9780387985619

Design and Analysis of Experiments

by ;
  • ISBN13:

    9780387985619

  • ISBN10:

    0387985611

  • Format: Hardcover
  • Copyright: 1/1/1999
  • Publisher: Springer Verlag

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Summary

The design and analysis of experiments is an essential part of investigation and discovery in science, of process and product improvement in manufacturing, and of comparison of competing protocols or treatments in the applied sciences. This book offers a step by step guide to the experimental planning process and the ensuing analysis of normally distributed data. Design and Analysis of Experiments emphasizes the practical considerations governing the design of an experiment based on the objectives of the study and a solid statistical foundation for the analysis. Almost all data sets in the book have been obtained from real experiments, either run by students in statistics and the applied sciences, or published in the scientific literature. Details of the planning stage of numerous different experiments are discussed. The statistical analysis of experimental data is based on estimable functions and is developed with some care. Design and Analysis of Experiments starts with basic principles and techniques of experimental design and analysis of experiments. It provides a checklist for the planning of experiments, and explains the estimation of treatment contrasts and analysis of variance. These basics are then applied in a wide variety of settings. Designs covered include completely randomized designs, complete and incomplete block designs, row-column designs, single replicate designs with confounding, fractional factorial designs, response surface designs, and designs involving nested factors and factors with random effects, including split-plot designs. The book is accessible to all readers who have a good basic knowledge of expected values, confidence intervals and hypothesis tests. It is ideal for use in the classroom at both the senior undergraduate and the graduate level. A guide to the use of the SAS System computer

