Six sigma and beyond statistics and probability, volume III

SixSigmaandBeyond:Statisticsand
Probability,VolumeIII
ISBN:1574443127
byD.H.Stamatis
St.LuciePress©2003(368pages)
Thistextexplainsthetoolsofstatisticsandhow
toapplythemeffectivelytoimproveprocesses
andprofitabilityinanorganization,andalso
delineatestheimportanceofcollecting,
analyzing,andinterpretingdata.
TableofContents
SixSigmaandBeyond—StatisticsandProbability,
VolumeIII
Preface
PartI-EssentialConceptsofStatistics

Introduction
Chapter1 - DesigningandusingFormsforStudies
Chapter2 - CountingFrequencies
Chapter3 - SummarizingData
Chapter4 - WorkingwiththeNormalDistribution
TestingHypothesesAboutTwo
Chapter5 IndependentMeans
TestingHypothesesAboutTwo
Chapter6 DependentMeans
Chapter7 - ComparingSeveralMeans
Chapter8 - MeasuringAssociation
Chapter9 - CalculatingRegressionLines
Chapter10 - CommonMiscellaneousStatisticalTests

Chapter11 - AdvancedTopicsinStatistics
Chapter12 - TimeSeriesandForecasting
PartII-EssentialConceptsofProbability

Chapter13 - FunctionsofRealandRandomVariables
Chapter14 - SetTheory
Chapter15 - PermutationsandCombinations
DiscreteandContinuousRandom
Chapter16 Variables
PartIII-Appendices

AppendixA - MatrixAlgebra:AnIntroduction
AppendixB - TheSimplexMethodinTwoDimensions
AppendixC - BernoulliTrials
AppendixD - MarkovChains
AppendixE - Optimization
AppendixF - RandomizedStrategies
AppendixG - LagrangeMultipliers
AppendixH - MonteCarloSimulation
AppendixI - StatisticalReportingContent
SelectedBibliography
Index
ListofFigures
ListofTables
ListofExamples


BackCover
Researchersandprofessionalsinallwalksoflifeneed
tousethemanytoolsofferedbythestatisticalworld,

butoftendonothavethenecessaryexperienceinboth
conceptandapplication.Nomatterwhatyour
profession,soonerorlaternumbersneedtobe
crunched,andoftenyouneedtounderstandhowtodo
it,andwhyitisimportant.Qualitycontrolisno
different.SixSigmaandBeyond:Statisticsand
Probabilitycoverstheconceptsofsomeuseful
statisticaltools,appropriateformulaeforspecifictools,
theconnectionofstatisticstoprobability,andhowto
usethem.
Thisvolumeintroducestherelationshipofstatistics,
probability,andreliabilityastheyapplytoqualityin
generalandtoSixSigmainparticular.Theauthor
bringsthetheoreticalintothepracticalbyproviding
statisticaltechniques,tests,andmethodsthatthe
readercanuseinanyorganization.Hereviewsbasic
parametricandnon-parametricstatistics,probability
conceptsandapplications,andaddressestopicsfor
bothmeasurableandattributecharacteristics.He
delineatestheimportanceofcollecting,analyzing,and
interpretingdatanotfromanacademicpointofview
butfromapracticalperspective.
Thisisnotatextbookbutaguideforanyone
interestedinstatistical,probability,andreliabilityto
improveprocessesandprofitabilityintheir
organizations.Whenyoubeginastudyofsomething,
youwanttodoitwell.Youwanttodesignagood


study,analyzetheresultsproperly,andpreparea

cogentreportthatsummarizeswhatyou'vefound.Six
SigmaandBeyond:StatisticsandProbabilityshows
youhowtousestatisticaltoolstoimproveyour
processesandgiveyourorganizationthecompetitive
edge.
AbouttheAuthor
D.H.Stamatis,Ph.D.,ASQC-Fellow,CQE,CMfgE,is
currentlypresidentofContemporaryConsultants,in
Southgate,Michigan.HereceivedhisB.S.andB.A.
degreesinmarketingfromWayneStateUniversity,his
Master'sdegreefromCentralMichiganUniversity,and
hisPh.D.degreeininstructionaltechnologyand
business/statisticsfromWayneStateUniversity.
Dr.Stamatisisacertifiedqualityengineerforthe
AmericanSocietyofQualityControl,acertified
manufacturingengineerfortheSocietyof
ManufacturingEngineers,andagraduateofBSIIsISO
9000leadassessortrainingprogram.
Heisaspecialistinmanagementconsulting,
organizationaldevelopment,andqualityscienceand
hastaughtthesesubjectsatCentralMichigan
University,theUniversityofMichigan,andFlorida
InstituteofTechnology.
Withmorethan30yearsofexperiencein
management,qualitytraining,andconsulting,Dr.
Stamatishasservedandconsultedfornumerous
industriesintheprivateandpublicsectors.His
consultingextendsacrosstheUnitedStates,Southeast

