| Preface | |
| Overture | |
| Introduction | p. 3 |
| Why a statistical theory of design? | p. 3 |
| History, computers and mathematics | p. 4 |
| The influence of analysis on design | p. 5 |
| Separate consideration of units and treatments | p. 7 |
| Elementary ideas of blocking: the randomised block design | p. 9 |
| Controlling variation in experimental units | p. 9 |
| The analysis of variance identity | p. 12 |
| Estimation of variance and the comparison of treatment means | p. 19 |
| Residuals and the meaning of error | p. 23 |
| The random allocation of treatment to units | p. 24 |
| Practical choices of blocking patterns | p. 27 |
| Elementary ideas of treatment structure | p. 31 |
| Choice of treatments | p. 31 |
| Factorial structure | p. 32 |
| Models for main effects and interactions | p. 33 |
| The analysis of variance identity | p. 36 |
| Interpretation of main effects and interactions | p. 40 |
| Advantages of factorial structures | p. 42 |
| General principles of linear models for the analysis of experimental data | p. 45 |
| Introduction and some examples | p. 45 |
| The principle of least squares and least squares estimators | p. 46 |
| Properties of least squares estimators | p. 48 |
| Overparameterisation, constraints and practical solution of least squares equations | p. 52 |
| Subdividing the parameters and the extra sum of squares | p. 58 |
| Distributional assumptions and inferences | p. 64 |
| Contrasts, treatment comparisons and component sums of squares | p. 66 |
| Appendix to Chapter 4 | p. 72 |
| Least squares estimators for linear models | p. 72 |
| Properties of least squares estimators | p. 72 |
| Overparameterisation and constraints | p. 75 |
| Partitioning the parameter vector and the extra SS principle | p. 78 |
| Distributional assumptions and inferences | p. 80 |
| Treatment comparisons and component sums of squares | p. 85 |
| Computers for analysing experimental data | p. 88 |
| Introduction | p. 88 |
| How general, how friendly | p. 90 |
| Requirements of packages for the analysis of experimental data | p. 96 |
| The factor philosophy of analysis programs | p. 98 |
| The regression model for analysis programs | p. 101 |
| Implications for design | p. 102 |
| First Subject | |
| Replication | p. 107 |
| Preliminary example | p. 107 |
| The need for replication | p. 108 |
| The completely randomised design | p. 109 |
| Different levels of variation | p. 112 |
| Identifying and allowing for different levels of variation | p. 117 |
| Sampling and components of variation | p. 122 |
| How much replication? | p. 124 |
| Exercises 6 | p. 129 |
| Blocking | p. 130 |
| Preliminary examples | p. 130 |
| Design and analysis for very simple blocked experiments | p. 130 |
| Design principles in blocked experiments | p. 134 |
| The analysis of block--treatment designs | p. 142 |
| Balanced incomplete block designs and classes of less balanced des | p. 150 |
| Orthogonality, balance and the practical choice of design | p. 154 |
| The analysis of within block and inter-block information | p. 163 |
| Exercises 7 | p. 172 |
| Multiple blocking systems and cross-over designs | p. 176 |
| Preliminary examples | p. 176 |
| Latin square designs and Latin rectangles | p. 177 |
| Multiple orthogonal classifications and sequences of experiments | p. 181 |
| Non-orthogonal row and column design | p. 183 |
| The practical choice of row and column design | p. 192 |
| Cross-over designs--time as a blocking factor | p. 197 |
| Cross-over designs for residual or interaction effects | p. 201 |
| Exercises 8 | p. 208 |
| Randomisation | p. 214 |
| What is the population? | p. 214 |
| Random treatment allocation | p. 216 |
| Randomisation tests | p. 218 |
| Randomisation theory of the analysis of experimental data | p. 224 |
| Practical implications of the two theories for the analysis of experimental data | p. 229 |
| Practical randomisation | p. 231 |
| Sequential allocation of treatments in clinical trials | p. 237 |
| Exercises 9 | p. 242 |
| Covariance--extension of linear models | p. 245 |
| Preliminary examples | p. 245 |
| The use of additional information | p. 245 |
| The general theory of covariance analysis | p. 249 |
| Covariance analysis for a randomised block design | p. 251 |
| Examples of the use of covariance analysis | p. 254 |
| Assumptions and implications of covariance analysis | p. 261 |
