Statistics for Archaeologists: A Common Sense Approach

327 Pages·2009·4.81 MB·English

by  Robert D. Drennan (auth.)

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
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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