Asia,Japan,China,India,andEurope.Dr.Stamatishas
writtenmorethan60articlesandpresentedmany
speechesatnationalandinternationalconferenceson
quality.Heisacontributingauthorinseveralbooks
andthesoleauthorof12books.Inaddition,hehas
performedmorethan100automotive-relatedaudits
and25preassessmentISO9000audits,andhas
helpedseveralcompaniesattaincertification.Heisan
activememberoftheDetroitEngineeringSociety,the
AmericanSocietyforTrainingandDevelopment,the
AmericanMarketingAssociation,andtheAmerican
ResearchAssociation,andafellowoftheAmerican
SocietyforQualityControl.


SixSigmaandBeyond—Statisticsand
Probability,VolumeIII
D.H.Stamatis

ST.LUCIEPRESSACRCPressCompany
BocaRatonLondonNewYorkWashington,D.C.
LibraryofCongressCataloging-in-PublicationData
Stamatis,D.H.,1947Sixsigmaandbeyond:statisticsandprobability,volumeIII
p.cm.—(SixSigmaandbeyondseries)
Includesbibliographicalreferencesandindex.
ISBN1-57444-3127
1.Qualitycontrol—Statisticalmethods.2.Productionmanagement—
Statisticalmethods.3.Industrialmanagement.I.Title.II.Series.
TS156.S732001
658.5'62—dc212001041635

CIP
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regardedsources.Reprintedmaterialisquotedwithpermission,and
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Neitherthisbooknoranypartmaybereproducedortransmittedinany
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Printedonacid-freepaper
ToStephen
AbouttheAuthor
D.H.Stamatis,Ph.D.,ASQC-Fellow,CQE,CMfgE,iscurrently
presidentofContemporaryConsultants,inSouthgate,Michigan.He
receivedhisB.S.andB.A.degreesinmarketingfromWayneState
University,hisMaster'sdegreefromCentralMichiganUniversity,andhis
Ph.D.degreeininstructionaltechnologyandbusiness/statisticsfrom
WayneStateUniversity.


Dr.StamatisisacertifiedqualityengineerfortheAmericanSocietyof
QualityControl,acertifiedmanufacturingengineerfortheSocietyof
ManufacturingEngineers,andagraduateofBSIIsISO9000lead
assessortrainingprogram.
Heisaspecialistinmanagementconsulting,organizationaldevelopment,
andqualityscienceandhastaughtthesesubjectsatCentralMichigan
University,theUniversityofMichigan,andFloridaInstituteofTechnology.
Withmorethan30yearsofexperienceinmanagement,qualitytraining,
andconsulting,Dr.Stamatishasservedandconsultedfornumerous
industriesintheprivateandpublicsectors.Hisconsultingextendsacross
theUnitedStates,SoutheastAsia,Japan,China,India,andEurope.Dr.
Stamatishaswrittenmorethan60articlesandpresentedmany
speechesatnationalandinternationalconferencesonquality.Heisa
contributingauthorinseveralbooksandthesoleauthorof12books.In
addition,hehasperformedmorethan100automotive-relatedauditsand
25preassessmentISO9000audits,andhashelpedseveralcompanies
attaincertification.HeisanactivememberoftheDetroitEngineering
Society,theAmericanSocietyforTrainingandDevelopment,the
AmericanMarketingAssociation,andtheAmericanResearch

