Social Inference and Mortuary Practices an Experiment in Numerical Classification

8/3/2019 Social Inference and Mortuary Practices an Experiment in Numerical Classification

1/16

Social Inference and Mortuary Practices: An Experiment in Numerical ClassificationAuthor(s): Joseph A. TainterSource: World Archaeology, Vol. 7, No. 1, Burial (Jun., 1975), pp. 1-15Published by: Taylor & Francis, Ltd.Stable URL: http://www.jstor.org/stable/124105 .

Accessed: 24/05/2011 02:31

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless

you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you

may use content in the JSTOR archive only for your personal, non-commercial use.

Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at .http://www.jstor.org/action/showPublisher?publisherCode=taylorfrancis. .

Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed

page of such transmission.

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of

content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms

of scholarship. For more information about JSTOR, please contact [email protected].

Taylor & Francis, Ltd. is collaborating with JSTOR to digitize, preserve and extend access to World

Archaeology.

http://www.jstor.org
http://www.jstor.org/action/showPublisher?publisherCode=taylorfrancishttp://www.jstor.org/stable/124105?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/action/showPublisher?publisherCode=taylorfrancishttp://www.jstor.org/action/showPublisher?publisherCode=taylorfrancishttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/stable/124105?origin=JSTOR-pdfhttp://www.jstor.org/action/showPublisher?publisherCode=taylorfrancis


2/16

World Archaeology Volume 7 No. z Burial

Social nferenceand mortuarypractices: nexperimentn numerical lassificationJosephA. Tainter

Mortuary practices and and social inferenceThe material residues created as the by products of human behaviour have beenrecognized for many years to contain the potential for yielding information concerningmany of the social characteristics of prehistoric communities. Of the various classes ofmaterial preserved in an archaeological context, perhaps no single category of data hasgreaterutility for the archaeologist attempting to draw social inferences than the physicalremains of mortuary procedures. The empirical justification for investigating the socialcorrelates of prehistoric mortuary patterns lies in recent cross-cultural studies ofethnographically recorded mortuary systems which have demonstrated that both thestructure and the organization of social systems, as well as the status positions occupiedby the members of such systems, are symbolized at death through variations in the formof mortuary ritual (Saxe 1970; Binford I97I). Since much of mortuary ritual is preservedin the archaeological record, the analysis of burial patterns can potentially yield detailedinformation concerning the social organization of prehistoric groups.Yet despite the potential for social inference which is inherent in mortuary data (aswell as other facets of the archaeological record), and despite the number of studieswhich have successfully concentrated on social modelling of prehistoric communities,no general goals for social inference have ever been set forth in the archaeologicalliterature. Archaeological residues provide the opportunity to determine several of thesocial characteristics of prehistoric groups. But there are two primary characteristics ofsocial systems which are of central importance in understanding the dynamic processesinvolved in social variation and change, and which should constitute a fundamental goalof archaeological identification. These central characteristics are the structure and theorganizationof social systems. The meanings of these two terms, as they are used here, aremost closely approximated by definitions derived from the fields of systems theory andcybernetics. The structure of a system is meant to indicate the number, nature andarrangement of its articulated components and subsystems (cf. Miller I965: 209), whileorganization is intended to encompass the constraints imposed upon the ranges ofbehaviour which may possibly be pursued by the elements of a social system (cf.Rothstein I958: 34-6). The determination of prehistoric social structure is in fact anessential first step in the study of mortuary patterning, for the analysis of organizationbecomes meaningful only when considered in relation to explicitly defined structures.Given the analytical priority of isolating structural patterns in mortuary data, an


3/16

z Joseph A. Tainterevaluation of the utility of different methods for such an isolation is required. Thispaper is intended to provide such an evaluation.