Table of Contents

Preface v
Principles and Techniques
1(6)
Design: Basic Principles and Techniques
1(4)
The Art of Experimentation
1(1)
Replication
2(1)
Blocking
3(1)
Randomization
3(2)
Analysis: Basic Principles and Techniques
5(2)
Planning Experiments
7(26)
Introduction
7(1)
A Checklist for Planning Experiments
7(7)
A Real Experiment---Cotton-Spinning Experiment
14(3)
Some Standard Experimental Designs
17(5)
Completely Randomized Designs
18(1)
Block Designs
18(1)
Designs with Two or More Blocking Factors
19(2)
Split-Plot Designs
21(1)
More Real Experiments
22(9)
Soap Experiment
22(4)
Battery Experiment
26(3)
Cake-Baking Experiment
29(2)
Exercises
31(2)
Designs with One Source of Variation
33(34)
Introduction
33(1)
Randomization
34(1)
Model for a Completely Randomized Design
35(2)
Estimation of Parameters
37(7)
Estimable Functions of Parameters
37(1)
Notation
37(1)
Obtaining Least Squares Estimates
38(2)
Properties of Least Squares Estimators
40(2)
Estimation of σ2
42(1)
Confidence Bound for σ2
43(1)
One-Way Analysis of Variance
44(5)
Testing Equality of Treatment Effects
44(4)
Use of p-Values
48(1)
Sample Sizes
49(4)
Expected Mean Squares for Treatments
50(1)
Sample Sizes Using Power of a Test
51(2)
A Real Experiment---Soap Experiment, Continued
53(4)
Checklist, Continued
53(1)
Data Collection and Analysis
54(2)
Discussion by the Experimenter
56(1)
Further Observations by the Experimenter
56(1)
Using SAS Software
57(4)
Randomization
57(1)
Analysis of Variance
58(3)
Exercises
61(6)
Inferences for Contrasts and Treatment Means
67(36)
Introduction
67(1)
Contrasts
68(5)
Pairwise Comparisons
69(1)
Treatment Versus Control
70(1)
Difference of Averages
70(1)
Trends
71(2)
Individual Contrasts and Treatment Means
73(5)
Confidence Interval for a Single Contrast
73(2)
Confidence Interval for a Single Treatment Mean
75(1)
Hypothesis Test for a Single Contrast or Treatment Mean
75(3)
Methods of Multiple Comparisons
78(14)
Multiple Confidence Intervals
78(2)
Bonferroni Method for Preplanned Comparisons
80(3)
Scheffe Method of Multiple Comparisons
83(2)
Tukey Method for All Pairwise Comparisons
85(2)
Dunnett Method for Treatment-Versus-Control Comparisons
87(2)
Hsu Method for Multiple Comparisons with the Best Treatment
89(2)
Combination of Methods
91(1)
Methods Not Controlling Experimentwise Error Rate
92(1)
Sample Sizes
92(2)
Using SAS Software
94(3)
Inferences on Individual Contrasts
94(2)
Multiple Comparisons
96(1)
Exercises
97(6)
Checking Model Assumptions
103(32)
Introduction
103(1)
Strategy for Checking Model Assumptions
104(3)
Residuals
104(1)
Residual Plots
105(2)
Checking the Fit of the Model
107(1)
Checking for Outliers
107(2)
Checking Independence of the Error Terms
109(2)
Checking the Equal Variance Assumption
111(8)
Detection of Unequal Variances
112(1)
Data Transformations to Equalize Variances
113(3)
Analysis with Unequal Error Variances
116(3)
Checking the Normality Assumption
119(3)
Using SAS Software
122(5)
Using SAS to Generate Residual Plots
122(4)
Transforming the Data
126(1)
Exercises
127(8)
Experiments with Two Crossed Treatment Factors
135(58)
Introduction
135(1)
Models and Factorial Effects
136(5)
The Meaning of Interaction
136(2)
Models for Two Treatment Factors
138(2)
Checking the Assumptions on the Model
140(1)
Contrasts
141(4)
Contrasts for Main Effects and Interactions
141(2)
Writing Contrasts as Coefficient Lists
143(2)
Analysis of the Two-Way Complete Model
145(13)
Least Squares Estimators for the Two-Way Complete Model
146(1)
Estimation of σ2 for the Two-Way Complete Model
147(2)
Multiple Comparisons for the Complete Model
149(3)
Analysis of Variance for the Complete Model
152(6)
Analysis of the Two-Way Main-Effects Model
158(10)
Least Squares Estimators for the Main-Effects Model
158(4)
Estimation of σ2 in the Main-Effects Model
162(1)
Multiple Comparisons for the Main-Effects Model
163(2)
Unequal Variances
165(1)
Analysis of Variance for Equal Sample Sizes
165(3)
Model Building
168(1)
Calculating Sample Sizes
168(1)
Small Experiments
169(6)
One Observation per Cell
169(1)
Analysis Based on Orthogonal Contrasts
169(3)
Tukey's Test for Additivity
172(1)
A Real Experiment---Air Velocity Experiment
173(2)
Using SAS Software
175(8)
Contrasts and Multiple Comparisons
177(4)
Plots
181(1)
One Observation per Cell
182(1)
Exercises
183(10)
Several Crossed Treatment Factors
193(50)
Introduction
193(1)
Models and Factorial Effects
194(7)
Models
194(1)
The Meaning of Interaction
195(2)
Separability of Factorial Effects
197(2)
Estimation of Factorial Contrasts
199(2)
Analysis---Equal Sample Sizes
201(4)
A Real Experiment---Popcorn-Microwave Experiment
205(6)
One Observation per Cell
211(6)
Analysis Assuming That Certain Interaction Effects Are Negligible
211(2)
Analysis Using Normal Probability Plot of Effect Estimates
213(2)
Analysis Using Confidence Intervals
215(2)
Design for the Control of Noise Variability
