Fundamental Concepts in the Design of Experiments

by Hicks, Charles R.; Turner, Kenneth V.

• ISBN13: 9780195122732
• ISBN10: 0195122739
• Edition: 5th
• Format: Hardcover
• Copyright: 1999-03-25
• Publisher: Oxford University Press

Summary

Fundamental Concepts in the Design of Experiments, 5/e offers comprehensive coverage of the key elements of experimental design used by applied researchers to solve problems in the field. Wide-ranging and accessible, it shows students how to use applied statistics for planning, running, andanalyzing experiments. Featuring over 350 problems taken from the authors' actual industrial consulting experiences, the text gives students valuable practice with real data and problem solving. The problems emphasize the basic philosophy of design and are simple enough for students with limitedmathematical backgrounds to understand. The authors provide extensive coverage of the analysis of residuals, the concept of resolution in fractional replications, Plackett-Burman designs, and Taguchi techniques. SAS (Statistical Analysis System) computer programs are incorporated to facilitateanalysis. Thoroughly revised and updated, this new edition includes sixty new problems, focuses more on computer use (adding computer outputs from statistical packages like Minitab, SPSS, and JMP), and emphasizes graphical procedures including residual plots and normal quantile plots. Ideal for variousadvanced undergraduate and graduate experimental methods courses taught in statistics, engineering, and mathematics departments, this book will also appeal to professionals and researchers doing experimental work.

