Table Of ContentPaul D. Berger · Robert E. Maurer
Giovana B. Celli
Experimental
Design
With Applications in Management,
Engineering, and the Sciences
Second Edition
Experimental Design
Paul D. Berger (cid:129) Robert E. Maurer
Giovana B. Celli
Experimental Design
With Applications in Management,
Engineering, and the Sciences
Second Edition
PaulD.Berger RobertE.Maurer
BentleyUniversity QuestromSchoolofBusiness
Waltham,MA,USA BostonUniversity
Boston,MA,USA
GiovanaB.Celli
CornellUniversity
Ithaca,NY,USA
Cengage/DuxburyrevertedallrightstoAuthors.RevisionletterattachedtoBFluxrecord.
ISBN978-3-319-64582-7 ISBN978-3-319-64583-4 (eBook)
DOI10.1007/978-3-319-64583-4
LibraryofCongressControlNumber:2017949996
©SpringerInternationalPublishingAG2002,2018
Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart
of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,
recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionor
informationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar
methodologynowknownorhereafterdeveloped.
The use of general descriptive names, registered names, trademarks, service marks, etc. in this
publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexempt
fromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse.
Thepublisher,theauthorsandtheeditorsaresafetoassumethattheadviceandinformationinthisbook
arebelievedtobetrueandaccurateatthedateofpublication.Neitherthepublishernortheauthorsorthe
editorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinorforanyerrors
oromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregardtojurisdictionalclaims
inpublishedmapsandinstitutionalaffiliations.
Printedonacid-freepaper
ThisSpringerimprintispublishedbySpringerNature
TheregisteredcompanyisSpringerInternationalPublishingAG
Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland
Preface
Thekeyobjectiveofthisbookistointroduceandprovideinstructiononthedesign
and analysis of experiments. This expanded edition contains additional examples,
exercises, and situations covering the science and engineering practice. We have
triedtomakethisbookspecialintwomajorways.First,wehavetriedtoprovidea
textthatminimizestheamountofmathematicaldetail,whilestilldoingfulljustice
to the mathematical rigor of the presentation and the precision of our statements.
Thisdecisionmakesthisbookmoreaccessibleforthosewhohavelittleexperience
withdesignofexperimentsandneedsomepracticaladviceonusingsuchdesignsto
solveday-to-dayproblems.Second,wehavetriedtofocusonprovidinganintuitive
understanding of the principles at all times. In doing so, we have filled this book
withhelpfulhints,oftenlabeledaswaysto“practicesafestatistics.”Ourperspec-
tivehasbeenformedbydecadesofteaching,consulting,andindustrialexperience
inthefieldofdesignandanalysisofexperiments.
Approach
Ourapproachseekstoteachboth the fundamentalconcepts andtheirapplications.
Specifically,weincludesimpleexamplesforunderstandingaswellaslarger,more
challenging examples to illustrate their real-world nature and applications. Many
of our numerical examples use simple numbers. This is a choice the authors con-
sciously make, and it embraces a statement by C. C. Li, Professor of Biometry at
the University of Pittsburgh, that the authors took to heart over 30 years ago and
have incorporated into their teaching and writing: “How does one first learn to
solve quadratic equations? By working with terms like 242.5189X2
(cid:1)683.1620Xþ19428.5149¼0,orwithtermslikeX2(cid:1)5Xþ6¼0?”Ourbeliefis
that using simpler numerical calculationsthat students can moreeasilyfollow and
verifyaidsthemintheintuitiveunderstandingofthematerialtoadegreethatmore
thanoffsetsanydisadvantagefromusingnumbersthatdonotlooklikethoseinreal
v
vi Preface
cases.Thisdoesnotmeanthatwefocussolelyonhandcalculations(tous,thisterm
includestheuseofacalculator);wedonot.Wealsohaveexamples,aswellasfollow-
upexercisesattheendofchapters,thatencourage,demonstrate,and,indeed,require
the use of statistical software. Nevertheless, we believe in the virtue of students’
doingitatleastoncebyhandor,ataminimum,seeingitdoneatleastoncebyhand.