217(6)
Analysis of Design-by-Noise Interactions
218(3)
Analyzing the Effects of Design Factors on Variability
221(2)
Using SAS Software
223(8)
Normal Probability Plots of Contrast Estimates
224(1)
Voss-Wang Confidence Interval Method
224(2)
Identification of Robust Factor Settings
226(1)
Experiments with Empty Cells
227(4)
Exercises
231(12)
Polynomial Regression
243(34)
Introduction
243(1)
Models
244(4)
Least Squares Estimation (Optional)
248(1)
Normal Equations
248(1)
Least Squares Estimates for Simple Linear Regression
248(1)
Test for Lack of Fit
249(2)
Analysis of the Simple Linear Regression Model
251(4)
Anaysis of Polynomial Regression Models
255(3)
Analysis of Variance
255(2)
Confidence Intervals
257(1)
Orthogonal Polynomials and Trend Contrasts (Optional)
258(4)
Simple Linear Regression
258(2)
Quadratic Regression
260(1)
Comments
261(1)
A Real Experiment---Bean-Soaking Experiment
262(6)
Checklist
262(2)
One-Way Analysis of Variance and Multiple Comparisons
264(3)
Regression Analysis
267(1)
Using SAS Software
268(5)
Exercises
273(4)
Analysis of Covariance
277(18)
Introduction
277(1)
Models
278(2)
Checking Model Assumptions and Equality of Slopes
279(1)
Model Extensions
279(1)
Least Squares Estimates
280(2)
Normal Equations (Optional)
280(1)
Least Squares Estimates and Adjusted Treatment Means
281(1)
Analysis of Covariance
282(4)
Treatment Contrasts and Confidence Intervals
286(2)
Individual Confidence Intervals
286(1)
Multiple Comparisons
287(1)
Using SAS Software
288(4)
Exercises
292(3)
Complete Block Designs
295(44)
Introduction
295(1)
Blocks, Noise Factors or Covariates?
296(1)
Design Issues
297(4)
Block Sizes
297(1)
Complete Block Design Definitions
298(1)
The Randomized Complete Block Design
299(1)
The General Complete Block Design
300(1)
How Many Observations?
301(1)
Analysis of Randomized Complete Block Designs
301(5)
Model and Analysis of Variance
301(4)
Multiple Comparisons
305(1)
A Real Experiment---Cotton-Spinning Experiment
306(3)
Design Details
306(1)
Sample-Size Calculation
307(1)
Analysis of the Cotton-Spinning Experiment
307(2)
Analysis of General Complete Block Designs
309(7)
Model and Analysis of Variance
309(3)
Multiple Comparisons for the General Complete Block Design
312(3)
Sample-Size Calculations
315(1)
Checking Model Assumptions
316(1)
Factorial Experiments
317(3)
Using SAS Software
320(4)
Exercises
324(15)
Incomplete Block Designs
339(48)
Introduction
339(1)
Design Issues
340(8)
Block Sizes
340(1)
Design Plans and Randomization
340(2)
Estimation of Contrasts (Optional)
342(1)
Balanced Incomplete Block Designs
343(2)
Group Divisible Designs
345(1)
Cyclic Designs
346(2)
Analysis of General Incomplete Block Designs
348(6)
Contrast Estimators and Multiple Comparisons
348(3)
Least Squares Estimation (Optional)
351(3)
Analysis of Balanced Incomplete Block Designs
354(6)
Multiple Comparisons and Analysis of Variance
354(1)
A Real Experiment---Detergent Experiment
355(5)
Analysis of Group Divisible Designs
360(2)
Multiple Comparisons and Analysis of Variance
360(2)
Analysis of Cyclic Designs
362(1)
A Real Experiment---Plasma Experiment
362(6)
Sample Sizes
368(1)
Factorial Experiments
369(3)
Factorial Structure
369(3)
Using SAS Software
372(6)
Analysis of Variance and Estimation of Contrasts
372(5)
Plots
377(1)
Exercises
378(9)
Designs with Two Blocking Factors
387(34)
Introduction
387(1)
Design Issues
388(6)
Selection and Randomization of Row-Column Designs
388(1)
Latin Square Designs
389(2)
Youden Designs
391(1)
Cyclic and Other Row-Column Designs
392(2)
Model for a Row-Column Design
394(1)
Analysis of Row-Column Designs (Optional)
395(6)
Least Squares Estimation (Optional)
395(2)
Solution for Complete Column Blocks (Optional)
397(1)
Formula for ssE (Optional)
398(1)
Analysis of Variance for a Row-Column Design (Optional)
399(2)
Confidence Intervals and Multiple Comparisons
401(1)
Analysis of Latin Square Designs
401(5)
Analysis of Variance for Latin Square Designs
401(2)
Confidence Intervals for Latin Square Designs
403(2)
How Many Observations?
405(1)
Analysis of Youden Designs
406(2)
Analysis of Variance for Youden Designs
406(1)
Confidence Intervals for Youden Designs
407(1)
How Many Observations?
407(1)
Analysis of Cyclic and Other Row-Column Designs
408(1)
Checking the Assumptions on the Model
409(1)
Factorial Experiments in Row-Column Designs
410(1)
Using SAS Software
410(5)
Factorial Model
413(2)
Plots
415(1)
Exercises
415(6)
Confounded Two-Level Factorial Experiments
421(40)
Introduction
421(1)
Single replicate factorial experiments
422(2)
Coding and notation
422(1)
Confounding
422(1)
Analysis
423(1)
Confounding Using Contrasts
424(9)
Contrasts
424(1)
Experiments in Two Blocks
425(5)
Experiments in Four Blocks
430(2)
Experiments in Eight Blocks
432(1)
Experiments in More Than Eight Blocks
433(1)
Confounding Using Equations
433(4)
Experiments in Two Blocks
433(2)
Experiments in More Than Two Blocks
