Theoretical Study for Adjusting ANOVA Procedures For The One-Way Random Effects Model Under Correlated Errors Within Class And Across Classes
DOI:
https://doi.org/10.29304/jqcm.2023.15.2.1251Keywords:
Random effect Model, Analysis of Variance, Correlation error termsAbstract
In this study, a method was developed to adjust the procedures of analysis of variance for the one-way balanced random effects model when error limits across classes are not independent, while the assumption of independence between the error terms among the different classes is essential in the analysis of variance. The variance-covariance structure and the correlation coefficients for the error limits were defined. The was assumed as the correlation coefficient of error terms within the class and the is the correlation coefficient for error terms in different classes. The work performed by deriving correction factor and calculating the expectation of the mean sum of squares of errors and treatments as well as correcting the f-statistic.
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References
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[16] A. Mallick, P. Subbaiah, and G. Xia, Modified testing procedures and multiple comparison methods for anova with ar (1) correlated errors, Computational and Mathematical Methods, 2(2), (2020), e1076.
[17] A. H. Andersen, E. B. Jensen, and G. Schou, Two-way analysis of variance with correlated errors, International Statistical Review/Revue Internationale de Statistique, 49(2), (1981), 153–167.
[18] R. Lund, G. Liu, and Q. Shao, A new approach to anova methods for autocorrelated data, The American Statistician, 70(1), (2016), 55–62.
[19] W. G. Cochran, The distribution of quadratic forms in a normal system, with applications to the analysis of covariance, In Mathematical Proceedings of the Cambridge Philosophical Society, 30(2), (1934), 178–191.
[20] Z. A. AL-Kaabawi and R. D. Abdul-wahab, Expected mean squares for 3-way crossed model with unbalanced correlated data, Basrah Journal of Science, 30(1), (2012), 97–111.
[21] R. D. Abdul-Wahab, Expected mean squares for 4-way crossed model with unbalanced correlated data, Basrah Journal of Science, 31(1), (2013), 1–27.
[2] D. Selvamuthu and D. Das, Introduction to statistical methods, design of experiments and statistical quality control, Springer Singapore, (2018).
[3] H. Sahai and M. Miguel Ojeda, Analysis of Variance for Random Models: Volume II: Unbalanced Data Theory, Methods, Applications, and Data Analysis, Springer, (2005).
[4] R. Littell, W. Stroup, and R. Freund, SAS for Linear Models, Fourth Edition (4th ed.), SAS Publishing, (2002).
[5] T. Hill and P. Lewicki, Statistics: Methods and Applications, StatSoft, Inc, (2005).
[6] Z. Abdulhussein Al-kaabawi, Expected mean squares for 4-way crossed model with balanced correlated data,” Journal of Basrah Researches ((Sciences)), 36(3), (2010), 45–71.
[7] R. J. Pavur and J. M. Davenport, The (large) effect of (small) correlations in anova, and correction procedures, American Journal of Mathematical and Management Sciences, 5(1-2), (1985), pp: 77–92.
[8] A. S. AL-Mouel, K. J. AL-Abdulla, and Z. A. AL-Rabeaa, Type i error rates for multiple comparison procedures with dependent data for 3-way nested anova model, Journal of Basrah Researches, 20(1), (1999), 39–48.
[9] R. Aylmer Fisher, Statistical methods for research workers. biological monographs and manuals. no. v. Statistical methods for research workers, Biological monographs and manuals. No. V. (11th ed.), (1950).
[10] A. Donner, A review of inference procedures for the intraclass correlation coefficient in the one-way random effects model, International Statistical Review/Revue Internationale de Statistique, 54(1), (1986), 67–82.
[11] J. Smith and T. Lewis, Determining the effects of intraclass correlation on factorial experiments,” Communications in Statistics-Theory and Methods, 9(13), (1980), 1353–1364.
[12] R. J. Pavur and T. Levis, Unbiased f tests for factorial experiments for correlated data, Communications in Statistics-Theory and Methods, 12(7), (1983), 829–840.
[13] S. M. Scariano and J. M. Davenport, “Corrected f-tests in the general linear model, Communications in Statistics-Theory and Methods, 13(25), (1984), 3155–3172.
[14] Z. Abdulhussein Al-kaabawi, The effect of dependent data on type i error rates for multiple comparison procedures for 3-way crossed balanced model, basrah journal of science, 25(1), (2007), 73–85.
[15] R. J. Pavur, Type i error rates for multiple comparison procedures with dependent data, The American Statistician, 42(3), (1988), 171–173.
[16] A. Mallick, P. Subbaiah, and G. Xia, Modified testing procedures and multiple comparison methods for anova with ar (1) correlated errors, Computational and Mathematical Methods, 2(2), (2020), e1076.
[17] A. H. Andersen, E. B. Jensen, and G. Schou, Two-way analysis of variance with correlated errors, International Statistical Review/Revue Internationale de Statistique, 49(2), (1981), 153–167.
[18] R. Lund, G. Liu, and Q. Shao, A new approach to anova methods for autocorrelated data, The American Statistician, 70(1), (2016), 55–62.
[19] W. G. Cochran, The distribution of quadratic forms in a normal system, with applications to the analysis of covariance, In Mathematical Proceedings of the Cambridge Philosophical Society, 30(2), (1934), 178–191.
[20] Z. A. AL-Kaabawi and R. D. Abdul-wahab, Expected mean squares for 3-way crossed model with unbalanced correlated data, Basrah Journal of Science, 30(1), (2012), 97–111.
[21] R. D. Abdul-Wahab, Expected mean squares for 4-way crossed model with unbalanced correlated data, Basrah Journal of Science, 31(1), (2013), 1–27.
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Published
2023-09-25
How to Cite
Jawad, A. M., & AL-Kaabawi, Z. (2023). Theoretical Study for Adjusting ANOVA Procedures For The One-Way Random Effects Model Under Correlated Errors Within Class And Across Classes. Journal of Al-Qadisiyah for Computer Science and Mathematics, 15(2), Math Page 87–101. https://doi.org/10.29304/jqcm.2023.15.2.1251
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Math Articles