Background and Prerequisites
Most of our readers have some prior knowledge of statistics. However,as experi-
enced teachers, we are aware that students often do not retain all the statistical
knowledgetheyacquiredpreviously.Sincehypothesistestingissofundamentalto
theentiretext,wereviewitheavily,essentiallyrepeatingthedepthofcoveragethe
topicisaccordedinanintroductorycourseinstatistics.Otherusefultopicsfroma
typicalintroductorystatisticscoursearereviewedonanadhocbasis:anexampleof
this isthe topicofconfidence intervals.With respect totopics such asprobability
and the Student t distribution, we occasionally remind the student of certain
principles that we are using (e.g., the multiplication rule for independent events).
In this new edition, we go into more detail on statistical principles that were
discussedbrieflyinthefirsteditionofthebook,suchasrandomizationandsample
sizes,amongothers.
We have taught experimental design courses in which the audience varied
considerably with respect to their application areas (e.g., chemical engineering,
marketingresearch,biology);weprefacethesecoursesbyastatementwefervently
believetobetrue:
Theprinciplesandtechniquesofexperimentaldesigntranscendtheareaoftheirapplica-
tion;theonlydifferencefromoneapplicationareatoanotheristhatdifferentsituations
arisewithdifferentfrequencyand,correspondingly,theuseofvariousdesignsanddesign
principlesoccurwithdifferentfrequency.
Still, itis always helpful for peopletoactuallysee applicationsintheir areaof
endeavor.Forthisreason,wehaveexpandedthenumberofexamplesandexercises
coveringtheengineeringandsciencefields.Afterall,manypeoplebeginningtheir
study of experimental design do not know what they do not know; this includes
envisioningthewaysinwhichthematerialcanbeappliedusefully.
Considering the broad audience to which this book is targeted, we assume a
workingknowledgeofhigh-schoolalgebra.Onoccasion,webelieveitisnecessary
to go a small distance beyond routine high-school algebra; we strive to minimize
thefrequencyoftheseoccasions,andwhenitisunavoidableweexplainwhyitisin
themostintuitivewaythatwecan.Thesecircumstancesexemplifywhereweaimto
walkthefinelineofminimalmathematicalcomplexitywithoutcompromisingthe
rigorofourpresentationortheprecisionofourstatements.Thiscanbeasurprising
consideration for a book written for engineers, who often use mathematics and
calculusona daily basis; however, we believe thatthis approach can increase the
appealandboosttheuseofdesignofexperimentsinvarioussituations.
Preface vii
Thesecondwayinwhichwehavetriedtomakethisbookspecialistoemphasize
theapplicationoftheexperimentaldesignmaterialinareasofmanagement,suchas
marketing, finance, operations, management information systems, and organiza-
tionalbehavior,andalsoinboththetraditionalbusinesssettingandnon-profitareas
such as education, health care, and government. In addition, we include some
applications that could be placed in other categories as well – say, engineering
andscience.
For example, a company needs to test whether different brands of D-cell
batteries differ with respect to average lifetime (with the same pattern of usage)
in order to convince a television network to accept a promotion that claims one
brand’ssuperiorityoverotherbrands.Evenifthemanagerorthepersonresponsible
forthiscampaigndoesnotknowinintimatedetailhowabatteryworks,heorshe
must have the ability to evaluate the validity of the experiment, and be able to
understand the analysis, results, and implications. The same example could be
viewed from a different perspective: a chemical engineer is working on a new
typeofbatteryandwantstocompareitwithotherbrandscurrentlyavailableinthe
market inorder to determinethe efficiency ofnew electrolyte solutions. What we
are trying to say is that the field of study does not change how we analyze and
interpretthedata,althoughourconclusionswilldependonourinitialobjectives.
Organization and Coverage
We have made some tough choices for which topics to include. Our goal was to
writeabookthatdiscussedthemostimportantandcommonlyusedmethodsinthe
fieldofexperimentaldesign.Wecoverextensivelythetopicsoftwo-levelcomplete
factorial designs, two-level fractional-factorial designs, and three-level complete
factorial designs, and their use in practice in depth. In the interest of space, we
prepare readers to study three-level fractional-factorial designs elsewhere and we
provideourfavoritereferencesonthetopic.Thetextcontainsachapterdevotedto
theuseofTaguchimethodsanditscomparisontomoretraditionaloptions,atopic
whichisnotcommonlyfoundintheliterature.Inthisnewedition,wealsoinclude
someadditionalchapterson(simpleandmultiple)regressionanalysisandmixture
designs.
