# Design of Comparative Experiments

Cambridge University Press, Apr 17, 2008 - Mathematics
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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### Contents

 Unstructured experiments 19 Simple treatment structure 43 Blocking 53 Factorial treatment structure 75 Rowcolumn designs 105 Experiments on people and animals 117 Small units inside large units 131 More about Latin squares 157
 Incompleteblock designs 219 Factorial designs in incomplete blocks 241 Fractional factorial designs 259 Backward look 271 Exercises 291 Sources of examples questions and exercises 313 Index 327 Copyright

 The calculus of factors 169

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