
The Design of Experiments
Statistical Principles for Practical Applications
By: R. Mead
Paperback | 24 September 1990
At a Glance
636 Pages
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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. |
ISBN: 9780521287623
ISBN-10: 0521287626
Published: 24th September 1990
Format: Paperback
Language: English
Number of Pages: 636
Audience: Professional and Scholarly
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.9 x 15.4 x 3.8
Weight (kg): 0.9
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