| Blocking or covariance | p. 263 |
| Spatial covariance and nearest neighbour analysis | p. 266 |
| Exercises 10 | p. 270 |
| Model assumptions and more general models | p. 274 |
| Preliminary examples | p. 274 |
| The model assumed for general linear model analysis | p. 275 |
| Examining residuals and testing assumptions | p. 277 |
| Transformations | p. 283 |
| More general statistical models for analysis of experimental data | p. 286 |
| Missing values and outliers | p. 291 |
| The separation of quantitative and qualitative information | p. 297 |
| Exercises 11 | p. 301 |
| Second Subject | |
| Experimental objectives, treatments and treatment structures | p. 307 |
| Preliminary examples | p. 307 |
| Different categories of treatment | p. 308 |
| Comparisons between treatments | p. 309 |
| Presentation of results | p. 315 |
| Qualitative or quantitative factors | p. 316 |
| Treatment structures | p. 326 |
| Incomplete structures and varying replication | p. 331 |
| Treatments as a sample | p. 336 |
| Screening and selection experiments | p. 338 |
| Exercises 12 | p. 340 |
| Factorial structure and particular forms of effects | p. 345 |
| Preliminary example | p. 345 |
| Factors with two levels only | p. 345 |
| Improved yield comparisons in terms of effects | p. 352 |
| Analysis by considering sums and differences | p. 357 |
| Factors with three or more levels | p. 361 |
| The use of only a single replicate | p. 366 |
| The use of a fraction of a complete factorial experiment | p. 370 |
| Exercises 13 | p. 378 |
| Split unit designs and repeated measurements | p. 382 |
| Preliminary examples | p. 382 |
| The practical need for split units | p. 384 |
| Advantages and disadvantages of split unit designs | p. 389 |
| Extensions of the split unit idea | p. 393 |
| Identification of multiple strata designs | p. 402 |
| Time as a split unit factor and repeated measurements | p. 407 |
| Systematic treatment variation within main units | p. 414 |
| Exercises 14 | p. 417 |
| Incomplete block size for factorial experiments | p. 422 |
| Preliminary examples | p. 422 |
| Small blocks and many factorial combinations | p. 432 |
| Factors with a common number of levels | p. 439 |
| Incompletely confounded effects | p. 442 |
| Partial confounding | p. 455 |
| The split unit design as an example of confounding | p. 459 |
| Confounding for general block size and factor levels | p. 468 |
| Some mathematical theory for confounding and fractional replication | p. 470 |
| Preliminary examples | p. 470 |
| The negative approach to confounding | p. 471 |
| Confounding theory for 2" factorial structures | p. 473 |
| Confounding theory for other factorial structure; dummy factors | p. 479 |
| Confounding for 3" | p. 485 |
| Fractional replication | p. 491 |
| Confounding in fractional replicates | p. 496 |
| Confounding in row and column designs | p. 502 |
| Exercises 16 | p. 509 |
| Quantitative factors and response functions | p. 514 |
| Preliminary examples | p. 514 |
| The use of response functions in the analysis of data | p. 515 |
| Design objectives | p. 517 |
| Specific parameter estimation | p. 521 |
| Optimal design theory | p. 526 |
| Discrimination | p. 528 |
| Designs for competing criteria | p. 530 |
| Systematic designs | p. 533 |
| Exercises 17 | p. 536 |
| Response surface exploration | p. 538 |
| Preliminary examples | p. 538 |
| General estimation objectives | p. 538 |
| Some response surface designs based on factorial treatment structures | p. 542 |
| Prediction, rotatability and testing fit | p. 549 |
| Blocking and orthogonality | p. 551 |
| Sequential experimentation | p. 554 |
| Analysis of response surface experimental data | p. 558 |
| Experiments with mixtures | p. 567 |
| Exercises 18 | p. 572 |
| Coda | |
| Designing useful experiments | p. 577 |
| Some more real problems | p. 577 |
| Design principles or practical design | p. 579 |
| Resources and experimental units | p. 580 |
| Treatments and detailed objectives | p. 583 |
| The resource equation | p. 587 |
| The marriage of resources and treatments | p. 588 |
| Three particular problems | p. 595 |
| The relevance of experimental results | p. 603 |
| Block [times] treatment and experiment [times] treatment interactions | p. 605 |
| Exercises | p. 609 |
| References | p. 615 |
| Index | p. 618 |
| Table of Contents provided by Syndetics. All Rights Reserved. |
