Statistics for Archaeologists: A Common Sense Approach PDF
Preview Statistics for Archaeologists: A Common Sense Approach
Statistics for Archaeologists INTERDISCIPLINARYCONTRIBUTIONSTOARCHAEOLOGY SeriesEditor:JelmerEerkens,UniversityofCaliforniaBerkeley,Berkeley,CA,USA FoundingEditor:RoyS.Dickens,Jr.LateofUniversityofNorthCarolina,ChapelHill,NC,USA Foracompletelistoftitlesinthisseries,pleasevisittheseriesonlineat:http://www.springer.com/series/6090 THEARCHAEOLOGIST’SLABORATORY TheAnalysisofArchaeologicalData E.B.Banning AURIGNACIANLITHICECONOMY EcologicalPerspectivesfromSouthwesternFrance BrookeS.Blades CASESTUDIESINENVIRONMENTALARCHAEOLOGY,2NDEDITION ElizabethJ.Reitz,MargaretScarry,andSylviaJ.Scudder EMPIREANDDOMESTICECONOMY TerenceN.D’AltroyandChristineA.Hastorf EUROPEANPREHISTORY:ASURVEY EditedbySaurunasMiliasuskas THEEVOLUTIONOFCOMPLEXHUNTER-GATHERERS ArchaeologicalEvidencefromtheNorthPacific BenFitzhugh FAUNALEXTINCTIONINANISLANDSOCIETY PygmyHippotamusHuntersofCyprus AlanH.Simmons AHUNTER-GATHERERLANDSCAPE SouthwestGermanyintheLatePaleolithicandNeolithic MichaelA.Jochim MISSISSIPPIANCOMMUNITYORGANIZATION ThePowersPhaseinSoutheasternMissouri MichaelJ.O’Brien NEWPERSPECTIVESONHUMANSACRIFICEANDRITUALBODY TREATMENTSINANCIENTMAYASOCIETY EditedbyVeraTieslerandAndreaCucina REMOTESENSINGINARCHAEOLOGY EditedbyJamesWisemanandFaroukEl-Baz THESCIOTOHOPEWELLANDTHEIRNEIGHBORS BioarhcoaelogicalDocumentationandCulturalUnderstanding ByD.TroyCaseandChristopherCarr THETAKINGANDDISPLAYINGOFHUMANBODYPARTSASTROPHIESBYAMERINDIANS EditedbyRichardJ.ChaconandDavidH.Dye Statistics for Archaeologists A Commonsense Approach Second Edition Robert D. Drennan 123 Dr.RobertD.Drennan UniversityofPittsburgh Dept.Anthropology PittsburghPA15260 USA [email protected] ISSN1568-2722 ISBN978-1-4419-0412-6 e-ISBN978-1-4419-0413-3 DOI10.1007/978-1-4419-0413-3 SpringerDordrechtHeidelbergLondonNewYork LibraryofCongressControlNumber:2009926038 (cid:2)c SpringerScience+BusinessMedia,LLC2004,2009 Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewritten permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY10013, USA),except forbrief excerpts inconnection with reviews orscholarly analysis. Usein connectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware, orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden. Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyare notidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubject toproprietaryrights. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface to the Second Edition Thisbookisintendedasanintroductiontobasicstatisticalprinciplesandtechniques forthearchaeologist.Itgrowsprimarilyfrommyexperienceinteachingcoursesin quantitative analysis for undergraduateand graduate students in archaeologyover a number of years. The book is set specifically in the contextof archaeology,not because the issues dealt with are uniquely archaeological in nature, but because manypeoplefinditmucheasiertounderstandquantitativeanalysisinafamiliarcon- text–oneinwhichtheycanreadilyunderstandthenatureofthedataandtheutility ofthetechniques.Theprinciplesandtechniques,however,areallofmuchbroader applicability. Physical anthropologists, cultural anthropologists, sociologists, psy- chologists,politicalscientists,andspecialistsinotherfieldsmakeuseofthesesame principlesandtechniques.Theparticularmixoftopics,therelativeemphasisgiven them,andtheexactapproachtakenhere,however,doreflectmyownviewofwhat ismostusefulintheanalysisofspecificallyarchaeologicaldata. It is impossible to fail to notice that many aspects of archaeological informa- tionarenumerical,andthatarchaeologicalanalysishasanunavoidablyquantitative component. Standard statistical approaches are commonly applied in straightfor- ward as well as unusualand ingeniousways to archaeologicalproblems,and new approaches have been invented to cope with the special quirks of archaeological analysis.Theliteratureonquantitativeanalysisinarchaeologyhasgrowntoprodi- gioussize.Someofthisliteratureisextremelygood,whilesomeofitrevealsonly thatpublishingonstatisticsinarchaeologyisanactivityopeneventothosewhose comprehension of the most fundamental statistical principles is primitive at best. The article attempting to point out which published work fits into which of these categories has itself become a recognizable genre. This book does not attempt to evaluate or criticize in such a mode, but it is motivated in part by the perception that, as a group,those of us responsiblefor training archaeologistsin quantitative