435(2)
A Real Experiment---Mangold Experiment
437(4)
Plans for Confounded 2p Experiments
441(1)
Multireplicate Designs
441(1)
Complete Confounding: Repeated Single-Replicate Designs
442(4)
A Real Experiment---Decontamination Experiment
442(4)
Partial Confounding
446(3)
Comparing the Multireplicate Designs
449(3)
Using SAS Software
452(2)
Exercises
454(7)
Confounding in General Factorial Experiments
461(22)
Introduction
461(1)
Confounding with Factors at Three Levels
462(9)
Contrasts
462(1)
Confounding Using Contrasts
463(1)
Confounding Using Equations
464(3)
A Real Experiment---Dye Experiment
467(3)
Plans for Confounded 3p Experiments
470(1)
Designing Using Pseudofactors
471(1)
Confounding in 4p Experiments
471(1)
Confounding in 2p x 4q Experiments
472(1)
Designing Confounded Asymmetrical Experiments
472(3)
Using SAS Software
475(2)
Exercises
477(6)
Fractional Factorial Experiments
483(64)
Introduction
483(1)
Fractions from Block Designs; Factors with 2 Levels
484(12)
Half-Fractions of 2p Experiments; 2p-1 Experiments
484(3)
Resolution and Notation
487(1)
A Real Experiment---Soup Experiment
487(3)
Quarter-Fractions of 2p Experiments; 2p-2 Experiments
490(4)
Smaller Fractions of 2p Experiments
494(2)
Fractions from Block Designs; Factors with 3 Levels
496(5)
One-Third Fractions of 3p Experiments; 3p-1 Experiments
496(5)
One-Ninth Fractions of 3p Experiments; 3p-2 Experiments
501(1)
Fractions from Block Designs; Other Experiments
501(2)
2p x 4q Experiments
501(1)
2p x 3q Experiments
502(1)
Blocked Fractional Factorial Experiments
503(3)
Fractions from Orthogonal Arrays
506(9)
2p Orthogonal Arrays
506(6)
Saturated Designs
512(1)
2p x 4q Orthogonal Arrays
513(1)
3p Orthogonal Arrays
514(1)
Design for the Control of Noise Variability
515(6)
A Real Experiment---Inclinometer Experiment
516(5)
Using SAS Software
521(8)
Fractional Factorials
521(3)
Design for the Control of Noise Variability
524(5)
Exercises
529(18)
Response Surface Methodology
547(46)
Introduction
547(2)
First-Order Designs and Analysis
549(12)
Models
549(2)
Standard First-Order Designs
551(1)
Least Squares Estimation
552(1)
Checking Model Assumptions
553(1)
Tests for Lack of Fit
554(5)
Path of Steepest Ascent
559(2)
Second-Order Designs and Analysis
561(8)
Models and Designs
561(1)
Central Composite Designs
562(2)
Generic Test for Lack of Fit of the Second-Order Model
564(1)
Analysis of Variance for a Second-Order Model
564(2)
Canonical Analysis of a Second-Order Model
566(3)
Properties of Second-Order Designs: CCDs
569(4)
Rotatability
569(1)
Orthogonality
570(1)
Orthogonal Blocking
571(2)
A Real Experiment: Flour Production Experiment, Continued
573(3)
Box-Behnken Designs
576(3)
Using SAS Software
579(7)
Analysis of a Standard First-Order Design
579(3)
Analysis of a Second-Order Design
582(4)
Exercises
586(7)
Random Effects and Variance Components
593(52)
Introduction
593(1)
Some Examples
594(2)
One Random Effect
596(11)
The Random-Effects One-Way Model
596(1)
Estimation of σ2
597(1)
Estimation of σ2T
598(3)
Testing Equality of Treatment Effects
601(2)
Confidence Intervals for Variance Components
603(4)
Sample Sizes for an Experiment with One Random Effect
607(3)
Checking Assumptions on the Model
610(1)
Two or More Random Effects
610(12)
Models and Examples
610(3)
Checking Model Assumptions
613(1)
Estimation of σ2
613(1)
Estimation of Variance Components
614(2)
Confidence Intervals for Variance Components
616(4)
Hypothesis Tests for Variance Components
620(2)
Sample Sizes
622(1)
Mixed Models
622(5)
Expected Mean Squares and Hypothesis Tests
622(3)
Confidence Intervals in Mixed Models
625(2)
Rules for Analysis of Random and Mixed Models
627(3)
Rules---Equal Sample Sizes
627(1)
Controversy (Optional)
628(2)
Block Designs and Random Blocking Factors
630(2)
Using SAS Software
632(7)
Checking Assumptions on the Model
632(3)
Estimation and Hypothesis Testing
635(4)
Exercises
639(6)
Nested Models
645(30)
Introduction
645(1)
Examples and Models
646(2)
Analysis of Nested Fixed Effects
648(6)
Least Squares Estimates
648(1)
Estimation of σ2
649(1)
Confidence Intervals
650(1)
Hypothesis Testing
650(4)
Analysis of Nested Random Effects
654(8)
Expected Mean Squares
654(2)
Estimation of Variance Components
656(1)
Hypothesis Testing
657(1)
Some Examples
658(4)
Using SAS Software
662(5)
Voltage Experiment
662(5)
Exercises
667(8)
Split-Plot Designs
675(20)
Introduction
675(1)
Designs and Models
676(2)
Analysis of a Split-Plot Design with Complete Blocks
678(6)
Split-Plot Analysis
678(2)
Whole-Plot Analysis
680(1)
Contrasts Within and Between Whole Plots
681(1)
A Real Experiment---Oats Experiment
681(3)
Split-Split-Plot Designs
684(2)
Split-Plot Confounding
686(1)
Using SAS Software
687(4)
Exercises
691(4)
A. Tables 695(30)
Bibilography 725(6)
Index of Authors 731(2)
Index of Experiments 733(2)
Index of Subjects 735

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