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Statistics for experimenters: an introduction to design, data analysis, and model building

Author: Box, George E. P. ; Hunter, William Gordon ; Hunter, J. Stuart Series: Wiley series in probability and mathematical statistics Publisher: Wiley, 1978.Language: EnglishDescription: xviii, 653 p. ; 24 cm.ISBN: 0471093157Type of document: BookNote: Includes bibliographies and index
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Item type Current location Collection Call number Status Date due Barcode Item holds
Book Asia Campus
Textbook Collection (PhD)
Print QA279 .B68 1978
(Browse shelf)
900243117
Available 900243117
Book Europe Campus
Main Collection
Print QA279 .B68
(Browse shelf)
000147383
Available 000147383
Total holds: 0

Includes bibliographies and index

Contents
I STATISTICS 1
1.1 The Learning Process 1.3 Difficulties Mitigated by Statistical Methods 7
A Typical Investigation COMPARING TWO TREATMENTS
2 USE OF EXTERNAL REFERENCE DISTRIBUTION TO COMPARE TWO
MEANS 21
2.1 Theory: Probability Distributions, Parameters, Statistics
24
The Industrial Experiment: External Reference Distribution
31
Theory: Normal Experiment : An Distribution
Based on the t Distribution 51
the Sample Average, Sample
Variance, and Sample Standard Deviation by
Coding Data 53
3 RANDOM SAMPLING AND THE DECLARATION OF INDEPENDENCE 57
3.1 Theory: Statistical Dependence and Independence and the
57
xi
Contents
1 SCIENCE AND STATISTICS I
1
1.2 The Role of Experimental Design 4
1.4 A Typical Investigation 9
1.5 How to Use Statistical Techniques 14
PART I COMPARINGT WOT REATMENTS
USE OF EXTERNALR EFERENCED ISTRIBUTION TOC OMPARTE WO
21
Relevant Reference Sets and Distributions 21
2.2 Theory: Probability Distributions, Parameters, and Statis
tics 24
2.3 The Industrial Experiment: External Reference Distribu
tion 31
2.4 Theory: Normal and t Distributions 38
2.5 The Industrial Experiment: An External Reference Distri
bution / Distribution 51
Appendix 2A Calculation of the Sample Average, Sample
and RANDOMSA MPLINGA NDT HED ECLARATIONO FI NDEPENDENCE 57
Theory: Statistical Dependence and Independence Random Sampling Model xi
xii CONTENTS
3.2 The Industrial Experiment: Reference Distribution Based
on Random Sampling Model, External Value for a 74
3.3 The Industrial Experiment: Reference Distribution Based
on Random Sampling Model, Internal Estimate of a 76
3.4 Summary: What Have We Learned from the Industrial
Experiment Example? 82
Appendix 3A Mean and Variance of a Linear Combination of
Observations 87
Appendix 3B Robustness of Some Statistical Procedures 89
Appendix 3C Fisher's Concept of Sufficiency 91
4 RANDOMIZATION AND BLOCKING WITH PAIRED COMPARISONS 93
4.1 Randomization to the Rescue: Tomato Plant Example 93
4.2 Randomized Paired Comparison Design : Boys' Shoes
Example 97
4.3 Blocking and Randomization 102
4.4 Noise Structure, Models, and Randomization 104
4.5 Summary:Comparison, Replication, Randomization, and
Blocking in Simple Comparative Experiments 105
5 SIGNIFICANCE TESTS AND CONFIDENCE INTERVALS FOR MEANS,
VARIANCES, PROPORTIONS, AND FREQUENCIES 107
5.1 A More Detailed Discussion of Significance Tests 107
5.2 Confidence Intervals for a Difference in Means: Paired
Comparison Design 110
5.3 Confidence Intervals for a Difference in Means: Unpaired
Design 115
5.4 Inferences about Variances of Normally Distributed Data 117
5.5 Inferences about Proportions: The Binomial Distribution
123
5.6 Inferences about Frequencies: The Poisson Distribution
137
5.7 Contingency Tables and Tests of Association 145
PROBLEMS FOR PART I 152
CONTENTS XIII
PART II COMPARING MORE THAN TWO
TREATMENTS
6 EXPERIMENTS TO COMPARE k TREATMENT MEANS 165
