Application of Statistical Method in Mathematical Models
DOI:
https://doi.org/10.29304/jqcsm.2026.18.32846Keywords:
Analysis of variance, Repeated measurements model, Variance components, Test statistics, Random effect.Abstract
In this paper, we define two mathematical models, the first of which is a repeated measurements model with two random effects and two fixed effects, while the second has one random effect and three fixed effects. Analysis of variance for each model investigated and applied to some data, and variance components estimated by using the maximum likelihood method.
Downloads
References
C. Eck, H. Garcke, and P. Knabner, Mathematical modeling, 1st ed., Springer Int. Publ. AG, 2017.
DOI:10.1007/978-3-319-55161-6
J. D. Brown, Linear models in matrix form, 1st ed., Springer, 2014. https://link.springer.com/book/10.1007/978-3-319-11734-8
F. H. Al-Kanan, “Confidence intervals in three-way repeated measurements model”, Basrah. J. Sci., 42(2024) 176-190.
https://basjsci.edu.iq/index.php/basjsci/ar/article/view/220/194
A. H. S. AL-Mouel, F.H. Al-Kanan, “A penalized likelihood estimator for variance components in repeated measurements model”, Basrah. J. Sci., 39(2021)192-203.
https://basjsci.edu.iq/index.php/basjsci/ar/article/view/104/84
A. A. A. AL-Hassan, A. H.S. AL-Moul, “Some inference of the repeated measurements model”, Int. J. Nonlinear Anal. Appl., 12(2021)569-581.
DOI: 10.22075/IJNAA.2021.5109
H. A. Kori, A. H.S. AL-Mouel, “Expected mean square rate estimation of repeated measurements model”, Int. J. Nonlinear Anal. Appl., 12(2021)75-83.
https://doi.org/10.22075/IJNAA.2021.5018.Hh
D. M. Saleh, D. H. Kadir, D. I. Jamil, “A comparison between some penalized methods for estimating parameters”, Qalaai. Zanistscientific. J., 8(2023)2518-6566.
Doi: 10.25212/lfu.qzj.8.1.44
B. Langenberg, M. Janczyk, V. Koob, R. Kliegl, A. Mayer, “A tutorial on using the paired t test for power calculationsin repeated measures anova with interaction”, Behav. Res. Methods., 55(2023)2467-2484
https://link.springer.com/article/10.3758/s13428-022-01902-8
F. H. Al-Kanan, “Estimation methods for three-way repeated measurements model”, Basrah. Res. Sci., 50(2024)35-45.
https://jou.jobrs.edu.iq/index.php/home/article/view/143
S. Serovajsky, Mathematical modelling, 1st ed., Chpman and hall/CRC, 2021.
https://doi.org/10.1201/9781003035602
D. L. Timmons, C. W. Johnson, S. M. McCook, Fundamentals of algebraic modeling, 5th ed., Cengage Learning, 2013.
M. C. Gacula, J. Singh, J. Bi, S. Altan, Statistical methods in food and consumer research, 2nd ed., Elsevier, 2008.
https://www.researchgate.net/publication
T. E. Essington, Introduction to quantitative Ecology: mathematical and statistical modelling for beginners, Oxford, 2021.
DOI:10.1093/oso/9780192843470.001.0001
H. I. Mustafa, A. S. Al-mouel, Reduced bias estimation of variance for repeated measurements model, J. Stat. Manag. Syst., 27(2024) 663-671.
DOI:10.47974/JSMS-1084
M. A. Ati, A. H. Al-taha, Effect of spraying drin, vegeamino and ascorbic acid on some physical and chemical properties of date palm fruits (phoenix dactylifera l.cv. hillawi), J. Basrah. Date. Palm. Res., 22(2023)52-71.
https://www.palm.uobasrah.edu.iq/index.php/paml/article/view/59/43
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Fatima Al-Kanan, Mohammed waleed AbdulRidaha, Takia Ahmed Jwad

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.








