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The Design of Experiments : Statistical Principles for Practical Applications - R. Mead

The Design of Experiments

Statistical Principles for Practical Applications

By: R. Mead

Paperback

Published: 24th September 1990
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Describes the statistical principles of good experimental design, explaining that good design of experiments is crucial to the success of research. Emphasizing the logical principles of statistical design, Professor Mead employs a minimum of mathematics. Throughout he assumes that the large-scale analysis of data will be performed by computers and he thus devotes more attention to discussions of how all of the available information can be used to extract the clearest answers to many questions. The principles are illustrated with a wide range of examples drawn from medicine, agriculture, industry, and other disciplines. Numerous exercises are given to help the reader practice techniques and to appreciate the difference that good design of experiments can make to a scientific project.

"Simply superlative...concepts and principles are presented with clarity, balance, and thoroughness." Ecology "A systematic and comprehensive coverage of statistical principles as applied to the design of scientific experiments...The book is well-written and contains very useful information that is relevant to a variety of scientific disciplines." Choice

Preface
Overture
Introductionp. 3
Why a statistical theory of design?p. 3
History, computers and mathematicsp. 4
The influence of analysis on designp. 5
Separate consideration of units and treatmentsp. 7
Elementary ideas of blocking: the randomised block designp. 9
Controlling variation in experimental unitsp. 9
The analysis of variance identityp. 12
Estimation of variance and the comparison of treatment meansp. 19
Residuals and the meaning of errorp. 23
The random allocation of treatment to unitsp. 24
Practical choices of blocking patternsp. 27
Elementary ideas of treatment structurep. 31
Choice of treatmentsp. 31
Factorial structurep. 32
Models for main effects and interactionsp. 33
The analysis of variance identityp. 36
Interpretation of main effects and interactionsp. 40
Advantages of factorial structuresp. 42
General principles of linear models for the analysis of experimental datap. 45
Introduction and some examplesp. 45
The principle of least squares and least squares estimatorsp. 46
Properties of least squares estimatorsp. 48
Overparameterisation, constraints and practical solution of least squares equationsp. 52
Subdividing the parameters and the extra sum of squaresp. 58
Distributional assumptions and inferencesp. 64
Contrasts, treatment comparisons and component sums of squaresp. 66
Appendix to Chapter 4p. 72
Least squares estimators for linear modelsp. 72
Properties of least squares estimatorsp. 72
Overparameterisation and constraintsp. 75
Partitioning the parameter vector and the extra SS principlep. 78
Distributional assumptions and inferencesp. 80
Treatment comparisons and component sums of squaresp. 85
Computers for analysing experimental datap. 88
Introductionp. 88
How general, how friendlyp. 90
Requirements of packages for the analysis of experimental datap. 96
The factor philosophy of analysis programsp. 98
The regression model for analysis programsp. 101
Implications for designp. 102
First Subject
Replicationp. 107
Preliminary examplep. 107
The need for replicationp. 108
The completely randomised designp. 109
Different levels of variationp. 112
Identifying and allowing for different levels of variationp. 117
Sampling and components of variationp. 122
How much replication?p. 124
Exercises 6p. 129
Blockingp. 130
Preliminary examplesp. 130
Design and analysis for very simple blocked experimentsp. 130
Design principles in blocked experimentsp. 134
The analysis of block--treatment designsp. 142
Balanced incomplete block designs and classes of less balanced desp. 150
Orthogonality, balance and the practical choice of designp. 154
The analysis of within block and inter-block informationp. 163
Exercises 7p. 172
Multiple blocking systems and cross-over designsp. 176
Preliminary examplesp. 176
Latin square designs and Latin rectanglesp. 177
Multiple orthogonal classifications and sequences of experimentsp. 181
Non-orthogonal row and column designp. 183
The practical choice of row and column designp. 192
Cross-over designs--time as a blocking factorp. 197
Cross-over designs for residual or interaction effectsp. 201
Exercises 8p. 208
Randomisationp. 214
