Design of Experiments Statistical Principles of Research Design and Analysis

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ISBN: 9780534368340 | 0534368344
Cover: Hardcover
Copyright: 8/13/1999

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Robert Kuehl's DESIGN OF EXPERIMENTS, Second Edition, prepares students to design and analyze experiments that will help them succeed in the real world. Kuehl uses a large array of real data sets from a broad spectrum of scientific and technological fields. This approach provides realistic settings for conducting actual research projects. Next, he emphasizes the importance of developing a treatment design based on a research hypothesis as an initial step, then developing an experimental or observational study design that facilitates efficient data collection. In addition to a consistent focus on research design, Kuehl offers an interpretation for each analysis.

Research Design Principles

(36)

The Legacy of Sir Ronald A. Fisher

(1)

Planning for Research

(1)

Experiments, Treatments, and Experimental Units

(2)

Research Hypotheses Generate Treatment Designs

(3)

Local Control of Experimental Errors

(8)

Replication for Valid Experiments

(2)

How Many Replications?

(2)

Randomization for Valid Inferences

(5)

Relative Efficiency of Experiment Designs

(1)

From Principles to Practice: A Case Study

(11)

Getting Started with Completely Randomized Designs

(36)

Assembling the Research Design

(2)

How to Randomize

(2)

Preparation of Data Files for the Analysis

(1)

A Statistical Model for the Experiment

(5)

Estimation of the Model Parameters with Least Squares

(3)

Sums of Squares to Identify Important Sources of Variation

(3)

A Treatment Effects Model

(1)

Degrees of Freedom

(1)

Summaries in the Analysis of Variance Table

(1)

Tests of Hypotheses About Linear Models

(2)

Significance Testing and Tests of Hypotheses

(1)

Standard Errors and Confidence Intervals for Treatment Means

(1)

Unequal Replication of the Treatments

(3)

How Many Replications for the F Test?

(10)

Appendix: Expected Values

(1)

Appendix: Expected Mean Squares

(2)

Treatment Comparisons

(50)

Treatment Comparisons Answer Research Questions

(1)

Planning Comparisons Among Treatments

(9)

Response Curves for Quantitative Treatment Factors

(8)

Multiple Comparisons Affect Error Rates

(3)

Simultaneous Statistical Inference

(4)

Multiple Comparisons with the Best Treatment

(6)

Comparison of All Treatments with a Control

104

(3)

Pairwise Comparison of All Treatments

107

(8)

Summary Comments on Multiple Comparisons

115

(8)

Appendix: Linear Functions of Random Variables

121

(2)

Diagnosing Agreement Between the Data and the Model

123

(25)

Valid Analysis Depends on Valid Assumptions

123

(1)

Effects of Departures from Assumptions

123

(1)

Residuals Are the Basis of Diagnostic Tools

124

(7)

Looking for Outliers with the Residuals

131

(2)

Variance-Stabilizing Transformations for Data with Known Distributions

133

(2)

Power Transformations to Stabilize Variances

135

(5)

Generalizing the Linear Model

140

(1)

Model Evaluation with Residual-Fitted Spread Plots

141

(7)

Appendix: Data for Example 4.1

147

(1)

Experiments to Study Variances

148

(27)

Random Effects Models for Variances

148

(3)

A Statistical Model for Variance Components

151

(1)

Point Estimates of Variance Components

152

(1)

Interval Estimates for Variance Components

153

(2)

Courses of Action with Negative Variance Estimates

155

(1)

Intraclass Correlation Measures Similarity in a Group

155

(2)

Unequal Numbers of Observations in the Groups

157

(1)

How Many Observations to Study Variances?

158

(1)

Random Subsamples to Procure Data for the Experiment

159

(4)

Using Variance Estimates to Allocate Sampling Efforts

163

(1)

Unequal Numbers of Replications and Subsamples

164

(11)

Appendix: Coefficient Calculations for Expected Mean Squares in Table 5.9

174

(1)

Factorial Treatment Designs

175

(57)

Efficient Experiments with Factorial Treatment Designs

175

(2)

Three Types of Treatment Factor Effects

177

(4)

The Statistical Model for Two Treatment Factors

181

(2)

The Analysis for Two Factors

183

(7)

Using Response Curves for Quantitative Treatment Factors

190

(9)

Three Treatment Factors

199

(6)

Estimation of Error Variance with One Replication

205

(3)

How Many Replication to Test Factor Effects?

208

(1)

Unequal Replication of Treatments

208

(24)

Appendix: Least Squares for Factorial Treatment Designs

225

(7)

Factorial Treatment Designs: Random and Mixed Models

232

(31)

Random Effects for Factorial Treatment Designs

232

(5)

Mixed Models

237

(6)

Nested Factor Designs: A Variation on the Theme

243

(8)

Nested and Crossed Factors Designs

251

(4)

How Many Replications?