One element of social patterning which has been of perennial concern in archaeologicalstudies is the nature, or absence, or hierarchical rank grading. So universal is thesymbolization of rank differentiation at burial that it is possible to develop generalprinciples for interpreting status indicators which should be applicable in most, if notall, primary and undisturbed mortuary contexts. These interpretive principles deriveinitially from Arthur Saxe's observation (1970: 6) that the occasion of death and burialinvolves the participation in interment ritual of potentially the entire range of individualswho at any time may have entered into social relationships with the deceased. It followsfrom this observation, as Lewis Binford has suggested (197I: 17, 21), that there aregenerally two components of social significance which participate in structuring theform of mortuary ritual. The first is what in anthropological role theory (Goodenough1965) has been called the socialpersona of the deceased, a term which refers to the rangeof social identities characterizing a person for any given interaction. The second is thesize and internal composition of the social unit recognizing status responsiblities to theindividual. Given the generally pyramidal structure of rank networks, it follows thatincreased relative ranking of status positions in a social system will positively co-vary withincreased numbers of persons recognizing duty-status relationships with individualsholding such status positions. Lewis Binford (I97I: 21) proposes that such a largerarray of status relationships, which is characteristic of persons of high rank, will entitlethe deceased to a larger amount of corporate involvement in the act of interment, and to alarger degree of disruption of normal community activities for the mortuary ritual.Expanding upon this proposal, we may observe that both the amount of corporateinvolvement, and the degree of activity disruption, will positively correspond to theamount of energy expended in the mortuary act. Directionally, higher social rank of adeceased individual will correspond to greater amounts of corporate involvement andactivity disruption, and hence should result in the expenditure of greater amounts ofenergy in the interment ritual. Energy expenditure should in turn be reflected in suchfeatures of burial as size and elaborateness of the interment facility, method of handlingand disposal of the corpse, and the nature of grave associations. It is anticipated then thatthe amount of energy expended in mortuary ceremonialism is the key archaeologicalfeature reflecting variations in prehistoric rank structure.

Social structure and mortuary attribute classificationIn archaeological research, the process of identifying a system's structure must be keyedto the ethnographic observations that membership in the components of a social system issymbolized at death through variations in the form of mortuary ritual (Binford I971:i8-20). This ethnographic fact indicates that when a set of mortuary data has beensegregated into classes of burials accorded similar forms of interment, the resultantburial clusters can be expected to reflect at least a portion of the structural components ofthe prehistoric social system. It becomes immediately apparent that the isolation of thestructure of a past social system can be initiated through the derivation of a suitable


4/16

Social inferenceand mortuarypractices: an experiment n numericalclassification 3classification of mortuary attributes which can serve to identify sets of burials accordedsimilar forms of interment. The classification of burial data therefore constitutes themost basic and essential aspect of the study of mortuary practices, and considerable careis warranted in the selection of a method of classification.

One classificationprocedure which has been suggested for use with burial data is formalanalysis (Saxe 1970; Brown 1971), a technique which progressively subdivides a popula-tion on the basis of the presence or absence of all variables utilized, but without regard tothe possibility that attributes may have varying degrees of importance in the domain inquestion (for a discussion of formal analysis, see Kay 1966). Formal analysis is generallyan unworkable technique when large and diverse data sets are involved, and is addition-ally very susceptible to focusing the classification procedure on variables which reflectidiosyncratic variations peculiar to individual burials. This last factor is particularlynoticeable in several studies which have applied formal analysis to mortuary data, withresulting classifications which often contain clusters with only one burial each (DeckerI969; Finnerty et al. I970; King 1970; cf. Rodeffer 1973). It can be contended thatwhen formal classification procedures isolate individual burials, it is difficult to gaininformation concerning the structural components of a social system. Such com-ponents will most likely be identified by statistical classification procedures whichisolate sets of burials accorded similar forms of interment, rather than by formal pro-cedures which tend to key out individual burials.A number of such statistical classification procedures are available for use withmortuary data, but the very range of these methods leads to the central problem con-sidered in this paper: which classification algorithm is most useful for isolating sets ofburials which reflect the structure of a social system? Until now there have been no reallyexplicit criteria against which to evaluate possible answers to this question. Here theorientation developed in the preceding pages becomes important. As a consequence ofthis orientation, it is possible to specify two criteria which must be met before anyclassification method may be regarded as useful for mortuary data. First, the proceduremust be relatively sensitive to the size of the derived burial clusters. It must not show atendency to form clusters composed of small numbers of burials possessing idiosyncraticattributeswhich are not of importance for defining majorgroups of burials. Any techniquewhich fails in this regard is no more useful than formal analysis. Second, and moreimportant, the classification method must be capable of partitioning the data set intoaggregates of burials which can be interpreted as socially distinctive. That is, the database must be segregated into clusters of burials accorded equivalent forms of interment.At the minimum, such aggregates of burials must be defined by attributes reflectingequivalent amounts of energy expenditure in mortuary ceremonialism.In essence, classification algorithms applied to mortuary data should be evaluated bythe patterns displayed in the size and composition of derived burial clusters. A rangeof procedures, falling into two categories, has been tested for utility on this basis. Thefirst category comprises a set of polythetic methods, averageand complete linkage clusteranalyses as well as factor analysis, while the second encompasses monothetic-divisiveprocedures utilizing the sum of chi-squares and the information statistic. All of theclassifications were run on the CDC 6400 computer at Northwestern University,utilizing David Wishart's CLUSTAN IA for the polythetic-agglomerative and most of


