Solving the incomplete data problem in Greco-Latin square experimental design by exact-scheme analysis of variance without data imputation

Kittiwat Sirikasemsuk; Sirilak Wongsriya; Kanogkan Leerojanaprapa; Kittiwat Sirikasemsuk; Sirilak Wongsriya; Kanogkan Leerojanaprapa

doi:10.3934/math.20241601

AIMS Mathematics

2024, Volume 9, Issue 12: 33551-33571. doi: 10.3934/math.20241601

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Research article

Solving the incomplete data problem in Greco-Latin square experimental design by exact-scheme analysis of variance without data imputation

1.
Department of Industrial Engineering, School of Engineering, King Mongkut's Institute of Technology Ladkrabang, Bangkok, Thailand
2.
Statistics Department, Faculty of Science, King Mongkut's Institute of Technology Ladkrabang, Bangkok, Thailand

Received: 06 August 2024 Revised: 21 October 2024 Accepted: 25 October 2024 Published: 26 November 2024
MSC : 15A06, 15A09, 62J10, 62K05, 62K10

This study introduced a novel exact-scheme analysis of variance to tackle the challenge of incomplete data within the Greco-Latin square experimental design (GLSED), specifically for scenarios with a single missing observation across any treatment and block level, thus eliminating the need for conventional data imputation methods. This approach innovatively addresses and mitigates the bias in the treatment sum of squares, a significant drawback of traditional missing plot techniques, by providing a precise, exact-scheme-based formula for calculating the treatment sum of squares in fixed-effect GLSED contexts with unrecorded values. Moreover, it offers a method for correcting biased treatment sum of squares values, presenting an adjustment mechanism for instances where the least squares method was previously employed to estimate missing values. This comprehensive strategy not only enhances the methodological accuracy and integrity of GLSED studies but also contributes significantly to the field by offering a solution to navigate the complexities of incomplete datasets without resorting to data imputation, thus improving the rigor and validity of experimental designs in the face of missing data challenges.
- design of experiment,
- ANOVA,
- linear algebra equations,
- Greco-Latin square design,
- unrecorded observation,
- missing value
Citation: Kittiwat Sirikasemsuk, Sirilak Wongsriya, Kanogkan Leerojanaprapa. Solving the incomplete data problem in Greco-Latin square experimental design by exact-scheme analysis of variance without data imputation[J]. AIMS Mathematics, 2024, 9(12): 33551-33571. doi: 10.3934/math.20241601

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Abstract

This study introduced a novel exact-scheme analysis of variance to tackle the challenge of incomplete data within the Greco-Latin square experimental design (GLSED), specifically for scenarios with a single missing observation across any treatment and block level, thus eliminating the need for conventional data imputation methods. This approach innovatively addresses and mitigates the bias in the treatment sum of squares, a significant drawback of traditional missing plot techniques, by providing a precise, exact-scheme-based formula for calculating the treatment sum of squares in fixed-effect GLSED contexts with unrecorded values. Moreover, it offers a method for correcting biased treatment sum of squares values, presenting an adjustment mechanism for instances where the least squares method was previously employed to estimate missing values. This comprehensive strategy not only enhances the methodological accuracy and integrity of GLSED studies but also contributes significantly to the field by offering a solution to navigate the complexities of incomplete datasets without resorting to data imputation, thus improving the rigor and validity of experimental designs in the face of missing data challenges.