Association,andafellowoftheAmericanSocietyforQualityControl.
Acknowledgments
Inatypicalbook,theauthorbeginsbythankingseveralindividualswho
havehelpedtocompleteit.Inthismammothwork,somanypeoplehave
helpedthatIamconcernedthatImayforgetsomeone.
Thewritingofabookisacollectiveundertakingbymanypeople.Towrite
abookthatconveyshundredsofthoughts,principles,andwaysofdoing
thingsistrulyaHerculeantaskforoneindividual.SinceIamdefinitely
notaHerculesoraSuperman,Ihavedependedonmanypeopleover
theyearstoguidemeandhelpmeformulatemythoughtsandopinions
aboutmanythings,includingthiswork.Tothankeveryonebynamewho
hascontributedtothisworkwouldbeimpossible,althoughIamindebted
toallofthemfortheircontributions.However,someorganizationsand
individualsdostandbeyondtherest,andwithoutthem,thisserieswould


notbepossible.
SpecialthanksgotoDr.A.Stuartforgrantingmepermissiontouseand
adoptmuchofthediscussionondiscreterandomvariables,continuous
RVs,uniformandbetadistributions,functionsofrandomvariables
(tolerances),exponentialdistributionandreliability,andhypothesis
testingandOCcurvesinPartIIofthisvolume.Theworkwasadapted
fromthenotesofStatisticsandProbabilityforEngineersusedastraining
materialatFordMotorCompany.
SpecialthanksalsogotoDuxburryPressforgrantingmepermissionto
usethematerialonHolt'sModelfortrendandWinters'Modelfor
seasonalityandeconometricmodels.TheworkisbasedonManagerial
StatisticsbyS.C.Albright,W.L.Winston,C.J.ZappeandP.Kolesar,
publishedin2001.
Inaddition,specialthanksgotoPrenticeHallforgrantingmepermission

tousethematerialonthesummaryofdifferencesbetweenMANOVAand
discriminantanalysis,whatisconjointanalysis,usesofconjointanalysis,
whatiscanonicalcorrelation,andwhatisclusteranalysis.Theworkis
basedonMultivariateDataAnalysis,5thed.,byJ.F.Hair,R.E.Anderson,
R.L.Tathan,andW.C.Black,publishedin1998.
IwouldliketothankmycolleaguesDr.R.Rosa,H.Jamal,Dr.A.Crocker,
andDr.D.Demis,aswellasJ.StewartandR.Start,fortheircountless
hoursofdiscussionsinformulatingthecontentofthesevolumesintheir
finalformat.
Inaddition,IwanttothankJ.Malicki,C.Robinson,andS.Stamatisfor
theircomputerworkinpreparingsomeoftheearlierdraftsandfinal
figuresinthetext.
Iwouldliketothankasalwaysmypersonalinspiration,bouncingboard,
navigatorandeditor,Carla,forhercontinuallyenthusiasticattitudeduring
mymosttryingtimes.Especiallyforthisworkshehasdemonstrated
extraordinarypatience,encouragement,andunderstandinginputtingup
withme.
Specialthanksgototheeditorsoftheseriesfortheirsuggestionsand


improvementsofboththetextanditspresentationinthefinalformat.
Finally,mygreatestappreciationisreservedformyseminarparticipants
andthestudentsofCentralMichiganUniversitywho,throughtheirinput,
concerns,anddiscussions,havehelpedmetoformulatethesevolumes.
Withouttheiractiveparticipationandcomments,thesevolumeswould
neverhavebeenfinished.Ireallyappreciatetheireffort.


Preface
Thelong-rangecontributionofstatisticsdependsnotsomuchupon

gettingalotofhighlytrainedstatisticiansintoindustry,asitdoesin
creatingastatisticallymindedgenerationofphysicists,chemists,
engineers,andotherswhowillinanywayhaveahandindevelopingand
directingtheproductionprocessesoftomorrow.
W.A.ShewhartandW.E.Deming
Muchhasbeensaidaboutstatisticsandtheiruse.Often,though,we
statisticiansoverlookthediscussionoftheobviousassoonaswemove
awayfromtheacademicarena.Weexpectresearchersand
professionalsinallwalksoflifetousethemanytoolsofferedbythe
statisticalworld,butwehavefailedtoeducatethemappropriatelybothin
conceptandapplication.Thefocusofmoststatisticsbooksseemstobe
formulautilization.
Thisvolumewillattempttoexplainthetoolsofstatisticsandtoprovide
guidanceonhowtousethemappropriatelyandeffectively.Thestructure
ofthisworkisgoingtofollow(1)theconceptualdomainofsomeuseful
statisticaltools,(2)appropriateformulasforspecifictools,and(3)the
connectionbetweenstatisticsandprobability.
Thisvolumeisnotintendedtobeatextbook.Itisintendedtobea
generalmanualforpeoplewhoareinterestedinusingstatistical,
probability,andreliabilityconceptstoimproveprocessesandprofitability
intheirorganizations.
Thediscussionbeginswithveryelementaryissuesandprogressesto
someveryadvancedtoolsfordecision-making.Specifically,thebook
beginsbydelineatingtheimportanceofcollecting,analyzing,and
interpretingdata,fromapracticalperspectiveratherthananacademic
pointofview.Theassumptionisthatyou(thereader)areabouttobegin
astudyofsomething,andyouwanttodoitwell.Youwanttodesigna
goodstudy,analyzetheresultsproperly,andprepareacogentreportthat
summarizeswhatyouhavefound.

