Abstract
This research deals with the analysis of incomplete Latin square designs using the exact approach. Specifically, the study investigated the 4 × 4 Latin square designs with two missing observations without replication. In the research, the general regression significance test (i.e. the exact approach) was used to derive the estimation formulae of fitted parameters for the full and reduced linear statistical models, thereby simplifying the calculation process. In addition, the proposed exact approach-based formulae facilitate the determination of the treatment sum of squares and the error sum of squares, both of which are subsequently employed in the analysis of variance (ANOVA).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Montgomery, D.C.: Design and Analysis of Experiments. Wiley, New York (2008)
Mead, R., Gilmour, S.G., Mead, A.: Statistical Principles for the Design of Experiments: Applications to Real Experiments, vol. 36. Cambridge University Press, Cambridge (2012)
Stones, D.S.: The many formulae for the number of Latin rectangles. Electron. J. Comb. 17(1), 46 (2010)
Youden, W.J.: Use of incomplete block replications in estimating tobacco-mosaic virus. Contrib. Boyce Thompson Inst. 9(1), 41–48 (1937)
Allan, F.E., Wishart J.: A method of estimating the yield of a missing plot in field -experimental work. J. Agric. Sci. 20(3), 399–406 (1930)
Yates, F.: The analysis of replicated experiments when the field results are incomplete. Emp. J. Exp. Agric. 1(2), 129–142 (1933)
Little, R.J.A., Rubin D.B.: Statistical Analysis with Missing Data, 2nd edn. Wiley, New York (2002)
Yates, F.: Incomplete Latin squares. J. Agric. Sci. 26(2), 301–315 (1936)
Yates, F., Hale, R.W.: The analysis of Latin squares when two or more rows, columns, or treatments are missing. J. Roy. Stat. Soc. 6(1), 67–79 (1939)
Sirikasemsuk, K.: 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, pp. 142–147. IEEE Press, Japan (2016)
Sirikasemsuk, K.: A Review on incomplete Latin square design of any order. In: Rusli, N., Zaimi, W.M., Khazali, K.A., Masnan, M.J., Daud, W.S., Abdullah, N., Yahya, Z., Amin, N.A., Aziz, N.H., Yusuf, Y.N. (eds.) AIP Conference Proceedings 2016, vol. 1775, p. 030022. AIP Publishing (2016)
De Lury, D.B.: The analysis of Latin squares when some observations are missing. J. Am. Stat. Assoc. 41(235), 370–389 (1946)
Kramer, C.Y., Glass, S.: Analysis of variance of a Latin square design with missing observations. Appl. Stat. 9(1), 43–50 (1960)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Sirikasemsuk, K., Leerojanaprapa, K. (2018). Analysis of Two-Missing-Observation 4 × 4 Latin Squares Using the Exact Approach. In: Meesad, P., Sodsee, S., Unger, H. (eds) Recent Advances in Information and Communication Technology 2017. IC2IT 2017. Advances in Intelligent Systems and Computing, vol 566. Springer, Cham. https://doi.org/10.1007/978-3-319-60663-7_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-60663-7_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-60662-0
Online ISBN: 978-3-319-60663-7
eBook Packages: EngineeringEngineering (R0)