Abstract
The analysis of unreplicated designs concentrates much of interest, since these designs enable us to estimate the factorial effects using contrasts, while no degrees of freedom are left to estimate the error variance, so conventional ANOVA techniques cannot be applied to detect the active effects. In this paper we review two effective methods (Angelopoulos and Koukouvinos, J. Appl. Statist 35:277–281, 2008; Angelopoulos et al., Qual. Reliab. Eng. Int 26:223–233, 2010) for the identification of active factors in unreplicated experiments. An illustrative example of the application of the two methods is presented, as also a comparative simulation study, revealing the effectiveness of the two methods.
AMS Subject Classification: Primary 62K15, Secondary 62J20
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References
Aboukalam, M.A.F.: Quick, easy and powerful analysis of unreplicated factorial designs. Commun.Statist.- Theory Meth. 34, 1169–1175 (2005)
Angelopoulos, P., Koukouvinos, C.: Detecting active effects in unreplicated designs, J. Appl. Statist. 35, 277–281 (2008)
Angelopoulos, P., Evangelaras, H., Koukouvinos, C.: Analyzing unreplicated 2k factorial designs by examining their projections into k − 1 factors. Qual. Reliab. Eng. Int. 26, 223–233 (2010)
Benski, H.C.: Use of a normality test to identify significant effects in factorial designs. J. Qual. Tech. 21, 174–178 (1989)
Box, G.E.P., Meyer, R.D.: An analysis for unreplicated fractional factorials. Technometrics. 28, 11–18 (1986)
Chen, Y., Kunert, J.: A new quantitative method for analysing unreplicated factorial designs. Biometrical J. 46, 125–140 (2004)
Daniel, C.: Use of half-normal plots in interpreting factorial two-level experiments. Technometrics. 1, 311–341 (1959)
Dong, F.: On the identification of active contrasts in unreplicated fractional factorials. Stat. Sinica. 3, 209–217 (1993)
Hadi, A.S., Simonoff, J.S.: Procedures for identification of multiple outliers in linear models. J. Am. Stat. Association. 88, 1264–1271 (1993)
Hamada, M., Balakrishnan, N.: Analysing unreplicated factorial experiments: A review with some new proposals. Stat. Sinica. 8, 1–41 (1998)
Lenth, R.V.: Quick and easy analysis of unreplicated factorial. Technometrics. 31, 469–473 (1989)
Miller, A.: The analysis of unreplicated factorial experiments using all possible comparisons. Technometrics. 47, 51–63 (2005)
Montgomery, D.C.: Design and analysis of experiments, 6th edn. John Willey and Sons, New York (2009)
Voss, D.T., Wang, W.: Analysis of othogonal saturated designs. In: Screening Methods for Experimentation in Industry, Drug Discovery and Genetics, pp. 268–281. Springer, New York (2006)
Voss, D.T., Wang, W.: On adaptive testing in orthogonal satutated designs. Stat. Sinica. 16, 227–234 (2006)
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Angelopoulos, P., Koukouvinos, C., Skountzou, A. (2012). Analysis Methods for Unreplicated Factorial Experiments. In: Daras, N. (eds) Applications of Mathematics and Informatics in Military Science. Springer Optimization and Its Applications, vol 71. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4109-0_15
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DOI: https://doi.org/10.1007/978-1-4614-4109-0_15
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