6.1 Blood Coagulation Times with Four Different Diets 165
6.2 Estimating the Amount of Variation Within and Between
Treatments 167
6.3 The Arithmetic and Geometry of the Analysis of Variance
Table 170
6.4 Decomposition of the Observations Implied by the Analysis 175
6.5 Diagnostic Checking of the Basic Model 182
6.6 Use of the Analysis of Variance Table 187
6.7 Use of a Reference Distribution to Compare Means 190
6.8 Summary 193
Appendix 6A Shortcut Method for Constructing the Analysis
of Variance Table 194
Appendix 6B Vectors and Geometry Associated with the
Analysis of a Sample 197
Appendix 6C Multiple Comparisons 203
7 RANDOMIZED BLOCKS AND TWO-WAY FACTORIAL DESIGNS 208
7.1 Example: Comparison of Four Variants of a Penicillin
Production Process 209
7.2 A Model with Corresponding Decomposition of Observations
210
7.3 Implications of the Additive Model 218
7.4 Diagnostic Checking of the Model 220
7.5 Use of the Analysis of Variance Table 223
7.6 The Use of Reference Distributions To Compare Individual
Means 226
7.7 A Two-Way (Factorial) Design 228
7.8 Simplification and Increased Sensitivity from Transformation
231
7.9 Likelihood Estimation of the Transformation 239
7.10 Summary 241
Appendix 7A Calculations for Constructing Analysis of Variance
Table for Randomized Block Design 241
CONTENTS
Appendix 7B Algebraic Demonstration of the Additivity of the
Sums of Squares in a Randomized Block
8 DESIGNS WITH MORE THAN ONE BLOCKING VARIABLE
8.1 Latin Square Designs: Automobile Emissions and Synthetic
Yarn Examples
8.2 Graeco- and Hyper-Graeco-Latin Squares: First Wear
Testing Example
8.3 Balanced Incomplete Block Designs: Second Wear Testing
Example
Appendix 8A Some Useful Latin Squares and How to Use
Them to Construct Graeco-Latin and Hyper-
Graeco-Latin Square Design
Appendix 8B Analysis of Variance for k x k Latin Square
Designs with r Replicates
Appendix 8C Some Useful Balanced Incomplete Block Designs
Appendix 8D Analysis of Variance and Computation of
Adjusted Treatment Averages for Balanced
Incomplete Block Designs
PROBLEMS FOR PART 11
PART III MEASURING THE EFFECTS OF VARIABLES
9 EMPIRICAL MODELING
9.1 Mathematical Models
9.2 Geometric Representation of-Empirical Relationships
9.3 The Problem of Experimental Design
9.4 Comprehensive Versus Sequential Approach WI Experimental
Investigations
10 FACTORIAL DESIGNS AT TWO LEVELS
10.1 General Factorial Designs and Designs at Two Levels
10.2 An Example of a 23 Factorial Design : Pilot Plant Investigation
243
245
245
255
258
261
263
269
275
281
291
296
298
303
306
306
307
xiv
II
9.3 The Problem of Experimental to, Experimental
Design: 291
CONTENTS XV
10.3 Calculation of Main Effects 309
10.4 Interaction Effects 313
10.5 Interpretation of Results 317
10.6 Calculation of Standard Errors for Effects Using Replicated
Runs 319
10.7 Quicker Methods for Calculating Effects 322
10.8 A 24 Factorial Design : Process Development Study 324
10.9 Analysis of Factorials Using Normal Probability Paper 329
10.10 Transformation of Data from Factorial Designs 334
10.11 Blocking 336
10.12 Summary 342
Appendix 10A Yates's Algorithm 342
Appendix 10B More on Blocking Factorial Designs 344
11 MORE APPLICATIONS OF FACTORIAL DESIGNS 352
11.1 Example 1: The Effects of Three Variables on Clarity of
Film
11.2 Example 2: The Effects of Three Variables on Physical
Properties of a Polymer Solution
11.3 Example 3: Development of Screening Facility for Storm
Water Overflows
11.4 Example 4: Simple Factorials Used Sequentially in Evolutionary
Operation—Petrochemical Plant
11.5 Example 5: Simple Factorials Used Sequentially in
Evolutionary Operation—Polymer Unit
11.6 Summary
Appendix 11A A Suggested Exercise
352
353
354
362
365
368
368
12 FRACTIONAL FACTORIAL DESIGNS AT TWO LEVELS 374
12.1 Redundancy 374
