Design of Experiments Statistical Principles of Research Design and Analysis

by Kuehl, Robert O.

• ISBN13: 9780534368340
• ISBN10: 0534368344
• Edition: 2nd
• Format: Hardcover
• Copyright: 1999-08-13
• Publisher: Cengage Learning

Summary

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.

Table of Contents

Research Design Principles	1	(36)
The Legacy of Sir Ronald A. Fisher	1	(1)
Planning for Research	2	(1)
Experiments, Treatments, and Experimental Units	3	(2)
Research Hypotheses Generate Treatment Designs	5	(3)
Local Control of Experimental Errors	8	(8)
Replication for Valid Experiments	16	(2)
How Many Replications?	18	(2)
Randomization for Valid Inferences	20	(5)
Relative Efficiency of Experiment Designs	25	(1)
From Principles to Practice: A Case Study	26	(11)
Getting Started with Completely Randomized Designs	37	(36)
Assembling the Research Design	37	(2)
How to Randomize	39	(2)
Preparation of Data Files for the Analysis	41	(1)
A Statistical Model for the Experiment	42	(5)
Estimation of the Model Parameters with Least Squares	47	(3)
Sums of Squares to Identify Important Sources of Variation	50	(3)
A Treatment Effects Model	53	(1)
Degrees of Freedom	54	(1)
Summaries in the Analysis of Variance Table	55	(1)
Tests of Hypotheses About Linear Models	56	(2)
Significance Testing and Tests of Hypotheses	58	(1)
Standard Errors and Confidence Intervals for Treatment Means	59	(1)
Unequal Replication of the Treatments	60	(3)
How Many Replications for the F Test?	63	(10)
Appendix: Expected Values	70	(1)
Appendix: Expected Mean Squares	71	(2)
Treatment Comparisons	73	(50)
Treatment Comparisons Answer Research Questions	73	(1)
Planning Comparisons Among Treatments	74	(9)
Response Curves for Quantitative Treatment Factors	83	(8)
Multiple Comparisons Affect Error Rates	91	(3)
Simultaneous Statistical Inference	94	(4)
Multiple Comparisons with the Best Treatment	98	(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