## Design of Comparative ExperimentsThis 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 |

The calculus of factors | 169 |

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### Common terms and phrases

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

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