This book provides a choice of material for a one-semester course. In the
authors’ experience, the entire text would likely require a period of time longer
thanonesemester.Twooftheauthorshavealsosuccessfullyusedpartsofmostof
thechaptersinthistextinanundergraduatecourseinmarketingresearch.Thefirst
edition of the book is currently used as reference material for a professional
education course offered at MIT, which once again indicates the need for more
accessible books for these professionals. Naturally, the 18 chapters in this new
edition comprise our choice of topics; however, most of Chaps. 7, 13, 14, 15, 16,
and 17 can be replaced by other material preferred by the instructor without
compromising the integrity of the remaining chapters. One might also choose to
viii Preface
covervariousothersubsetsofchapters;forexample,onecancoverChaps.1,2,3,4,
5,6,7,8,9,10,11,12,13,and17onmixturedesignsinaseamlessway.
Withtheadditiontonewchapters,thisversionisorganizedinfourparts:
Part I – Statistical Principles for Design of Experiments, Chaps. 2, 3, 4, and 5
cover the basic statistical principles that are necessary for our study of design of
experiments, including one-factor designs, analysis of variance (ANOVA), multi-
ple comparison testing, orthogonality, and orthogonal decomposition. In Chap. 3,
entitled Some Further Issues in One-Factor Designs and ANOVA, we introduce
severaltopicsthatarewithusthroughoutthetext,suchasunderlyingassumptions
of the F-test, hypothesis testing (encompassing the concept and calculation of
power),andnonparametrictests(inthischapter,theKruskal-Wallistest).Follow-
ing this chapter, we cover the topics of multiple-comparison testing and the
orthogonal partitioning of sums of squares, topics that take the macro result of
theF-testandinquiremoredeeplyintothemessagethedatahaveforus.
PartII–IdentifyingActiveFactors,Chaps.6,7,and8includetheintroductionto
two-factorexperimentation–bothcross-classificationdesigns(includingintroduc-
tiontotheconceptsofblockingandinteraction)andnesteddesigns.Italsoincludes
designs having three or more factors – notably, Latin-square and Graeco-Latin
squaredesigns.Forthemostpart,thedesignandanalysisconceptsinChaps.6,7,
and8donotvarysubstantiallyasafunctionofthenumberoflevelsofthefactors,
butfocusonthenumberoffactorsunderstudy.
PartIII–StudyingFactors’Effects,Chaps.9,10,11,12,and13discussthetwo-
and three-level experimentation, including factorial and confounding designs with
factorsattwolevels,fractional-factorialdesignswithfactorsattwolevels,anddesigns
withfactorsatthreelevels.ItalsoincludesanintroductiontoTaguchimethods.
Part IV – Regression Analysis, Response Surface Designs, and Other Topics,
Chaps. 14, 15, 16, 17, and 18 wrap up with introductory chapters on simple and
multiple regression, followed by an introduction to response-surface methods and
mixture designs, and a concluding chapter discussing the literature and resourcesin
thefieldofexperimentaldesign,ourchoicesoftextsandothersourcesasreferencesfor
specifictopics,andthediscussionofvarioustopicsnotcoveredinthetext.Although
several of our references are quite recent, many references are from the 1980s and
earlier. In our view, the best references for many of the fundamental topics are
relativelyoldertextsorjournalarticles,andwehaveincludedtheseexcellentsources.
Statistical Software Packages
JMPversion13software(aregisteredproductofSASInstituteInc.)isusedforthe
experimental design and statistical analysis of the examples covered in the main
body of the chapters. When appropriate, we perform the same analysis using MS
Excel(Microsoft),SPSSStatisticsversion23(aregisteredproductofIBMCorp),
Preface ix
andthefreepackageRversion3.3(RFoundationforStatisticalComputing),andthe
resultsarepresentedasanappendixofthecorrespondingchapter.Thisissomething
newinthisedition,toimprovetheflowofthediscussioninthechapters,whilestill
providing the required information for those readers who prefer other software
packages. There are also other software packages not covered in this book (such
asMinitabandDesign-Expert)thatcanperformexperimentaldesignandanalysis.
Exercises
The quality of a text in the area of design and analysis of experiments is, to an
important extent, influenced by the end-of-chapter exercises. We present notonly
exercises that illustrate the basics of the chapter, but also some more challenging
exercisesthatgobeyondthetextexamples.Manyofthemorechallengingproblems
haveappearedontake-homeexamsincourseswehavetaught.Althoughafewother
textsalsooffersuchchallengingexercises,theyare,sadly,stillinthesmallminority.