5/16

4 Joseph A. Tainterthe monothetic-divisive algorithms; Robert Whallon's (197I) programme TYPE for onemonothetic-divisive classification using the sum of chi-squares; and the StatisticalPackagefor the Social Sciencesfor the factor analysis. Before proceeding to the analysis ofthe classification results, the data set employed in this experiment must be brieflydescribed.

Middle Woodland mortuary patterning in the lower Illinois River valleyThe mortuary data classified in this study derive from a set of 512 Middle Woodland(c. 150 B.C. to A.D. 400) burials from the Klunk and Gibson mound groups in the lowerIllinois Rivervalley. From this population, a subset of 439 burials was found to be suitablefor statistical evaluation. Viewed within the frameworkpresented here, Middle Woodlandmounds in the lower Illinois River valley can be seen to contain a number of distinctivestructural elements, many of which indicate variations in the energy expended onconstruction. In these mounds there are one or more centrally-located, excavated tombs,surrounded by ramps of loaded earth. Termed 'central features' (Buikstra I972: 65),these tombs will often display such variations in energy expenditure as the presence orabsence of a log roof, as well as log, slab or earth walls (cf. Perino i968). There areindications that the interment of persons in the central feature was not considered aterminal act. It appears rather that from time to time these tombs were reopened, thecontents exhumed and deposited as disarticulated bundles of bones, above or adjacentto the central feature, and subsequent individuals interred in the same grave (Perinoi968: 38; Buikstra I972: 33-4).

Generally organized around the first central feature constructed at a location, the areain and under the primary mound comprised the place of interment for the majority ofMiddle Woodland individuals. Burials in this location were either placed on accretionalsurfaces of the mound, and earth piled over them, or were placed in excavated sub-floorgraves. These latter features may often display log or limestone slab coverings over theburial, or inclusive slabs within the grave. Finally, there is at most mounds a set ofindividuals who were buried in a location somewhat peripheral to the primary mound.

Evaluation of classification resultsA set of eighteen binary attributes has been recorded from the Middle Woodland datafor use in this experiment (table I). The attribute list was structured so that alldistinctions were truly binary, and no redundant or auto-associated attributes werepresent. For the polythetic classification procedures, a matching coefficient for binarydata, which excludes negative matches from consideration, was chosen as a measure ofsimilarity. The reason for choosing a measure which excludes negative matches from thecalculation was based on the necessity of avoiding the formation of clusters composed ofburials which are similar only because they all lack certain attributes. The study ofmortuary data must begin with burial clusters which are composed of individualsdisplaying strong positive attribute associations. The measure chosen for use is known as


6/16

Social inference ndmortuary ractices:an experimentn numericallassification 5Kulczynski's Matching Coefficient 2 (SK2)(Sokal and Sneath I963: I30). This coefficientserved as the basis for both the factor and polythetic cluster analyses.In the clustering procedures tested (that is, in all methods excluding the factorTABLE IVariables mployedn statisticalanalysis

CodingI/O I/O

I Uncremated/cremated xx Supine/notsupine2 Articulated/disarticulated I2 Single/multiple3 Extended/notextended I3 Ochre/noochre4 Earthwalls/logwalls I4 Hematite/nohematite5 Ramps/noramps x5 Miscellaneousanimal6 Surface/sub-surface bone/none7 Log covered/notlog covered i6 Importedsociotechnic*items8 Slab covered/notslab covered I7 Locallyproduced9 Slabs in grave/noslabs sociotechnic* temso1 Interred n central ocation/ I8 Technomic*itemsinterred n primarymound

