Abstract
In this chapter we introduce some additional topics in experimental design beyond those discussed in Chapters 6, 12, and 13. The principle of confounding is used to design efficient experiments having many factors but using only a small subset of all possible treatment combinations. Split plot designs involve placing a restriction on the randomization of treatments to experimental units in order to achieve more precision for comparisons involving levels of one factor in exchange for reduced precision for comparisons involving levels of another factor. We illustrate crossover designs that allow for the estimation of treatment effects that can linger across time periods. We show how to test for interaction in two-way designs having exactly one observation at each treatment combination. We show how to extend ANCOVA to designs with blocking factors.
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References
R.L. Anderson, T.A. Bancroft, Statistical Theory in Research (McGraw-Hill, New York,1952)
M.K. Barnett, F.C. Mead, A 24 factorial experiment in four blocks of eight. Appl. Stat. 5, 122–131 (1956)
G.E.P. Box, W.G. Hunter, J.S. Hunter, Statistics for Experimenters (Wiley, New York, 1978)
W.G. Cochran, G.M. Cox, Experimental Designs, 2nd edn. (Wiley, New York, 1957)
R.S. Fouts, Acquisition and testing of gestural signs in four young chimpanzees. Science 180, 978–980 (1973)
D.J. Hand, F. Daly, A.D. Lunn, K.J. McConway, E. Ostrowski, A Handbook of Small Data Sets (Chapman and Hall, London, 1994)
R.M. Heiberger, Computation for the Analysis of Designed Experiments (Wiley, New York, 1989)
D.C. Hoaglin, F. Mosteller, J.W. Tukey (eds.), Understanding Robust and Exploratory Data Analysis (Wiley, New York, 1983)
N.L. Johnson, F.C. Leone, Statistics and Experimental Design in Engineering and the Physical Sciences, vol. 2 (Wiley, New York, 1967)
P.O. Johnson, F. Tsao, Factorial design and covariance in the study of individual educational development. Psychometrika 10, 133–162 (1945)
D.C. Montgomery, Design and Analysis of Experiments, 5th edn. (Wiley, New York, 2001)
J. Neter, M.H. Kutner, C.J. Nachtsheim, W. Wasserman, Applied Linear Statistical Models, 4th edn. (Irwin, Homewood, 1996)
S.C. Pearce, The Agricultural Field Experiment (Wiley, New York, 1983)
R.G. Peterson, Design and Analysis of Experiments (Marcel Dekker, New York/Basel, 1985)
J.W. Tukey, One degree of freedom for nonadditivity. Biometrics 5(3), 232–242 (1949)
A.F. Williams, Teenage passengers in motor vehicle crashes: a summary of current research. Technical report (Insurance Institute for Highway Safety, Arlington, 2001)
F. Yates, The Design and Analysis of Factorial Experiments (Imperial Bureau of Soil Science, Harpenden, 1937)
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Heiberger, R.M., Holland, B. (2015). Design of Experiments—Complex Designs. In: Statistical Analysis and Data Display. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2122-5_14
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DOI: https://doi.org/10.1007/978-1-4939-2122-5_14
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