Table of Contents

Preface	ix
The Experiment, the Design, and the Analysis	1	(16)
Introduction to Experimental Design	1	(2)
The Experiment	3	(2)
The Design	5	(3)
The Analysis	8	(1)
Examples	9	(7)
Summary in Outline	16	(1)
Further Reading	17	(1)
Problems	17	(33)
Review of Statistical Inference	18	(32)
Introduction	18	(2)
Estimation	20	(2)
Tests of Hypotheses	22	(3)
The Operating Characteristic Curve	25	(3)
How Large a Sample?	28	(1)
Application to Tests on Variances	29	(2)
Application to Tests on Means	31	(6)
Assessing Normality	37	(5)
Application to Tests on Proportions	42	(2)
Analysis of Experiments with Sas	44	(6)
Further Reading	50	(1)
Problems	50	(47)
Single-Factor Experiments with No Restrictions on Randomization	55	(42)
Introduction	55	(3)
Analysis of Variance Rationale	58	(6)
After Anova---What?	64	(1)
Tests on Means	64	(11)
Orthogonal Contrasts	65	(6)
Multiple Comparison Procedures	71	(4)
Confidence Limits on Means	75	(2)
Components of Variance	77	(6)
Checking the Model	83	(6)
Plot the Residuals Against Other Variables	87	(2)
Sas Programs for Anova and Tests after Anova	89	(7)
Summary	96	(1)
Further Reading	96	(1)
Problems	97	(29)
Single-Factor Experiments: Randomized Block and Latin Square Designs	103	(23)
Introduction	103	(2)
Randomized Complete Block Design	105	(5)
Anova Rationale	110	(1)
Missing Values	111	(3)
Computer Analysis with Missing Values	113	(1)
Latin Squares	114	(2)
Interpretations	116	(1)
Assessing the Model	117	(3)
Graeco-Latin Squares	120	(1)
Extensions	120	(1)
Sas Programs for Randomized Blocks and
Latin Squares	121	(4)
Summary	125	(1)
Further Reading	125	(1)
Problems	126	(32)
Factorial Experiments	133	(25)
Introduction	133	(5)
Factorial Experiments: an Example	138	(4)
Interpretations	142	(2)
The Model and its Assessment	144	(2)
Anova Rationale	146	(5)
One Observation Per Treatment	151	(1)
Sas Programs for Factorial Experiments	152	(5)
Summary	157	(1)
Further Reading	157	(1)
Problems	158	(28)
Fixed, Random, and Mixed Models	168	(18)
Introduction	168	(1)
Single-Factor Models	169	(1)
Two-Factor Models	170	(2)
Ems Rules	172	(3)
Ems Derivations	175	(3)
The Pseudo-F Test	178	(2)
Expected Mean Squares Via Statistical
Computing Packages	180	(2)
Remarks	182	(1)
Repeatability and Reproducibility for a
Measurement System	183	(1)
Sas Programs for Random and
Mixed Models	184	(2)
Further Reading	186	(1)
Problems	186	(26)
Nested and Nested-Factorial Experiments	190	(22)
Introduction	190	(1)
Nested Experiments	190	(7)
Anova Rationale	197	(1)
Nested-Factorial Experiments	198	(5)
Repeated-Measures Design and Nested-Factorial Experiments	203	(5)
Sas Programs for Nested and Nested-Factorial Experiments	208	(3)
Summary	211	(1)
Further Reading	212	(1)
Problems	212	(21)
Experiments of Two or More Factors: Restrictions on Randomization	222	(11)
Introduction	222	(1)
Factorial Experiment in a Randomized
Block Design	222	(6)
Factorial Experiment in a Latin
Square Design	228	(1)
Remarks	229	(1)
Sas Programs	230	(2)
Summary	232	(1)
Problems	233	(25)
2f Factorial Experiments	239	(19)
Introduction	239	(1)
22 Factorial	239	(7)
23 Factorial	246	(4)
2f Remarks	250	(1)
The Yates Method	251	(2)
Analysis of 2f Factorials When n = 1	253	(2)
Some Comments About Computer Use	255	(2)
Summary	257	(1)
Further Reading	257	(1)
Problems	258	(30)
3f Factorial Experiments	268	(20)
Introduction	268	(1)
32 Factorial	269	(11)
33 Factorial	280	(7)
Computer Programs	287	(1)
Summary	287	(1)
Problems	288	(18)
Factorial Experiment: Split-Plot Design	292	(14)
Introduction	292	(1)
A Split-Plot Design	293	(7)
A Split-Split-Plot Design	300	(4)
Using Sas to Analyze a Split-Plot Experiment	304	(2)
Summary	306	(1)
Further Reading	306	(1)
Problems	306	(29)
Factorial Experiment: Confounding in Blocks	311	(24)
Introduction	311	(2)
Confounding Systems	313	(3)
Block Confounding, no Replication	316	(6)
Block Confounding with Replication	322	(5)
Complete Confounding	323	(2)
Partial Confounding	325	(2)
Confounding in 3f Factorials	327	(5)
Sas Progams	332	(3)
Summary	335	(1)
Further Reading	335	(1)
Problems	335	(29)
Fractional Replication	340	(24)
Introduction	340	(1)
Aliases	341	(3)
2f Fractional Replications	344	(6)
The Yates Method with 2f-k Fractional Factorials	349	(1)
Fractional Replicates in Blocks	349	(1)
Plackett--Burman Designs	350	(4)
Design Resolution	354	(4)
3f-k Fractional Factorials	358	(4)
Sas Programs	362	(1)
Summary	363	(1)
Further Reading	364	(1)
Problems	364	(35)
The Taguchi Approach to the Design of Experiments	370	(29)
Introduction	370	(1)
The L4(23) Orthogonal Array	371	(5)
Outer Arrays	376	(2)
Signal-to-Noise Ratio	378	(2)
The L8(27) Orthogonal Array	380	(7)
The L16(215) Orthogonal Array	387	(2)
The L9(34) Orthogonal Array	389	(7)
Some Other Taguchi Designs	396	(1)
Summary	397	(1)
Further Reading	398	(1)
Problems	399	(33)
Regression	403	(29)
Introduction	403	(1)
Linear Regression	403	(11)
The Simple Linear Model	405	(1)
The Least Squares Line	406	(4)
Departure from the Linear Model: A Lack of Fit Test	410	(3)
The Use of Equispaced Levels	413	(1)
Curvilinear Regression	414	(8)
Departure from the Quadratic Model: A Lack of Fit Test	417	(2)
Two Factors: One Qualitative and One Quantitative	419	(3)
Orthogonal Polynomials	422	(2)
Multiple Regression	424	(7)
A Sas Program	428	(2)
Testing for Significance of the Coefficient of Determination	430	(1)
Summary	431	(1)
Further Reading	432	(1)
Problems	432	(56)
Miscellaneous Topics	442	(46)
Introduction	442	(1)
Covariance Analysis	442	(13)
Covariance Analysis by Example	443	(6)
The Assumptions of Covariance Analysis	449	(3)
Covariance Analysis Using Sas	452	(3)
Response Surface Experimentation	455	(12)
Evolutionary Operation (Evop)	467	(9)
Analysis of Attribute Data	476	(2)
Randomized Incomplete Blocks: Restriction on Experimentation	478	(6)
Youden Squares	484	(3)
Further Reading	487	(1)
Problems	488	(5)
Summary and Special Problems	493	(6)
Glossary of Terms	499	(6)
References	505	(2)
Statistical Tables	507	(1)
Table A Areas Under the Normal Curve	507	(2)
Table B Student's t Distribution	509	(1)
Table C Cumulative Chi-Square Distribution	510	(1)
Table D Cumulative F Distribution	511	(10)
Table E.1 Upper 5% of Studentized Range q	521	(1)
Table E.2 Upper 1% of Studentized Range q	522	(1)
Table F Coefficients of Orthogonal Polynomials	523	(2)
Answers to Selected Problems	525	(34)
Index	559