* Terminology sensu Binford I962.analysis), the cut-off point in the classification process was found by graphing the magni-tude of the 'jump' in the value of the similarity or association coefficient utilized, at eachnode in the fusion or division process. The point of significant deceleration in the curveproduced on this graph can be taken as a stopping point, since all subsequent clusters aresimply minor variations of the patterns established by higher-order groups. The clustersformed from nodes at, and immediately higher than, this point of deflection are utilizedas the terminal clusters in the analysis.Polythetic-agglomerativeclusteranalysesAverage-linkage analysis is a commonly used clustering procedure which fusessubordinate clusters based upon the average similarity between all cases previouslyexisting in a cluster and the potential new member. In the complete linkage procedure ajuncture between two clusters is effected only when the joining case is sufficiently similarto all members of the existing set. Complete linkage-analysis was chosen for this experi-ment because the criterion for stipulating similarity to all members of an existing clustershould be explored as a possible device for ensuring the derivation of homogeneous burialclusters. The average and complete linkage-cluster analyses derived a total of eight andten clusters respectively, at the point where the clustering procedure was terminated. Theresults, as recorded in tables 2 and 3, and figs i and 2, show these clustering algorithmsto be almost totally inadequate for the purpose of isolating sets of burials accordedequivalent forms of interment. Both of these procedures failed consistently to segregateburials on the basis of such major variations in energy expenditure as custodial careleading to ultimate skeletal disarticulation (average-linkage clusters I, 4 and 7; complete-linkage clusters I and 7), the placement of logs or limestone slabs about the grave


7/16

6 Joseph A. TainterTABLE 2Percentage-variableoccurrencen average-linkagecluster-analysis

H N k F m O\ oo0- ._,4 sz w^ . an Q , a) 0 0 0^ t 3 ~ ry t3 c3 t3 t

I I00o0 98.8 I00o0 IOOO I00oo0 100i. I00o- 100-02 83-4 Ioo0 0.0o 52.7 0'0 Io00o 40.0 o0o3 I0o.0 95.I 0.0 Ixo6 0o0 0.0 0.0 0o04 33'4 99'4 95'3 IOOO I100-0 10ooo O1000 0o5 Ioo0 0.0o o00 o0.0 1oo 0o.o 0o0 0oo-o6 0.o o0.000o 0.0 0.0 0.0 IOo 0.07 Ioo.o I8.7 0.o o0o o00 Ioo0o o0. I0ooo8 50.0 iso6 4.8 0.0 0.0 o0o oo I00o09 o.o II.2 o.o Io.6 Ioo.o 0O.0 o0 I00.0o10 oo1o 2.5 90g5 o00 1oo0. o.o o00 00.0oII Ioo0o 93.8 0.0 0.0 0.0 0.0 0.0 0.012 0-0 68-4 66-7 IOO00 0.0 0.0 0.0 IO0.013 0.0 0.0 0-0 00 i0oo0o 0.0 o0. 0.0

I4 0-0 0o7 o0.0 0 0.0 0.0 0.0 0.015 i6'7 0.0 o?o o'o o0. o0o o?o o5 i6.7 0.0 0-0 0.0 0.0 0.0 00 0.016 83.4 1.9 4.8 0.0 1oo0oO 0 000 0.017 50.0 3.8 0.0 5.8 ioo0. 0.0 io.O 0.018 I6.7 4.4 o0. 2I-I 0.0 0.0 0.0 0.0

TABLE 3Percentage-variableoccurrencen complete-linkagecluster-analysis

o

2 83-4 Ioo.o ei 6

C) C c) C)f C C Cg) ) C)

U 0v U UvI I00-0 99.0 97.0 I1000 I00?0 500.0 I00-0 500.0 100eO IOOeO

4 33.4 I00-0 97-o Ioo0o 85.8 i00oo i00o0 I00oo 100.0 0.05 Ioo-o o.0 0.o o .o o0. o .0.oo.0o o.o oo00o6 0.o o0o 0.o o0.o 0oo0 75'0 0.00o0 0.0 0*07 Iooo0 7-I 3.I 93.6 0.0 00 0.0 0.0 0-0 I000o8 50.0 9.8 o00 29-. 14.3 0..0 .0 0o0 0.0 oo0009 o.o o109 I5.2 6.5 0.0 0.0 I2o0 o00o0 0.0 o00o010 Ioo0o 0.o o0o 13.0 iooo0 6o.o o.o Ioo0o o0. ioo-otI ioo0o 97'9 0oo00 90.4 00o o0.o o0.0 0o o0o 0o12 0.o Ioo-o 0.0 38-8 oo 70.0 0ooo o.o o0.o 100*0

13 0o0 0.0 0-0 0o 0 0.0 o.0 00 Io000 0.0 0.0I4 0o0 0o0 3.* 0.0 0.0 0.0 0.0 0.0 0.0 0.015 I6-7 0.0 0o0 0.0 0.0 0.0 0.0 0.0 0.0 o0oi6 83.4 2-2 3.I o0.o 143 0.o 0.0 I00o0 o.0 0*oI7 5?'0 3.3 3.' 6.5 0.0 0.0 12-0 1000 25-0 0.0I8 I6-7 3.3 6I6i 5 0.0 o .o I6.o o.o o.o o.o