12.2 A Half-Fraction of a 25 Design: Reactor Example 376
12.3 Construction and Analysis of Half-Fractions: Reactor
Example 381
12.4 The Concept of Design Resolution : Reactor Example 385
12.5 Resolution III Designs: Bicycle Example 390
12.6 Resolution IV Designs: Injection Molding Example 398
12.7 Elimination of Block Effects in Fractional Designs 404
xvi CONTENTS
12.8 Designs of Resolution V and Higher 407
12.9 Summary 409
Appendix 12A Structure of the Fractional Designs 409
Appendix 12B Choosing Additional Runs To Resolve Ambiguities
from Fractional Factorials 413
13 MORE APPLICATIONS OF FRACTIONAL FACTORIAL DESIGNS
13.1 Example 1: Effects of Five Variables on Some Properties
of Cast Films
13.2 Example 2: Stability of New Product
13.3 Example 3: Bottleneck at the Filtration Stage of an
Industrial Plant
13.4 Example 4: Sensitivity Analysis of a Simulation Model —
Controller-Aircraft System
13.5 Summary
419
419
422
424
429
432
PROBLEMS FOR PART III 434
PART IV BUILDING MODELS AND USING THEM
14 SIMPLE MODELING WITH LEAST SQUARES (REGRESSION ANALYSIS) 453
14.1 One-Parameter Model (Straight Line through the Origin):
Aerosol Example 453
14.2 Two-Parameter Model: Impurity Example 462
14.3 Straight Line Model: Welding Example 473
14.4 General Case for Models Linear in the Parameters 479
14.5 Polynomial Model: Growth Rate Example 480
14.6 Nonlinear Model: Biochemical Oxygen Demand Example 483
14.7 Hazards of Fitting Regression Equations to Happenstance
Data 487
Appendix 14A Why Do the Normal Equations Yield Least
Squares Estimates? 498
Appendix 14B Matrix Version of the Normal Equations 501
I 2A I : Controller—Aircraft System
Model :
Analysis of Factorials, Botched and Otherwise Appendix 14D Unweighted and Weighted Least Squares 15 Methodology : 513
Applications of Response Surface Methods Empirical and Mechanistic Possible Advantages of Mechanistic Models Techniques for Mechanistic Modeling The Model-Building Process Model Testing with Diagnostic Parameters 550
Importance of Plotting Data in the Age of Computers Summary 17 STUDY OF VARIATION 17.1 Graphs and Control Charts: Impurity Determination
Example Transmission of Error 563
17.3 Variance Components: Pigment Paste Appendix 17A Calculating Variance Components from an
Analysis of Variance Table 18 18.1 The Industrial Data of Chapter 2 Reconsidered 585
Statistical Modeling Revisited 588
CONTENTS xvii
Appendix 14C Analysis of Factorials, Botched and 503
Appendix 14D Unweighted and Weighted Least 505
15 RESPONSE SURFACE METHODS 510
15.1 Weakness of Classical One-Variable-at-a-Time Strategy:
Chemical Example 510
15.2 Illustration of Response Surface Methodology: Chemical
Example 15.3 A Specification Problem 526
15.4 Maxima, Ridges, and Canonical Analysis 526
15.5 534
15.6 Summary 535
16 MECHANISTIC MODEL BUILDING 540
16.1 Empirical and Mechanistic Models 540
16.2 Possible Advantages of Mechanistic 544
16.3 Techniques for Mechanistic Modeling 546
16.4 The Model-Building Process 548
16.5 Model Testing with Diagnostic Parameters 16.6 Importance of Plotting Data in the Age of 552
16.7 Summary 552
17 STUDY OF VARIATION 556
17.1 Graphs and Control Charts: Impurity 556
17.2 Transmission of 17.3 Variance Components: Pigment Paste Example 571
Appendix 17A Calculating Variance 581
MODELING DEPENDENCE: TIME SERIES 584
18.1 The Industrial Data of Chapter 2 Reconsidered as a Time
Series 18.2 Statistical Modeling Revisited
xviii CONTENTS
18.3 Forecasting: Refrigerator Sales Example 591
18.4 Feedback Control: Dye Level Example 598
18.5 Intervention Analysis : Los Angeles Air Pollution Example 602
Appendix 18A Derivation of Equation 18.4 604
PROBLEMS FOR PART IV 606
APPENDIX : TABLES 629
INDEX 645

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