255

(1)

Expected Mean Square Rules

255

(8)

Complete Block Designs

263

(47)

Blocking to Increase Precision

263

(1)

Randomized Complete Block Designs Use One Blocking Criterion

264

(11)

Latin Square Designs Use Two Blocking Criteria

275

(14)

Factorial Experiments in Complete Block Designs

289

(2)

Missing Data in Blocked Designs

291

(1)

Experiments Performed Several Times

292

(18)

Appendix: Selected Latin Squares

307

(3)

Incomplete Block Designs: An Introduction

310

(29)

Incomplete Blocks of Treatments to Reduce Block Size

310

(2)

Balanced Incomplete Block (BIB) Designs

312

(1)

How to Randomize Incomplete Block Designs

313

(2)

Analysis of BIB Designs

315

(5)

Row--Column Designs for Two Blocking Criteria

320

(2)

Reduce Experiment Size with Partially Balanced (PBIB) Designs

322

(3)

Efficiency of Incomplete Block Design

325

(14)

Appendix: Selected Balanced Incomplete Block Designs

330

(2)

Appendix: Selected Incomplete Latin Square Designs

332

(4)

Appendix: Least Squares Estimates for BIB Designs

336

(3)

Incomplete Block Designs: Resolvable and Cyclic Designs

339

(23)

Resolvable Designs to Help Manage the Experiment

339

(3)

Resolvable Row--Column Designs for Two Blocking Criteria

342

(3)

Cyclic Designs Simplify Design Construction

345

(7)

Choosing Incomplete Block Designs

352

(10)

Appendix: Plans for Cyclic Designs

360

(1)

Appendix: Generating Arrays for α Designs

360

(2)

Incomplete Block Designs: Factorial Treatment Designs

362

(29)

Taking Greater Advantage of Factorial Treatment Designs

362

(1)

2n Factorials to Evaluate Many Factors

363

(6)

Incomplete Block Designs for 2n Factorials

369

(9)

A General Method to Create Incomplete Blocks

378

(5)

Incomplete Block Designs for 3n Factorials

383

(4)

Concluding Remarks

387

(4)

Appendix: Incomplete Block Design Plans for 2n Factorials

390

(1)

Fractional Factorial Designs

391

(32)

Reduce Experiment Size with Fractional Treatment Designs

391

(2)

The Half Fraction of the 2n Factorial

393

(5)

Design Resolution Related to Aliases

398

(1)

Analysis of Half Replicate 2n--1 Designs

399

(7)

The Quarter Fractions of 2n Factorials

406

(3)

Construction of 2n--p Designs with Resolution III and IV

409

(4)

Genichi Taguchi and Quality Improvement

413

(2)

Concluding Remarks

415

(8)

Appendix: Fractional Factorial Design Plans

421

(2)

Response Surface Designs

423

(46)

Describe Responses with Equations and Graphs

423

(3)

Identify Important Factors with 2n Factorials

426

(5)

Designs to Estimate Second-Order Response Surfaces

431

(9)

Quadratic Response Surface Estimation

440

(4)

Response Surface Exploration

444

(5)

Designs for Mixtures of Ingredients

449

(4)

Analysis for Mixtures Experiments

453

(16)

Appendix: Least Squares Estimation of Regression Models

463

(3)

Appendix: Location of Coordinates for the Stationary Point

466

(1)

Appendix: Canonical Form of the Quadratic Equation

467

(2)

Split-Plot Designs

469

(23)

Plots of Different Size in the Same Experiment

469

(3)

Two Experimental Errors for Two Plot Sizes

472

(1)

The Analysis for Split-Plot Designs

473

(5)

Standard Errors for Treatment Factor Means

478

(2)

Features of the Split-Plot Design

480

(1)

Relative Efficiency of Subplot and Whole-Plot Comparisons

481

(2)

The Split-Split-Plot Design for Three Treatment Factors

483

(1)

The Split-Block Design

483

(3)

Additional Information About Split-Plot Designs

486

(6)

Repeated Measures Designs

492

(28)

Studies of Time Trends

492

(3)

Relationships Among Repeated Measurements

495

(3)

A Test for the Huynh--Feldt Assumption

498

(1)

A Univariate Analysis of Variance for Repeated Measures

499

(3)

Analysis When Univariate Analysis Assumptions Do Not Hold

502

(8)

Other Experiments with Repeated Measures Properties

510

(1)

Other Models for Correlation Among Repeated Measures

511

(9)

Appendix: The Mauchly Test for Sphericity

518

(1)

Appendix: Degrees of Freedom Adjustments for Repeated Measures Analysis of Variance

519

(1)

Crossover Designs

520

(30)

Administer All Treatments to Each Experimental Unit

520

(4)

Analysis of Crossover Designs

524

(6)

Balanced Designs for Crossover Studies

530

(6)

Crossover Designs for Two Treatments

536

(14)

Appendix: Coding Data Files for Crossover Studies

545

(2)

Appendix: Treatment Sum of Squares for Balanced Designs

547

(3)

Analysis of Covariance

550

(26)

Local Control with a Measured Covariate

550

(3)

Analysis of Covariance for Completely Randomized Designs

553

(12)

The Analysis of Covariance for Blocked Experiment Designs

565

(5)

Practical Consequences of Covariance Analysis

570

(6)

References

576

(11)

Appendix Tables

587

(46)

Answers to Selected Exercises

633

(28)

Index

661

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Design of Experiments Statistical Principles of Research Design and Analysis

Summary

Table of Contents

Supplemental Materials