References

[1]	D. C. Montgomery, Design and analysis of experiments, 10th Eds., John Wiley & Sons, 2019.
[2]	R. E. Kirk, Experimental design: Procedures for the behavioral sciences, 4th Eds., SAGE Publications Inc., 2013. https://doi.org/10.4135/9781483384733
[3]	R. A. Johnson, G. K. Bhattacharyya, Statistics: Principles and methods, 7th Eds., New Jersey: John Wiley & Sons, 2014.
[4]	G. Canavos, J. Koutrouvelis, Introduction to the design & analysis of experiments, 1st Ed., Pearson, 2008.
[5]	N. Diawara, A. Demuren, E. Gyuricsko, Impairment of continuous insulin delivery therapy and analysis from graeco-latin square design model, J. Biosci. Med., 4 (2016), 40–51. https://doi.org/10.4236/jbm.2016.48006 doi: 10.4236/jbm.2016.48006
[6]	M. R. Mahamud, D. J. Gomes, Enzymatic saccharification of sugar cane bagasse by the crude enzyme from indigenous fungi, J. Sci. Res., 4 (2012), 227. https://doi.org/10.3329/jsr.v4i1.7745 doi: 10.3329/jsr.v4i1.7745
[7]	A. G. Woodside, W. G. Pearce, Testing market segment acceptance of new designs of industrial services, J. Prod. Innovat. Manag., 6 (1989), 185–201. https://doi.org/10.1111/1540-5885.630185 doi: 10.1111/1540-5885.630185
[8]	J. A. Tovar-Aguilar, P. F. Monaghan, C. A. Bryant, A. Esposito, M. Wade, O. Ruíz-Barzola, et al., Improving eye safety in citrus harvest crews through the acceptance of personal protective equipment, community-based participatory research, social marketing, and community health workers, J. Agromedicine, 19 (2014), 107–116. https://doi.org/10.1080/1059924x.2014.884397 doi: 10.1080/1059924x.2014.884397
[9]	R. Mead, S. G. Gilmour, A. Mead, Statistical principles for the design of experiments: Applications to real experiments, Cambridge University Press, 2012. https://doi.org/10.1017/CBO9781139020879
[10]	W. J. Youden, Use of incomplete block replications in estimating tobacco-mosaic virus, Contrib. Boyce Thomps., 9 (1937), 41–48.
[11]	F. Yates, Incomplete randomized blocks, Ann. Eugen., 7 (1936), 121–140. https://doi.org/10.1111/j.1469-1809.1936.tb02134.x doi: 10.1111/j.1469-1809.1936.tb02134.x
[12]	M. Ai, K. Li, S. Liu, D. K. J. Lin, Balanced incomplete Latin square designs, J. Statist. Plann. Inference, 143 (2013), 1575–1582. https://doi.org/10.1016/j.jspi.2013.05.001 doi: 10.1016/j.jspi.2013.05.001
[13]	R. L. Anderson, Missing-plot techniques, Biometrics Bull., 2 (1946), 41–47. https://doi.org/10.2307/3001999 doi: 10.2307/3001999
[14]	R. Rangaswamy, A textbook of agricultural statistics, 2nd Eds., New Age International, 2010.
[15]	K. Sirikasemsuk, A review on incomplete Latin square design of any order, AIP Conf. Proc., 1775 (2016), 030022. https://doi.org/10.1063/1.4965142 doi: 10.1063/1.4965142
[16]	R. J. A. Little, D. B. Rubin, Statistical analysis with missing data, 3rd Eds., John Wiley & Sons, 2019.
[17]	F. E. Allan, J. Wishart, A method of estimating the yield of a missing plot in field experimental work, J. Agri. Sci., 20 (1930), 399–406. https://doi.org/10.1017/S0021859600006912 doi: 10.1017/S0021859600006912
[18]	F. Yates, The analysis of replicated experiments when the field results are incomplete, Emprie J. Exp. Agri., 1 (1933), 129–142.
[19]	J. A. Kupolusi, O. O. Ojo, One missing observation in graeco Latin square design: An approximate analysis of variance, Amer. Based Res. J., 10 (2021), 1–8.
[20]	E. A. Cornish, The estimation of missing values in incomplete randomized block experiments, Ann. Eugen., 10 (1940), 112–118. https://doi.org/10.1111/j.1469-1809.1940.tb02240.x doi: 10.1111/j.1469-1809.1940.tb02240.x
