Design of Comparative Experiments
This book should be on the shelf of every practising statistician who designs experiments. Good design considers units and treatments first, and then allocates treatments to units. It does not choose from a menu of named designs. This approach requires a notation for units that does not depend on the treatments applied. Most structure on the set of observational units, or on the set of treatments, can be defined by factors. This book develops a coherent framework for thinking about factors and their relationships, including the use of Hasse diagrams. These are used to elucidate structure, calculate degrees of freedom and allocate treatment subspaces to appropriate strata. Based on a one-term course the author has taught since 1989, the book is ideal for advanced undergraduate and beginning graduate courses. Examples, exercises and discussion questions are drawn from a wide range of real applications: from drug development, to agriculture, to manufacturing.
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Simple treatment structure
Factorial treatment structure
Experiments on people and animals
Small units inside large units
More about Latin squares
The calculus of factors
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allocated analysis of variance analysis-of-variance table applied balanced incomplete-block design block design calculate calves Chapter characters completely randomized design Construct control treatment Cov(Y cultivar Deﬁnition degrees of freedom Detergent dose Draw the Hasse drug efﬁciency eigenvalue equal estimate expectation models experiment experimental units F and G factors F ﬁeld ﬁnd ﬁrst ﬁt ﬁve ﬁxed four freedom mean mean fungicide gives Graeco-Latin square Hasse diagram large block Latin square levels of F main effect mean square ment method MS(residual nitrogen nonzero observational units patients pens plot factor plot structure random permutation random-effects model replication revisited row–column design satisﬁes Section shown in Figure shows skeleton analysis spray standard error statistician Stratum Source Degrees stratum variance sum of squares Theorem treatment factors treatment structure treatment subspace trial variance in Table vector zero τττ
Page 326 - A method for constructing valid restricted randomization schemes using the theory of .D-optimal design of experiments.
Page 326 - JA, Pye BJ (1994) Development of field strategies incorporating semiochemicals for the control of the pea and bean weevil, Sitona lineatus L. Crop Protection 13: 127135 Symmons P (1992) Strategies to combat the desert locust.
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Page 324 - A comparison of ANOVA tests and alternative analyses, Journal of Agricultural, Biological and Environmental Statistics, 5, (2000), pp.