Statistical Analysis of Designed Experiments: Theory and Applications

708 Pages·2009·11.64 MB·English

by  Ajit C. Tamhane(auth.)

Statistical Analysis of
Designed Experiments
WILEY SERIES IN PROBABILITY AND STATISTICS
Established by WALTER A. SHEWHART and SAMUEL S. WILKS
Editors: David J. Balding, Noel A. C. Cressie, Garrett M. Fitzmaurice,
Iain M. Johnstone, Geert Molenberghs, David W. Scott,
Adrian F. M. Smith, Ruey S. Tsay, Sanford Weisberg
Editors Emeriti: Vic Barnett, J, Stuart Hunter, JozefL. Teugels
A complete list of the titles in this series appears at the end of this volume.
Statistical Analysis of
Designed Experiments
Theory and Applications
AJIT C. TAMHANE
Northwestern University
WILEY
A JOHN WILEY & SONS, INC., PUBLICATION
Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey.
Published simultaneously in Canada
No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any
form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise,
except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without
either the prior written permission of the Publisher, or authorization through payment of the
appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers,
MA 01923, 978-750-8400, fax [phone], or on the web at www.copyright.com. Requests to
the Publisher for permission should be addressed to the Permissions Department, John Wiley &
Sons, Inc., Ill River Street, Hoboken, NJ 07030, 201-748-6011, fax [phone], or online at
http://www.wiley.com/go/permission.
Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best
efforts in preparing this book, they make no representations or warranties with respect to the
accuracy or completeness of the contents of this book and specifically disclaim any implied
warranties of merchantability or fitness for a particular purpose. No warranty may be created or
extended by sales representatives or written sales materials. The advice and strategies contained
herein may not be suitable for your situation. You should consult with a professional where
appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other
commercial damages, including but not limited to special, incidental, consequential, or other
damages.
For general information on our other products and services or for technical support, please contact
our Customer Care Department within the United States at 877-762-2974, outside the United States
at 317-572-3993 or fax [phone].
Wiley also publishes its books in a variety of electronic formats. Some content that appears in print
may not be available in electronic formats. For more information about Wiley products, visit our
web site at www.wiley.com.
Library of Congress Cataloging-in-Publication Data:
Tamhane, Ajit C.
Statistical analysis of designed experiments : theory and applications /
Ajit C. Tamhane.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-471-75043-7 (cloth)
1. Experimental design. I. Title.
QA279.T36 2008
519.5'7—dc22
2008009432
Printed in the United States of America
109876543 2 1
To All My Teachers —
From Grade School to Grad School
Contents
Preface
Abbreviations
1 Introduction
1.1 Observational Studies and Experiments / 1
1.2 Brief Historical Remarks / 4
1.3 Basic Terminology and Concepts of Experimentation / 5
1.4 Basic Principles of Experimentation / 9
1.4.1 How to Minimize Biases and Variability? / 9
1.4.2 Sequential Experimentation / 14
1.5 Chapter Summary / 15
Exercises / 16
2 Review of Elementary Statistics
2.1 Experiments for a Single Treatment / 20
2.1.1 Summary Statistics and Graphical Plots / 21
2.1.2 Confidence Intervals and Hypothesis Tests / 25
2.1.3 Power and Sample Size Calculation / 27
2.2 Experiments for Comparing Two Treatments / 28
2.2.1 Independent Samples Design / 29
2.2.2 Matched Pairs Design / 38
2.3 Linear Regression / 41
2.3.1 Simple Linear Regression / 42
2.3.2 Multiple Linear Regression / 50
2.4 Chapter Summary / 62
Exercises / 62
viii CONTENTS
3 Single Factor Experiments: Completely Randomized Designs 70
3.1 Summary Statistics and Graphical Displays / 71
3.2 Model / 73
3.3 Statistical Analysis / 75
3.3.1 Estimation / 75
3.3.2 Analysis of Variance / 76
3.3.3 Confidence Intervals and Hypothesis Tests / 78
3.4 Model Diagnostics / 79
3.4.1 Checking Homoscedasticity / 80
3.4.2 Checking Normality / 81
3.4.3 Checking Independence / 81
3.4.4 Checking Outliers / 81
3.5 Data Transformations / 85
3.6 Power of F-Test and Sample Size Determination / 87
3.7 Quantitative Treatment Factors / 90
3.8 One-Way Analysis of Covariance / 96
3.8.1 Randomized Block Design versus Analysis of
Covariance / 96
3.8.2 Model / 96
3.8.3 Statistical Analysis / 98
3.9 Chapter Notes / 106