[21]	H. R. Baird, C. Y. Kramer, Analysis of variance of a balanced incomplete block design with missing observations, J. Roy. Statist. Soc. Ser. C, 9 (1960), 189–198. https://doi.org/10.2307/2985719 doi: 10.2307/2985719
[22]	M. S. Bartlett, Some examples of statistical methods of research in agriculture and applied biology, J. R. Stat. Soc., 4 (1937), 137–183. https://doi.org/10.2307/2983644 doi: 10.2307/2983644
[23]	I. Coons, The analysis of covariance as a missing plot technique, Biometrics, 13 (1957), 387–405. https://doi.org/10.2307/2527922 doi: 10.2307/2527922
[24]	W. G. Cochran, Analysis of covariance: Its nature and uses, Biometrics, 13 (1957), 261–281. https://doi.org/10.2307/2527916 doi: 10.2307/2527916
[25]	G. N. Wilkinson, Estimation of missing values for the analysis of incomplete data, Biometrics, 14 (1958), 257–286. https://doi.org/10.2307/2527789 doi: 10.2307/2527789
[26]	C. E. Ogbonnaya, E. C. Uzochukwu, Estimation of missing data in analysis of covariance: A least-squares approach, Commun. Stat. Theory Methods, 45 (2016), 1902–1909. https://doi.org/10.1080/03610926.2013.868000 doi: 10.1080/03610926.2013.868000
[27]	M. H. Kutner, C. J. Nachtsheim, J. Neter, W. Li, Applied linear statistical models, 5th Eds., New York: McGraw-Hill Irwin, 2005.
[28]	G. P. Quinn, M. J. Keough, Experimental design and data analysis for biologists, 1st Ed., Cambridge University Press, 2002. https://doi.org/10.1017/CBO9780511806384
[29]	K. Sirikasemsuk, K. Leerojanaprapa, S. Sirikasemsuk, Regression sum of squares of randomized complete block design with one unrecorded observation, AIP Conf. Proc., 2016 (2018), 020136. https://doi.org/10.1063/1.5055538 doi: 10.1063/1.5055538
[30]	K. Sirikasemsuk, K. Leerojanaprapa, Analysis of two-missing-observation 4×4 Latin squares using the exact approach, In: Recent advances in information and communication technology 2017, Cham: Springer, 566 (2018), 69–81. https://doi.org/10.1007/978-3-319-60663-7_7
[31]	K. Sirikasemsuk, One missing value problem in Latin square design of any order: Regression sum of squares, In: 2016 Joint 8th international conference on soft computing and intelligent systems (SCIS) and 17th international symposium on advanced intelligent systems (ISIS), Japan: IEEE, 2016,142–147. https://doi.org/10.1109/SCIS-ISIS.2016.0041
[32]	K. Sirikasemsuk, K. Leerojanaprapa, One missing value problem in Latin square design of any order: Exact analysis of variance, Cogent Eng., 4 (2017), 1411222. https://doi.org/10.1080/23311916.2017.1411222 doi: 10.1080/23311916.2017.1411222
[33]	J. Subramani, Non-iterative least squares estimation of missing values in graeco-Latin square designs, Biometrical J., 33 (1991), 763–769. https://doi.org/10.1002/bimj.4710330619 doi: 10.1002/bimj.4710330619
[34]	D. C. Montgomery, Design and analysis of experiments, John Wiley & Sons, 1984.
[35]	R. Ott, M. Longnecker, An introduction to statistical methods and data analysis, 7th Eds., Cengage Learning, 2021.
[36]	A. AlAita, M. Aslam, K. Al Sultan, M. Saleem, Analysis of graeco-latin square designs in the presence of uncertain data, J. Big Data, 11 (2024), 109. https://doi.org/10.1186/s40537-024-00970-1 doi: 10.1186/s40537-024-00970-1
[37]	K. Hinkelmann, O. Kempthorne, Design and analysis of experiments: Introduction to experimental design, John Wiley & Sons, 2007.
[38]	R. J. Freund, W. J. Wilson, D. L. Mohr, Statistical methods, student solutions manual (e-only), Academic Press, 2010. Available from: http://www.sars-expertcom.gov.hk/english/reports/reports.html

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