Becauseoftheseassumptions,thisbookdoesnotdwellonformulasand
significancetablesorproofsforthatmatter.Theassumptionisthata
statisticalsoftwarepackagewillbeutilized,andthatthereaderwill
benefitmorefromlearningtounderstandandinterprettheresults
generatedbythatsoftwarethanfrommemorizingformulas.


PartI:EssentialConceptsofStatistics


ChapterList
Chapter1:DesigningandusingFormsforStudies
Chapter2:CountingFrequencies
Chapter3:SummarizingData
Chapter4:WorkingwiththeNormalDistribution
Chapter5:TestingHypothesesAboutTwoIndependentMeans
Chapter6:TestingHypothesesAboutTwoDependentMeans
Chapter7:ComparingSeveralMeans
Chapter8:MeasuringAssociation
Chapter9:CalculatingRegressionLines
Chapter10:CommonMiscellaneousStatisticalTests
Chapter11:AdvancedTopicsinStatistics
Chapter12:TimeSeriesandForecasting


Introduction
Thisintroductionwilldiscussthebasicconceptsofallstatistics.The
intentoftheintroductionistosensitizethereadertotheimportanceof
takingstatisticsintoconsiderationinthedesignandplanningof

experiments.Unlesstheexperimenterplansastudyappropriately,
accountsforcertainissuesthatareinherentinanystudy,and
understandswhatisneededforasuccessfulexperiment,allwillbefor
naught.


WHATAREDATA?
Everythingwedoisbasedondata.So,thequestionquiteoftenis:should
thewordbedatumordata?Grammaticallyspeaking,thesingularwordis
datumandthepluralisdata.However,becausegenerallyspeakingwe
havemorethanone,theconventionisthatweusedata.Incommon
usage,dataareanymaterialsthatserveasabasisfordrawing
conclusions.(Noticethatthewordweuseis"materials."Thatisbecause
materialsmaybequantifiableornumericalandmeasurableoronthe
otherhandmaybeattributeorqualitative.Ineithercasetheycanbe
usedfordrawingconclusions.)Drawingconclusionsfromdataisan
activityinwhicheveryoneengages—bankers,scholars,politicians,
doctors,andcorporatepresidents.Intheory,webaseourforeignpolicy,
methodsoftreatingdiseases,corporatemarketingstrategies,and
processefficiencyandqualityon"data."
Datacomefrommanysources.Wecanconductourownsurveysor
experiments,lookatinformationfromsurveysotherpeoplehave
conducted,orexaminedatafromallsortsofexistingrecords—suchas
stocktransactions,electiontallies,orinspectionrecords.Butacquiring
dataisnotenough.Wemustdeterminewhatconclusionsarejustified
basedonthedata.Thatisknownas"dataanalysis."Peopleand
organizationsdealwithdatainmanydifferentways.Somepeople
accumulatedatabutdonotbothertoevaluateitobjectively.Theythink
thattheyknowtheanswersbeforetheystart.Otherswanttoexaminethe
databutdonotknowwheretobegin.Sometimespeoplecarefully

analyzedata,butthedataareinappropriatefortheconclusionsthatthey
wanttodraw.Unlessthedataarecorrectlyanalyzed,the"conclusions"
basedonthemmaybeinerror.Asuperiortreatmentforadiseasemay
bedismissedasineffectual;youmaypurchasestocksthatdonot
performwellandloseyourlife'ssavings;youmaytargetyourmarketing
campaigntothewrongaudience,costingyourcompanymillionsof
dollars;oryoumayadjustthewrongiteminaprocess,andasa
consequence,youmayaffecttheresponseofthecustomerinavery
unexpectedway.Theconsequencesofbaddataanalysiscanbesevere
andfar-reaching.Thatiswhyyouneedtoknowhowtoanalyzedatawell.