What is the population?p. 214
Random treatment allocationp. 216
Randomisation testsp. 218
Randomisation theory of the analysis of experimental datap. 224
Practical implications of the two theories for the analysis of experimental datap. 229
Practical randomisationp. 231
Sequential allocation of treatments in clinical trialsp. 237
Exercises 9p. 242
Covariance--extension of linear modelsp. 245
Preliminary examplesp. 245
The use of additional informationp. 245
The general theory of covariance analysisp. 249
Covariance analysis for a randomised block designp. 251
Examples of the use of covariance analysisp. 254
Assumptions and implications of covariance analysisp. 261
Blocking or covariancep. 263
Spatial covariance and nearest neighbour analysisp. 266
Exercises 10p. 270
Model assumptions and more general modelsp. 274
Preliminary examplesp. 274
The model assumed for general linear model analysisp. 275
Examining residuals and testing assumptionsp. 277
Transformationsp. 283
More general statistical models for analysis of experimental datap. 286
Missing values and outliersp. 291
The separation of quantitative and qualitative informationp. 297
Exercises 11p. 301
Second Subject
Experimental objectives, treatments and treatment structuresp. 307
Preliminary examplesp. 307
Different categories of treatmentp. 308
Comparisons between treatmentsp. 309
Presentation of resultsp. 315
Qualitative or quantitative factorsp. 316
Treatment structuresp. 326
Incomplete structures and varying replicationp. 331
Treatments as a samplep. 336
Screening and selection experimentsp. 338
Exercises 12p. 340
Factorial structure and particular forms of effectsp. 345
Preliminary examplep. 345
Factors with two levels onlyp. 345
Improved yield comparisons in terms of effectsp. 352
Analysis by considering sums and differencesp. 357
Factors with three or more levelsp. 361
The use of only a single replicatep. 366
The use of a fraction of a complete factorial experimentp. 370
Exercises 13p. 378
Split unit designs and repeated measurementsp. 382
Preliminary examplesp. 382
The practical need for split unitsp. 384
Advantages and disadvantages of split unit designsp. 389
Extensions of the split unit ideap. 393
Identification of multiple strata designsp. 402
Time as a split unit factor and repeated measurementsp. 407
Systematic treatment variation within main unitsp. 414
Exercises 14p. 417
Incomplete block size for factorial experimentsp. 422
Preliminary examplesp. 422
Small blocks and many factorial combinationsp. 432
Factors with a common number of levelsp. 439
Incompletely confounded effectsp. 442
Partial confoundingp. 455
The split unit design as an example of confoundingp. 459
Confounding for general block size and factor levelsp. 468
Some mathematical theory for confounding and fractional replicationp. 470
Preliminary examplesp. 470
The negative approach to confoundingp. 471
Confounding theory for 2" factorial structuresp. 473
Confounding theory for other factorial structure; dummy factorsp. 479
Confounding for 3"p. 485
Fractional replicationp. 491
Confounding in fractional replicatesp. 496
Confounding in row and column designsp. 502
Exercises 16p. 509
Quantitative factors and response functionsp. 514
Preliminary examplesp. 514
The use of response functions in the analysis of datap. 515
Design objectivesp. 517
Specific parameter estimationp. 521
Optimal design theoryp. 526
Discriminationp. 528
Designs for competing criteriap. 530
Systematic designsp. 533
Exercises 17p. 536
Response surface explorationp. 538
Preliminary examplesp. 538
General estimation objectivesp. 538
Some response surface designs based on factorial treatment structuresp. 542
Prediction, rotatability and testing fitp. 549
Blocking and orthogonalityp. 551
Sequential experimentationp. 554
Analysis of response surface experimental datap. 558
Experiments with mixturesp. 567
Exercises 18p. 572
Coda
Designing useful experimentsp. 577
Some more real problemsp. 577
Design principles or practical designp. 579
Resources and experimental unitsp. 580
Treatments and detailed objectivesp. 583
The resource equationp. 587
The marriage of resources and treatmentsp. 588
Three particular problemsp. 595
The relevance of experimental resultsp. 603
Block [times] treatment and experiment [times] treatment interactionsp. 605
Exercisesp. 609
Referencesp. 615
Indexp. 618
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521287623
ISBN-10: 0521287626
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 636
Published: 24th September 1990
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 22.86 x 15.88  x 3.18
Weight (kg): 0.91