A New Mood’s Median Test for Imprecise Data

Main Article Content

Abdulrahman AlAita, Muhammad Aslam, Florentin Smarandache

Abstract

The existing Mood’s median test is a non-parametric test used to compare two or more sample data sets whether they are from the same population or not. There can be no application of this test to uncertain and indeterminate data. Therefore, it is necessary to find a generalization of this test that will enable us to apply it in uncertain environments. This study will present a new approach that utilizes neutrosophic statistics to apply Mood’s median test. The approach involves defining hypotheses, determining a decision rule, and performing the test in an uncertain environment. An evaluation of the performance of the proposed test will be conducted using numerical examples. The results reveal that the proposed test under neutrosophic statistics is more informative, efficient, and flexible than the existing test under classical statistics in the presence of uncertain data.

Article Details

References

  1. A.M. Mood, Introduction to the Theory of Statistics, McGraw-Hill, (1950).
  2. G.W. Brown, A.M. Mood, On Median Tests for Linear Hypotheses, in: Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, pp. 159–166.
  3. A.M. Mood, On the Asymptotic Efficiency of Certain Nonparametric Two-Sample Tests, Ann. Math. Stat. 25 (1954). 514-522. https://www.jstor.org/stable/2236833.
  4. M.A. Fligner, S.W. Rust, A Modification of Mood's Median Test for the Generalized Behrens-Fisher Problem, Biometrika, 69 (1982), 221-226. https://doi.org/10.1093/biomet/69.1.221.
  5. Z. Chen, Extension of Mood’s Median Test for Survival Data, Stat. Prob. Lett. 95(2014), 77-84. https://doi.org/10.1016/j.spl.2014.08.006.
  6. D. Cramer, Fundamental Statistics for Social Research: Step-By-Step Calculations and Computer Techniques Using SPSS for Windows, Psychology Press, 1998.
  7. M. Desu, D. Raghavarao, Nonparametric Statistical Methods for Complete and Censored Data, CRC Press, 2004. https://doi.org/10.1201/9781482285895.
  8. M.J. De Smith, Statistical Analysis Handbook, The Winchelsea Press, 2015.
  9. F. Smarandache, Neutrosophic Logic-A Generalization of the Intuitionistic Fuzzy Logic, In: Multispace & Multistructure. Neutrosophic Transdisciplinarity (100 Collected Papers of Science), Vol. 4, 396-402, (2010).
  10. F. Smarandache, Introduction to Neutrosophic Statistics: Infinite Study, Romania-Educational Publisher, Columbus, 2014.
  11. 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.
  12. 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.
  13. A. AlAita, M. Aslam, Analysis of Covariance Under Neutrosophic Statistics, J. Stat. Comp. Simul. 93 (2023), 397-415. https://doi.org/10.1080/00949655.2022.2108423.
  14. 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.
  15. 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. Method. 21 (2021), 215. https://doi.org/10.1186/s12874-021-01410-x.
  16. M. Aslam, M.S. 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.
  17. M. Miari, M.T. Anan, M.B. Zeina, Single Valued Neutrosophic Kruskal-Wallis and Mann Whitney Tests, Neutrosophic Sets Syst. 51 (2022), 948-957.
  18. P. Grzegorzewski, M. Śpiewak, Two-Sample Median Test for Interval-Valued Data, in: K.T. Atanassov, V. Atanassova, J. Kacprzyk, A. Kaluszko, M. Krawczak, J.W. Owsinski, S. Sotirov, E. Sotirova, E. Szmidt, S. Zadrozny (Eds.), Uncertainty and Imprecision in Decision Making and Decision Support: New Challenges, Solutions and Perspectives, Springer International Publishing, Cham, 2021: pp. 113–128. https://doi.org/10.1007/978-3-030-47024-1_13.
  19. M. Aslam, M. Saleem, Neutrosophic Test of Linearity with Application, AIMS Math. 8 (2023), 7981-7989. https://doi.org/10.3934/math.2023402.
  20. 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.
  21. [1] U. Afzal, M. Aslam, Analysis of Changes in Blood Pressure of Women During Pregnancy Through Neutrosophic Statistics, in: Cognitive Intelligence with Neutrosophic Statistics in Bioinformatics, Elsevier, 2023: pp. 137–152. https://doi.org/10.1016/B978-0-323-99456-9.00010-6.
  22. I. Shahzadi, Neutrosophic Statistical Analysis of Temperature of Different Cities of Pakistan, Neutrosophic Sets Syst. 53 (2023), 157-164.
  23. 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.
  24. M. Aslam, Analysing Gray Cast Iron Data using a New Shapiro-Wilks test for Normality under Indeterminacy, Int. J. Cast Metals Res. 34 (2021), 1-5. https://doi.org/10.1080/13640461.2020.1846959.
  25. M. Aslam, O. H. Arif, and R. A. K. Sherwani, New Diagnosis Test Under the Neutrosophic Statistics: An Application to Diabetic Patients, BioMed Res. Int. 2020 (2020), 2086185. https://doi.org/10.1155/2020/2086185.
  26. 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.