Design and Analysis of Experiments

by Dean, Angela; Voss, D. T.

• ISBN13: 9780387985619
• ISBN10: 0387985611
• Format: Hardcover
• Copyright: 1999-01-01
• Publisher: Springer Verlag

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