A First Course in Design and Analysis of Experiments

1 A First Course inDesign and Analysisof ExperimentsA First Course inDesign and Analysisof ExperimentsGary W. OehlertUniversity of MinnesotaCover Design by Victoria TomaselliCover illustration by Peter HamlinMinitab is a registered trademark of Minitab, is a registered trademark of SAS Institute, is a registered trademark of Mathsoft, is a registered trademark of Stat-Ease, of Congress Cataloging-in-Publication , Gary First Course in Design and Analysis of Experiments / Gary W. bibligraphical references and 0-7167-3510-51. Experimental DesignI. dc2199-059934 Copyrightc 2010 Gary W. Oehlert. All rights work is licensed under a Creative Commons license. Briefly, you are free tocopy, distribute, and transmit this work provided the following conditions are met:1.

2 You must properly attribute the You may not use this work for commercial You may not alter, transform, or build upon this complete description of the license may be found Beckywho helped me all the way throughand for Christie and Ericawho put up with a lot while it was getting Experiment? .. of an Experiment .. and Concepts .. About Experimental Units .. About Responses ..102 Randomization and Against Confounding .. Other Things .. a Randomization .. for Inference .. pairedt-test .. inference and standard inference . Reading and Extensions ..283 Completely Randomized of a CRD .. Exploratory Analysis .. and Parameters .. Parameters .. Models: The Analysis of Variance .. of ANOVA .. ANOVA Works .. to Model Comparison.

3 Plots .. Modeling .. Reading and Extensions ..604 Looking for Specific Differences Basics .. for Contrasts .. Contrasts .. Contrasts .. Reading and Extensions ..755 Multiple Rates .. Methods .. Scheff e Method forAllContrasts .. Comparisons .. the results .. Studentized range .. confidence intervals .. familywise error rate .. discovery rate .. error rate .. error rate .. testing reprise .. comparisons methods that donotcontrolcombined Type I error rates .. Confident directions .. with Control or the Best .. with a control .. with the best .. Check on Coverage Rates .. Warning About Conditioning .. Controversy .. Reading and Extensions .. 1086 Checking.

4 Violations of Assumptions .. nonnormality .. nonconstant variance .. dependence .. Problems .. nonnormality .. nonconstant variance .. dependence .. of Incorrect Assumptions .. of nonnormality .. of nonconstant variance .. of dependence .. for Design .. Reading and Extensions .. 1437 Power and Sample to Sample Size Selection .. Size for Confidence Intervals .. and Sample Size for ANOVA .. and Sample Size for a Contrast .. about Units and Measurement Units .. of Units for Two Special Cases .. Reading and Extensions .. 1628 Factorial Treatment Structure .. Analysis : Main Effect and Interaction .. of Factorials .. Interaction.

5 With Parameters .. Analysis of Variance for Balanced Factorials .. Factorial Models .. and Transformations .. Replicates .. Terms into Error .. 1979A Closer Look at Factorial for Factorial Data .. Interaction .. plots .. interaction .. factors .. one-degree-of-freedom for nonadditivity .. Reading and Extensions .. 22210 Further Topics in Data .. Sums of squares in unbalanced data .. Building models .. Testing hypotheses .. Empty cells .. Comparisons .. and Sample Size .. Factorials .. Contrasts .. Single replicates .. Reading and Extensions .. 24511 Random for Random Effects .. Use Random Effects?

6 For Random Effects .. Tests .. Estimates of Variance Components .. Intervals for Variance Components .. Reading and Extensions .. Problems .. 27512 Nesting, Mixed Effects, and Expected Mean Versus Crossing .. Nesting? .. and Nested Factors .. Effects .. a Model .. Diagrams and Expected Mean Squares .. Test denominators .. Expected mean squares .. Constructing a Hasse diagram .. of Means and Contrasts .. Data and Random Effects .. Nested Designs .. Problems .. 307xiiCONTENTS13 Complete Block .. Randomized Complete Block Design .. Why and when to use the RCB .. Analysis for the RCB .. How well did the blocking work?

7 Balance and missing data .. Squares and Related Row/Column Designs .. The crossover Design .. Randomizing the LS Design .. Analysis for the LS Design .. Replicating Latin Squares .. Efficiency of Latin Squares .. Designs balanced for residual effects .. Squares .. Reading and Extensions .. 34514 Incomplete Block Incomplete Block Designs .. Intrablock Analysis of the BIBD .. Interblock information .. and Column Incomplete Blocks .. Balanced Incomplete Blocks .. Designs .. , Cubic, and Rectangular Lattices .. Designs .. Reading and Extensions .. 379 CONTENTS xiii15 Factorials in Incomplete Blocks the Two-Series Factorial.

8 Two blocks .. Four or more blocks .. Analysis of an unreplicated confounded two-series Replicating a confounded two-series .. Double confounding .. the Three-Series Factorial .. Building the Design .. Confounded effects .. Analysis of confounded three-series .. Reading and Extensions .. 41016 Split-Plot Is a Split Plot? .. Split Plots .. of a Split Plot .. Plots .. Generalizations of Split Plots .. Measures .. Designs .. Reading and Extensions .. 44217 Designs with Basic Covariate Model .. Treatments Change Covariates .. Covariate Models .. Reading and Extensions .. 466xivCONTENTS18 Fractional Fraction?

9 The Two-Series .. a2k q.. and Projection .. a Fractional Factorial .. of Fractions .. the Three-Series .. Problems with Fractional Factorials .. Using Fractional Factorials in Off-Line Quality Control .. Designing an off-line quality experiment .. Analysis of off-line quality Experiments .. Further Reading and Extensions .. Problems .. 49919 Response Surface the Response .. Models .. Designs .. First -Order Data .. Models .. Designs .. Analysis .. Experiments .. Designs for mixtures .. Models for mixture designs .. Reading and Extensions .. Problems .. 536 CONTENTSxv20 On Your Context.

10 By the Numbers .. Project .. 548 Bibliography549A Linear Models for Fixed .. Squares .. of Models .. Variation .. Functions .. Scheff e Method .. 580B Notation583C Experimental Design Squares .. Latin Squares .. Latin Squares .. Incomplete Block Designs .. Cyclic Designs .. Designs .. Confounding and Fractioning Plans .. 617D Tables621 Index647 PrefacexviiPrefaceThis text covers the basic topics in experimental Design andanalysis andis intended for graduate students and advanced undergraduates. Studentsshould have had an introductory statistical methods courseat about the levelof Moore and McCabe sIntroduction to the Practice of Statistics(Moore andMcCabe 1999) and be familiar witht-tests,p-values, confidence intervals,and the basics of regression and ANOVA.