analysis can claim only mixed success to date. Consequently, this book is in part a discussionof howquantitativedataanalysisis donein archaeologybutin larger part a discussion of how quantitative data analysis could be done in archaeology. Itsfocusisresolutelyonsomefundamentalprinciplesandhowtheycanbeapplied most usefully in archaeology.It is tempting to discuss the numerousvariationsin v vi PrefacetotheSecondEdition theseapplicationsthatmightbemadeinanalyzingarchaeologicaldataandtopro- videexamplesofwaysinwhichtheseprincipleshaveactuallybeenputtoworkby archaeologists.Ihave,however,attemptedtoresistthesetemptationsinaneffortto keepthefocusfirmlyonbasicprinciplesandtoprovidebriefandclearexplanations ofthem.Itis to maintainsimplicityandclaritythatboththe examplesused inthe textand the practiceproblemsat the endsof the chaptersare made up ratherthan selectedfromrealarchaeologicaldata.Iassumethatthereadersofthisbookknow enoughaboutarchaeologynottoneeddescriptionsandpicturesofpostholes,house floors, scrapers, or sherds – that we all know what it means to say that we have conductedaregionalsurveyandmeasuredtheareasof53sites. Mostofthe techniquesin thisbookare fairlystandard,eitherinthe “classical” statisticsdevelopedbetween1920and1950orinthemorerecent“exploratorydata analysis”school.Theapproachor,perhapsmoreimportant,thegeneralattitudeof thisbookderivesultimatelyfromtheworkofJohnW.Tukeyandhiscolleaguesand students,progenitorsofexploratorydataanalysis,orEDAforshort.Asisusualin generalbooksonstatistics,Ihavenotincludedbibliographiccitationsinthetext,but SuggestedReadingappearsatthe end.Thisbookleanstowardthe terminologyof EDA,althoughtheequivalentmoretraditionaltermsareusuallymentioned.Where it makes the explanations easier to understand in the context of archaeology, the terminologyusedhereissimplynonstandard. Archaeologists(andothers)sometimesareaswaryofstatisticsasschoolchildren areoftheclassroomholdingthemostimposingdisciplinarianamongtheteachers. Statistics seems a place filled with rules the rationale of which is opaque, but the slightest infraction of which may bring a painful slap across the knuckles with a ruler. This attitude has certainly been reinforced by critiques that take published workin archaeologyto task forbreakingsacredstatistical rules.Itmaycomeasa surprisetomanytolearnthatanumberofconflictingversionsexistofmanystatis- ticalrules.Statisticians,likethepractitionersofanyotherdiscipline,oftendisagree aboutwhatareproductiveapproachesandlegitimateapplications.Useofstatistical tools often involves making subjective judgments. In an effortto providea sound basisforsuchjudgments,introductorytextsoftenattempttoreducethemtoclear- cutrules,therebycreatingconsiderableconfusionaboutwhatarereallyfundamental principlesandwhataremerelyguidelinesfordifficultsubjectivedecisions. Inshort,therulesofstatisticswerenotonthestonetabletsMosesbroughtdown from the mountain. This book openly advocates the overthrow of rules found in some texts (by reason and common sense rather than force and violence). Since it is intended as an introduction to statistical principles, long arguments against alternative approaches are not appropriate. One issue, however, is of such central importance that it must be mentioned. The approach taken to significance testing heredoesnotinvolverigidinsistenceoneitherrejectingorfailingtorejecta“null hypothesis.”Inarchaeologyitismuchmoreinformativeinmostinstancessimplyto indicatehowlikelyitisthatthenullhypothesisiscorrect.Therigorousformulation of the null hypothesis, then, does not get the all-consuming attention here that is sometimes devoted to it elsewhere. In this approach to significance testing and to severalissuesrelatedtosampling,IhavefollowedtheleadofGeorgeCowgill(see PrefacetotheSecondEdition vii SuggestedReadingattheendofthebook),althoughIhavenotcarriedintopractice allofthethoroughlysensiblesuggestionshehasmade.