7093. https://doi.org/10.1007/s00500-021-05661-0.
  30. M. Aslam, K. Khan, M. Albassam, L. Ahmad, Moving Average Control Chart Under Neutrosophic Statistics, AIMS Math. 8 (2023), 7083–7096. https://doi.org/10.3934/math.2023357.
  31. M. Aslam, Design of the Bartlett and Hartley Tests for Homogeneity of Variances Under Indeterminacy Environment, J. Taibah Univ. Sci. 14 (2019), 6–10. https://doi.org/10.1080/16583655.2019.1700675.
  32. M. Miari, M. T. Anan, M. B. Zeina, Neutrosophic Two Way ANOVA, Int. J. Neutrosophic Sci. 18 (2022), 73–83. https://doi.org/10.54216/ijns.180306.