Supplementary Material
Thedatasetsforthemanyexamplesusedinthisbookareprovidedassupplemen-
tarymaterial,inadditiontodataformostend-of-chapterexercises.
Acknowledgments
Many people deserve our thanks for their contributions toward making this book
what it is. First, we are grateful to the several individuals who gave us the
opportunitytobeexposedtoalargevarietyofapplicationsofexperimentaldesign
to real-world situations. Most notable among them is Dr. Kevin Clancy,
Ex-Chairman and CEO of Copernicus Marketing Consulting and Research. For
many years, working with Kevin throughout various incarnations of his company
and with many excellent coworkers such as Dr. Steven Tipps, Robert Shulman,
Peter Krieg, and Luisa Flaim, among others, author PDB has observed more
experimental design application areas, discussed more experiments, and designed
more experiments than would seem possible. Many of the examples in this book
havetheirbasisinthisexperience.AnotherpersontobethankedisDouglasHaley,
former Managing Partner of Yankelovich Partners, who also afforded PDB the
opportunity to be exposed to a large variety of experimental design application
areas.Manyotherindividuals–toonumeroustolist–havealsoprovidedPDBwith
consulting experience in the field of experimental design, which has contributed
significantlytothesetofexamplesinthisbook.
x Preface
Author REM acknowledges the influence of his many colleagues, and particu-
larlyDr.LewisE.Franks,atBellTelephoneLaboratories.BellLabswasformany
years the country’s premier R&D organization, where the commitment to funda-
mental understanding was endemic. Many of the principles and techniques that
constitutetheessenceofexperimentaldesignweredeveloped atBellLabs andits
sisterorganization,WesternElectric.REMexpresseshisgratitudetohiscolleague
and coauthor, PDB, who contributed greatly to the depth and breadth of his
knowledgeandunderstandingofDOE.And,finally,REMgratefullyacknowledges
the influence of his first teacher, his father, Edward, who showed by example the
importance ofacommitment toquality inallendeavors, and his mother, Eleanor,
whowastheinspirationforbothfatherandson.
AuthorGBCacknowledgestheencouragementprovidedbyherPhDsupervisor,
Dr. Su-Ling Brooks. GBC is also grateful for the continuous supportand mentor-
shipprovidedbyDr.Bergersinceshemethimattheprofessionaleducationcourse.
Shealsoacknowledgesoneofthemanagersshehadworkedwithwhoclaimedthat
“you cannot change many variables at the same time as you wouldn’t be able to
assesstheirimpactinthefinalproduct”–infact,youcanandthemethodsdescribed
inthisbookareproofofit!
AveryspecialthankyouisdueposthumouslytoProfessorHaroldA.Freemanof
theEconomicsDepartmentatMIT.ProfessorFreemanwasoneof“thegreatones,”
both as a statistician and teacher of experimental design as well as, more impor-
tantly,aperson.ProfessorFreeman,whodiedatage88inMarch1998,wasPDB’s
experimentaldesignteacherandmentor,instillinginhimaloveforthesubjectand
offering him his first opportunity to teach experimental design in 1966, while a
graduate student at MIT. Professor Freeman’s teaching, as well as his way of
teaching,hashadacontinuingandprofoundeffectonPDB’steachingandwriting
inthefieldofexperimentaldesign.Ifthisbookisdedicatedtoanyoneindividual,
thisindividualis,indeed,HaroldA.Freeman.
Finally, thanks are due to our families for affording us the ability to focus on
writing this book. Susan Berger patiently waited for her husband to “tear himself
away”fromthecomputerto(finally)joinherfordinner.Sheoftenwonderedifhe
knew she was in the house. Mary Lou Maurer was never too busy to help her
digitallyimpairedhusbandwiththetyping,alongwithprovidingcopiousamounts
of encouragement and coffee. Luiz Augusto Pacheco was a constant questioner
even though most topics covered in this book were abstract to him and gave
significantinsightswheneverhiswifeneededthem.
Thankstoallofyou.
Waltham,MA,USA PaulD.Berger
Boston,MA,USA RobertE.Maurer
Ithaca,NY,USA GiovanaB.Celli