Youcananalyzedatainmanydifferentways.Sometimesallyouneedto
doisdescribethedata.Forexample,howmanypeoplesaytheyare
goingtobuyanewproductyouareintroducing?Whatproportionofthem
aremenandwhatproportionarewomen?Whatistheiraverageincome?
Whatproductcharacteristicisthecustomerdelightedwith?Inother
situations,youwanttodrawmorefar-reachingconclusionsbasedonthe
datayouhaveathand.Youwanttoknowwhetheryourcandidatestands
achanceofwinninganelection,whetheranewdrugisbetterthanthe
oneusuallyused,orhowtoimprovethedesignofaproductsothatthe
customerwillbereallyexcitedaboutit.Youdonothaveallofthe
informationyouwouldliketohave.Youhavedatafromsomepeopleor
samples,butyouwouldliketodrawconclusionsaboutamuchlarger
audienceorpopulation.
Atthisjunctureyouranswermaybe,"Idonothavetoworryaboutallthis
becausethecomputerwilldoitforme."Thatisnotanabsolutetruth.
Computerssimplifymanytasks,includingdataanalysis.Byusinga
computertoanalyzeyourdata,yougreatlyreduceboththepossibilityof
errorandthetimerequired.Learningaboutcomputersandpreparing

dataforanalysisbycomputerdorequiretime,butinthelongrunthey
substantiallydecreasethetimeandeffortrequired.Usingacomputer
alsomakeslearningaboutdataanalysismucheasier.Youdonothaveto
spendtimelearningformulas.Thecomputercandothecalculatingfor
you.Instead,youreffortcangointothemoreinterestingcomponentsof
dataanalysis—generatingideas,choosinganalyses,andinterpreting
theirresults.
Becausecalculationsarethecomputer'sjob,notyours,thisvolumedoes
notemphasizeformulas.Itemphasizesunderstandingtheconcepts
underlyingdataanalysis.Thecomputercanbeusedtocalculateresults.
Youneedtolearnhowtointerpretthem.


DESCRIBINGDATA
Onceyouhavepreparedadatafile,youarereadytostartanalyzingthe
data.Thefirststepindataanalysisisdescribingthedata.Youlookatthe
informationyouhavegatheredandsummarizeitinvariousways.You
countthenumberofpeoplegivingeachofthepossibleresponses.You
describethevaluesbycalculatingaveragesandseeinghowmuchthe
responsesvary.Youlookatseveralcharacteristicstogether.Howmany
menandhowmanywomenaresatisfiedwithyournewproduct?What
aretheiraverageages?Youalsoidentifyvaluesthatappeartobe
unusual,suchasagesintheonehundredsorincomesinthemillions,
andyouchecktheoriginalrecordstomakesurethatthesevalueswere
pickedupcorrectly.Youdonotwanttowastetimeanalyzingincorrect
data.


TESTINGHYPOTHESES
Sometimesyouhaveinformationavailableforeveryoneoreverything

thatyouareinterestedindrawingconclusionsabout,andallyouneedto
doissummarizeyourdata.Butusuallythatisnotthecase.Instead,you
usuallywanttodrawconclusionsaboutmuchlargergroupsofpeopleor
objectsthanthoseincludedinyourstudy.Youwanttoknowwhat
proportionofallpurchasersofyourproductaresatisfiedwithit,basedon
theopinionsoftherelativelysmallnumberofpurchasersincludedinyour
survey.Youwanttoknowwhetherbuyersofyourproductdifferfrom
nonbuyers.Aretheyyounger,richer,bettereducated?Youwanttobe
abletodrawconclusionsaboutallbuyersandnonbuyersbasedonthe
peopleyouhaveincludedinyourstudy.
Todothis(andunderstandit),youhavetolearnsomethingabout
statisticalinference.Laterchaptersinthisvolumewillshowyouhowto
testhypothesesanddrawconclusionsaboutpopulationsbasedon
samples.Youwilllearnhowtotestwhetheryouhavesufficientevidence
tobelievethatthedifferencesorrelationshipsyoufindinyoursampleare
trueforthewholepopulation.