(Oneobstacletofollowing someofhissuggestionscontinuestobe,ashenoted,thatfewoftheavailablestatis- ticscomputerprogramsprovidethenecessaryinformationintheiroutput.)Tothose who were taught that significance testing was built upon the rock of rejecting or failingtorejectthenullhypothesis,Irecommendthoughtfulattentiontothepoints Cowgillmakes. The approach taken to significance testing makes clear thinking about popu- lations, samples, and sampling procedures especially important. Indeed, in many contexts,itmakessimplyusingsamplestomakestatementsaboutthepopulations they came from a more appealingapproachthan significance testing. It is for this reason that samplesand sampling are given muchlengthier treatmenthere than is commonin introductorybookson statistics. PartI of this bookis aboutexploring batchesofnumbersinwaysthatareinterestingandusefulinandofthemselves,but that are especially chosen for their relevance when batches are considered sam- ples from larger populations. Part II develops this notion of batches as samples and makes a frontal assault on some of the central principles that relate samples topopulations.PartIIIpresentsafairlystandardsuiteofbasictestsofthestrength and significance of relationships between two variables, together with alternative approaches derived directly from sampling estimation. Part IV returns to take up a series of separate issues related to sampling – issues of special importance in archaeology.These chapters relate most directly to those in Part II, but they have beenplacedlaterontoavoidinterruptingthesteadyprogressionofideasthatlinks PartsIIandIII.Finally,PartVattemptsarapidintroductiontoexploringmultivari- atedatasetsforpatterning.Itbringsusbacktotheexploratorydataanalysisattitude moststronglyreflectedinPartI. Inarchaeology,asinmostfields,quantitativeconceptscomeeasilyandnaturally to some,andonlyatconsiderablecostto others.Theabsenceofa naturalinclina- tion toward numerical reasoning is often reinforced by the social acceptability of professingignoranceofmathematics–asocialacceptabilitynurturedbythenotion thatmathematicsisanarcaneandspecializedsubjectofnousetoverymanypeople. Anotherwisewell-educatedpersoncanprofessacompleteinabilitytocomprehend anythingaboutnumbersbeyondadditionandsubtractionwithoutincurringthedis- dain to be expected if he or she admitted to verbal skills so limited as to make everythinginthedailynewspaperbutthecomicsunintelligible. Varying degrees of natural talent should be no more surprising for mathemat- icsthanforwriting,playingfootball,orotheractivities.Theviewthatmathematics isonlyanecessaryevilofelementaryschool,however,aggravatestheproblemby encouragingthose who havefoundquantitativereasoningdifficultto minimizeits importanceandtoavoiddevelopingquantitativeskillsthatwouldbeusefultothem. Consequently,agoodmanystudentsseemtoembarkongraduatestudyofarchae- ologyequippedonlywithhighschoolalgebra–victims,perhaps,ofthesamekind of bad advice I myself received as a first-semester freshman in college, when my academic advisor scornfully dismissed the math course I intended to enroll in as irrelevanttomyinterests. viii PrefacetotheSecondEdition Thisbookiswritteninthehopeofprovidingusefultoolsforquantitativeanalysis inarchaeologytothosenaturallyadeptatquantitativereasoningaswellastothose whofindmathematicsnotonlydifficultbutevenintimidating.Itisnochallengeto presentstatisticstothosealreadycomfortablewithandadeptatmathematicalthink- ing;itrequiresonlyanudgeintherightdirection.Theperennialchallengeofbooks suchasthis,however,istopresentquantitativeanalysiseffectivelytothosetowhom itdoesnotcomenaturally.Itiswithparticularconcernforthislattergroupthatthe approachtakenherewaschosen.Partofthatapproachistoplungerightaheadtothe toolsthisbookisaboutwithoutaseriesofpreliminarychapterslayingbasicground- work,theimportanceofwhichonlybecomesapparentlateron.These“basics”are, instead,discussedasbrieflyaspossibleatthepointswheretheybecomerelevant. Fortunately,itispossibletoapproachbasicstatisticaltoolswithcommonsense andincommonlanguagesoastoconveynotonlythemechanicsofusingthetools ofstatisticsbutalsoagenuineunderstandingofthewaythetoolswork.Productive use of statistical tools in archaeology springs not so much from abstract mathe- maticalknowledgeasfromsolidintuitiveunderstandingofprinciples,appliedwith commonsense and unwaveringattention to the final productdesired – that is, the ultimate research objective. It is worth pausing to emphasize that this book, fun- damentally,isabouttools–toolsforidentifyingpatternsinnumbersandtoolsfor assessing howprecisely andhow reliablythe patternswe identifyin ourdata rep- resentrealpatternsin the broaderworldourconclusionsreallyareabout.Aswith carpenters’tools,forexample,skillfuluseofstatisticaltoolsdoesnotrequirecom- pleteknowledgeofhowthetoolsaremade.Consequently,Ihavenotattemptedto showhowstatisticalequationsarederivedfromcertainassumptionsthroughmathe- maticallogic(theapproachfollowedbysomebooksonstatistics).Aspowerfuland elegantasthe languageof abstractmathematicsmaybe, itremainsutterly impen- etrableto manyarchaeologists.I havealwaysfoundithelpfulto avoidan abstract