3.9.1 Randomization Distribution of F-Statistic / 106
3.9.2 F-Test for Heteroscedastic Treatment
Variances / 108
3.9.3 Derivations of Formulas for Orthogonal
Polynomials / 110
3.9.4 Derivation of LS Estimators for One-Way Analysis
of Covariance / 112
3.10 Chapter Summary / 113
Exercises / 114
4 Single-Factor Experiments: Multiple Comparison and Selection
Procedures 126
4.1 Basic Concepts of Multiple Comparisons / 127
4.1.1 Family / 127
4.1.2 Family wise Error Rate / 128
4.1.3 Bonferroni Method / 129
4.1.4 Union-Intersection Method / 130
4.1.5 Closure Method / 131
CONTENTS ix
4.2 Pairwise Comparisons / 132
4.2.1 Least Significant Difference and Bonferroni
Procedures / 133
4.2.2 Tukey Procedure for Pairwise Comparisons / 134
4.2.3 Step-Down Procedures for Pairwise Comparisons / 136
4.3 Comparisons with a Control / 139
4.3.1 Dunnett Procedure for Comparisons with a
Control / 139
4.3.2 Step-Down Procedures for Comparisons with a
Control / 142
4.4 General Contrasts / 144
4.4.1 Tukey Procedure for Orthogonal Contrasts / 145
4.4.2 Scheffe Procedure for All Contrasts / 146
4.5 Ranking and Selection Procedures / 148
4.5.1 Indifference-Zone Formulation / 148
4.5.2 Subset Selection Formulation / 154
4.5.3 Multiple Comparisons with the Best / 155
4.5.4 Connection between Multiple Comparisons with
Best and Selection of Best Treatment / 157
4.6 Chapter Summary / 158
Exercises / 159
5 Randomized Block Designs and Extensions 168
5.1 Randomized Block Designs / 169
5.1.1 Model / 169
5.1.2 Statistical Analysis / 171
5.1.3 Randomized Block Designs with Replicates / 177
5.2 Balanced Incomplete Block Designs / 180
5.2.1 Statistical Analysis / 182
5.2.2 Interblock Analysis / 185
5.3 Youden Square Designs / 188
5.3.1 Statistical Analysis / 189
5.4 Latin Square Designs / 192
5.4.1 Choosing a Latin Square / 192
5.4.2 Model / 195
5.4.3 Statistical Analysis / 195
5.4.4 Crossover Designs / 198
5.4.5 Graeco-Latin Square Designs / 202
5.5 Chapter Notes / 205
X CONTENTS
5.5.1 Restriction Error Model for Randomized Block
Designs / 205
5.5.2 Derivations of Formulas for BIB Design / 206
5.6 Chapter Summary / 211
Exercises / 212
General Factorial Experiments 224
6.1 Factorial versus One-Factor-at-a-Time Experiments / 225
6.2 Balanced Two-Way Layouts / 227
6.2.1 Summary Statistics and Graphical Plots / 227
6.2.2 Model / 230
6.2.3 Statistical Analysis / 231
6.2.4 Model Diagnostics / 235
6.2.5 Tukey's Test for Interaction for Singly Replicated
Two-Way Layouts / 236
6.3 Unbalanced Two-Way Layouts / 240
6.3.1 Statistical Analysis / 240
6.4 Chapter Notes / 245
6.4.1 Derivation of LS Estimators of Parameters for
Balanced Two-Way Layouts / 245
6.4.2 Derivation of ANOVA Sums of Squares and
/''-Tests for Balanced Two-Way Layouts / 246
6.4.3 Three- and Higher Way Layouts / 248
6.5 Chapter Summary / 250
Exercises / 250
Two-Level Factorial Experiments 256
7.1 Estimation of Main Effects and Interactions / 257
7.1.1 22 Designs / 257
7.1.2 23 Designs / 261
7.1.3 2p Designs / 266
7.2 Statistical Analysis / 267
7.2.1 Confidence Intervals and Hypothesis Tests / 267
7.2.2 Analysis of Variance / 268
7.2.3 Model Fitting and Diagnostics / 270
7.3 Single-Replicate Case / 272
7.3.1 Normal and Half-Normal Plots of Estimated
Effects / 272
7.3.2 Lenth Method / 278
CONTENTS xi
7.3.3 Augmenting a 2P Design with Observations at the
Center Point / 279
7.4 2P Factorial Designs in Incomplete Blocks: Confounding of
Effects / 282
7.4.1 Construction of Designs / 282
7.4.2 Statistical Analysis / 286
7.5 Chapter Notes / 287
7.5.1 Yates Algorithm / 287
7.5.2 Partial Confounding / 288
7.6 Chapter Summary / 289
Exercises / 290
Two-Level Fractional Factorial Experiments 300
8.1 2p-q Fractional Factorial Designs / 301
8.1.1 2p~l Fractional Factorial Design / 301
8.1.2 General 2p~q Fractional Factorial Designs / 307
8.1.3 Statistical Analysis / 312
8.1.4 Minimum Aberration Designs / 316
8.2 Plackett-Burman Designs / 317
8.3 Hadamard Designs / 323
8.4 Supersaturated Designs / 325
8.4.1 Construction of Supersaturated Designs / 325
8.4.2 Statistical Analysis / 327
8.5 Orthogonal Arrays / 329
8.6 Sequential Assemblies of Fractional Factorials / 333
8.6.1 Foldover of Resolution III Designs / 334
8.6.2 Foldover of Resolution IV Designs / 337
8.7 Chapter Summary / 338
Exercises / 339
Three-Level and Mixed-Level Factorial Experiments 351
9.1 Three-Level Full Factorial Designs / 351
9.1.1 Linear-Quadratic System / 353
9.1.2 Orthogonal Component System / 361
9.2 Three-Level Fractional Factorial Designs / 364
9.3 Mixed-Level Factorial Designs / 372
9.3.1 2p\q Designs / 373
9.3.2 2ρ7><> Designs / 378
9.4 Chapter Notes / 386