DESCRIBINGRELATIONSHIPS
Youoftenwanttodeterminewhattherelationshipisbetweentwo
variables.Forexample,whatistherelationshipbetweendollarsspenton
advertisingandsales?Howcanyoupredicthowmanyadditionalsalesto
expectifyouincreaseyouradvertisingbudgetby25%?Whatisthe
relationshipbetweenthedosageofadrugandthereductioninblood
pressure?Howcanyoupredicttheeffectonbloodpressureifyoucutthe
doseinhalf?Youcanstudyandmodeltherelationshipbetweenpairsof
variablesinmanydifferentways.Youcancomputeindexesthatestimate
thestrengthoftherelationship.Youcanbuildamodelthatallowsyouto
predictvaluesofonevariablebasedonthevaluesofanother.Thatis
whatthelastpartofthebookisabout.

Youmuststateyourideasclearlyifyouplantoevaluatethem.This
adviceappliestoanykindofworkbutespeciallytoresearchdesignand
statisticalanalysis.Beforeyoubeginworkingondesignandanalysis,you
needtohaveaclearlydefinedtopictoinvestigate.


ASKINGAQUESTION
Youmayhaveageneralsuspicionthatsmokinglessmakespeoplefeel
better.YoumaythinkthatcomponentAisbetterthancomponentB.Or
youmayhaveanideaforastudymethodthatwillmakepeoplelearn
more.Beforeyoubeginastudyaboutsuchintuitions,youshouldreplace
vagueconceptssuchas"feelingbetter"or"smokingless"or"learning
more"withdefinitionsthatdescribemeasurementsthatyoucanmake
andcompare.Youmightdefine"better"withaspecificperformance
improvementorareductioninfailure.Youmightreplace"feelingbetter"
withanobjectivedefinitionsuchas"thesubjectexperiencesnopainfora
week."Oryoumightrecordtheactualdosageofmedicationrequiredto
controlpain.Ifyouareinterestedinsmoking,youneedalotof
informationtodescribeit.Whatdoeseachofthesubjectssmoke—a
pipe,cigars,orcigarettes?Howmuchtobaccodothesubjectsuseina
day?Howlonghavetheybeensmoking?Hasthenumberofcigarettes
(orcigarsorpipes)thattheysmokechanged?
Ontheotherhand,youmustbalanceyourscientificcuriositywiththe
practicalproblemsofobtaininginformation.Ifyoumustrelyonpeople's
memory,youcannotaskquestionslike"Whatdidyouhavefordinnerten
yearsago?"Youmustaskquestionsthatpeoplewillbeabletoanswer
accurately.Ifyouaretryingtoshowarelationshipbetweendietand
disease,forexample,youcannotrelyonpeople'smemoryofwhatthey
ateatindividualmeals.Instead,youhavetobesatisfiedwithoverall
patternsthatpeoplecanrecall.Someinformationissimplynotavailable

toyou,howevermuchyouwouldliketohaveit.Itisbettertorecognize
thisfactbeforeyoubeginastudythanwhenyougetyourquestionnaires
backandfindthatpeoplewerenotabletoansweryourfavoritequestion.
Ifyouthinkaboutyourtopicinadvance,youcansubstituteabetter
question—onethatwillgiveyouinformationyoucanuse,evenifitisnot
theinformationyouwishyoucouldhave.


WHATINFORMATIONDOYOUNEED?
Acriticalstepinthedesignofanystudyisthedecisionaboutwhat
informationyouaregoingtorecord.Ofcourse,youcannotrecordevery
possiblepieceofinformationaboutyoursubjectsandtheirenvironment.
Therefore,youshouldthinkhardaboutwhatinformationyouwilltryto
get.Ifyouaccidentallyforgettofindoutaboutanimportantcharacteristic
ofyoursubjects,youmaybeunabletomakesenseofthepatternsyou
findinyourdata.Whenindoubt,itisusuallybettertorecordmore
informationthanless.Itiseasytoleaveunnecessaryvariablesoutof
yourdataanalysis,butitisoftendifficult(andexpensive)togobackand
gatheradditionalinformation.Forexample,ifyouarestudyingwhattypes
ofpeoplearelikelytobuyahigh-pricednewproduct,youmaynotbe
abletoadequatelycomparebuyerswithnonbuyersifyouforgetto
includeinformationaboutincome.