mathematicalapproach.Thisseemsespeciallyimportanttothosealreadyfrightened atthethoughtofmathematics. Althoughlearning to use a table saw doesnotrequire developingthe ability to makeone,skillfuluseofatablesawdoesrequiresomeunderstandingoftheprinci- plesaccordingtowhichitdoesitswork.Failuretounderstandthesebasicprinciples willleadtoerroneousandunevencuttingandeventheoccasionalseveredfingeror worse.Injustthesameway,skillfuluseofstatisticaltoolsrequirestrueunderstand- ingofunderlyingprinciples.Withoutsuchunderstanding,evenverykeenstatistical toolsproduceonlycruderesults,andtheycancauseinjury(althoughgenerallynot thekindthatrequiresmedicalattention). For this reason, I have also tried to avoid the cookbook approach common to booksonappliedstatistics.Easyrecipesforstatisticalanalysisappealstrongly,espe- cially to those afraid of mathematics. No real mental labor seems to be required; no difficultconceptsneed be mastered;just carefullyfollow the instructions.This approachmayactuallyworkindisciplineswherecertainkindsofdataareregularly producedincertainformats.Onlythemostroutinedataanalysistaskscanbe suc- cessfullyhandledinthismanner,however,andarchaeologicaldataareneverroutine. The nature of the archaeologicalrecordand the mannerin which we mustextract PrefacetotheSecondEdition ix datafromitinevitablyproduceidiosyncrasiesthatpractitionersinotherdisciplines are taught to avoid through appropriate research design. Coping with such messy datarequiresthatthearchaeologisthaveabettergraspofunderlyingprinciplesthan acookbookapproachcanprovide. Thisbook,then,seeksamiddleground.Itattemptsmorethansimplyproviding instructionsforthe use ofstatistical tools;yetit makesno pretenseofprovidinga completemathematicaljustificationforthem.Itsaimistohelpthereaderunderstand the principlesunderlyingstatistical toolswellenoughto use themskillfullyin the contextof archaeologicaldata analysis. The reader I had in mind while writing is primarilythegraduateorundergraduatestudentofarchaeologytakingafirstcourse in archaeological data analysis. Like most textbooks, this is the book the author always wanted but never found for his own course. I hope it may also be useful to archaeologists who wish to develop or consolidate skills in statistical tool use whethertheyareenrolledincoursesornot. Thestatisticaltoolsdiscussedinthisbookbynomeansmakeupthecompleteset ever needed by the archaeologist.They are basic general-purposetools, but many otherspecializedtoolsexist.Someofthetoolspresentedherearequitesimpleand easytoapply,requiringnothingmorethanpencilandpaperorperhapsanordinary calculator.Othersaremorecomplicatedorinvolveverycumbersomecalculations.I takeitforgrantedthatanyseriousarchaeologicaldataanalysiseffortwillbeunder- takenwiththeaidofacomputer.Learningtousestatisticalsoftwarepackagesisbest incorporateddirectlyinto the processoflearningaboutthe statistical tools. I have thus omitted the often time-consumingand complexexplanationsof how to com- pute certain complicated statistics by hand. While calculating some things out by handcanfacilitateunderstanding,onesoonreachesthepointwherepreoccupation withthemechanicsofcalculationsinterfereswithattentionthatshouldbedevoted directlytounderlyingprinciples. (cid:2) ManyoftheresultsandexamplesinthisbookwereproducedwithSYSTATR ; otherpackagesthatcouldbeusedaretoonumerouseventolist.Sincethepossibili- tiesaresovaried(andchangesocontinually),itisuselesstoattempttoincorporate instructionsforusingstatisticalsoftwareintothisbook.Iassume,however,thatthe bookwillbeusedinconjunctionwithsomepackageofstatisticalprogramsandthe correspondingmanuals,andsomegeneralcommentsaboutusingsuch“statpacks” areincluded. Almostanysoftwarepackagewillprovideoptionsandchoicesnotdiscussedin thisbook.Somesoftwaremanualsprovidegoodexplanationsofwhattheseoptions are and bibliographic citations for those interested in learning more about them; other manuals do not. (This is one feature worth weighing in choosing statistical software.)Serendipitousencounterswithoptionsinstatisticalsoftwarecanprovide a usefulmeansof expandingone’sexpertisein quantitativeanalysis. On the other hand, they can distract the analyst’s attention from the task at hand to the many other tasks that could be performed but that there is really no need to perform. The professionalcarpenterdoesnot first choose a pretty tooland then go looking for something to use it on. Just so, the skilled data analyst first determines what analysistoperformandthenturnstopencil,paper,calculator,orcomputer(asmay
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