DEFININGAPOPULATION
Whenyouconductastudy,youwantyourconclusionstobefar-reaching.
Ifyouareapsychologystudent,youmaywantyourresultstoapplytoall
laboratoryrats,notjusttheonesinyourlab.Similarly,ifyouaredoinga
marketresearchsurveyonwhetherpeopleinLosAngeleswouldbuy
disposableumbrellas,youmaywanttodrawconclusionsabout

everybodyinthecity.Ifyouareanengineerandyouareinvolvedinthe
developmentofaparticularproduct,youwanttoknowwhatkindofa
baseorpopulationtheproductisfor.Thepeopleorobjectsaboutwhom
youwanttodrawconclusionsarecalledapopulation.
Oneoftheearlystepsinanystudyisnailingdownexactlywhatyouwant
yourpopulationtobe.Themoredefiniteyouareindefiningpopulations,
thebetteryourunderstandingofsamplesandtheresultsofyourstudy
willbe.
Definingapopulationmayseemstraightforward,butoftenitisnot.
Supposethatyouareacompanypersonnelmanager,andyouwantto
studywhypeoplemisswork.Youprobablywanttodrawconclusionsonly
aboutemployeesinyourparticularcompany.Yourpopulationiswell
defined.However,ifyouareagraduatestudentwritingadissertation
aboutthesametopic,youfaceamuchmorecomplicatedproblem.Do
youwanttodrawconclusionsaboutprofessionals,laborers,orclerical
staff?Aboutmenorwomen?Whichpartoftheworldisofinterest—a
city,acountry,ortheworldasawhole?Nodoubt,you(andyouradvisor)
wouldbedelightedifyoucouldcomeupwithanexplanationfor
absenteeismthatwouldapplytoallsortsofworkersinallsortsofplaces.
Youarenotlikelytocomeupwiththatkindofexplanation,though.Even
ifyoudo,youarenotlikelytocomeupwiththeevidencetosupportit.
Allkindsofpeoplemissworkbecausetheyaresick,butunlikeothers,
thepresidentofMajorCorporationprobablydoesnotneedtostayhome
waitingforaphonetobeinstalled.Theafternoonshetakesofftoplay
golfwithhisbuddiesareprobablynotrecordedbythepersonnelofficeas
absenteeism,either.Peoplemissworkforlotsofreasons,andthe
reasonsarequitedifferentfordifferentkindsofemployees.Berealistic
andstudyonlyapartofthelaborforce.Absenteeismamonglaborersin

autofactoriesinDetroit,forexample,isaproblemwithawell-defined
populationaboutwhichyouwouldhaveafightingchancetodrawsome
interestingconclusions.


DESIGNINGASTUDY
Evenwhenthepopulationofinterestseemstobewelldefined,youmay
notactuallybeabletostudyit.Ifyouareevaluatinganewmethodfor
weightloss,youwouldideallyliketodrawconclusionsabouthowwellit
worksforalloverweightpeople.Youcannotreallystudyalloverweight
people,though,orevenagroupthatistypicalofalloverweightpeople.
Peoplewhodonotwanttoloseweightorwhohavebeendisheartened
bypasteffortstoreducemaynotagreetotryyetanothermethod.You
willprobablybeabletotryoutyournewmethodonlyonpeoplewhowant
toloseweightandwhohavenotgivenuptrying.Thesepeople,notall
overweightpeople,formyourpopulation.
Rememberthatapopulationdefinedrealisticallyinthiswaymaybe
differentfromtheidealpopulation.Forexample,thepopulationinyour
weightlossstudymaybelighter,younger,orhealthierthantheideal
populationofalloverweightpeople.Therefore,yourconclusionsfrom
studyingpeoplewhowanttoloseweightdonotnecessarilyapplyto
peoplewhoarenotmotivated.Forexample,thetreatmentmayhave
someunpleasantconsequences,suchasmakingpeoplewanttochew
onthenearestthingavailable,suchasgum,apencil,orthecornerofa
desk.Peoplewhoreallywanttoloseweightmaybewillingtoputupwith
suchminorinconveniencesinordertoreachtheirgoal.Peoplewhodo
notcaremuchabouttheirweightprobablywillnotbe.Thus,thenew
treatmentmayworkquitedifferentlyforthosewhoaremotivatedversus
thosewhoarenot.