8/16

-.028 -

.525

.036

.100

.161

.228579

.606 .292 -

.357

.661

*688 .486 -

.549 -.715

.742-O 0o O C =: cO w0 cs

FigureI Average-linkage luster-analysisof Klunk and Gibson datausing Sx2

cn a L

_ w

Figure2 Complete-linkage luster-analysisof Klunkand Gibson datausing SK2

I

E.

I

:

k

I

a

i

-

I

v

..6


9/16

8 Joseph A. Tainter

(average-linkage clusters I, 2, 3, and 4; complete-linkage clusters I, 2, 3, 4, 5 and 7), aswell as the construction of log walls around central features (average-linkage clustersI, 2 and 3; complete-linkage clusters i, 3 and 5). Following the argument relating energyexpenditure in mortuary ritual to the rank of the deceased, it would seem that the clustersderived from these classifications often contain individuals representing two or perhapsthree discrete grades of hierarchical ranking. Such a failure to partition the data set intosocially distinctive burial groups must indicate that these polythetic-agglomerativeclustering procedures are not appropriate for mortuary data.Factor analysisThe factor-analysis technique employed here was the principal factoring type withiterations and varimax orthogonal rotation. A total of nine factors was derived for whichat least moderately high loadings were evident, and these accounted for a cumulativetotal of 99-1% of the variance in the data set. The ninth factor displayed an eigenvalueof o.I9.The rotated factor matrix is displayed in table 4. In contrast to the polythetic cluster-analyses, this classification has isolated several constellations of attributes which dis-criminate between classes of burials accorded variable amounts of energy expenditure.The factor analysis has successfully isolated log-walled central features (Factor I),TABLE 4Varimax rotated-factormatrix

Cl 'fMCQ


10/16

Social inferencesand mortuarypractices: an experiment n numericalclassification 9of reflecting the structure of an extinct social system than do the results of the polytheticcluster-analyses.Monothetic-divisiveproceduresA set of classification methods is available designed progressively to subdivide apopulation into groups defined by the presence or absence of attributes arranged in ahierarchical tree. The goal of the subdivisive process is to split the population in such away as to effect maximum reduction in the variance of all attributes in the resultingsub-groups. The creation of attribute hierarchies in these monothetic-divisive proceduresis based upon the use of one of several alternative statistical algorithms. One algorithmwhich has been suggested for use with archaeological data is the sum of chi-squares(Whallon 1971; I972). In the classification procedure, division into subordinate clustersis effected upon the attribute which, at any subdivision step, has the highest sum of chi-squares when considered in association with all other attributes.

Application of chi-square in classification does not always yield good results, since theprocedure tends to fragment the final solution by splitting outliers off from the population(Lance and Williams I965; 1971). Robert Whallon (197I) has developed a computerprogramme for monothetic-divisive classification (TYPE) which provides a potentialsolution to this problem by allowing the user to set a lower expected cell-value foreliminating tables from the chi-square calculations. Use of this option with mortuarydata should be approached with caution, however, because there is no a priori way toestimate the expected cell values for the formation of clusters which are sociallysignificant. Setting this value too high may result in a classification which fails todiscriminate between burials accorded varying forms of interment.Two separate experimental classifications employing the sum of chi-squares were runon the Klunk and Gibson data. The first computation was run with David Wishart's(I969) CLUSTAN IA set of programmes in which the specification of lower cell-valuelimits is not possible. The results obtained with this programme are illustrated in fig. 3.A total of sixteen clusters were derived at the point where the subdivisive process wasterminated. This classification yielded results which are far more acceptable than thoseobtained through the polythetic-clustering procedures. Satisfactory divisions were madeon such energy expenditure variations as log coverings over peripheral graves andskeletal disarticulation. Unfortunately, in a manner characteristic of chi-square classi-fications, the algorithm produced a number of clusters which isolated idiosyncraticoutliers from the population. Most noticeably, the procedure tended to allocate anunacceptably large portion of the divisive process to splitting off burial clusters on thebasis of animal bone in the grave, a trivial attribute which occurs with an insignificantnumber of burials. Fully 50% of the terminal clusters were structured by the presenceor absence of this attribute, yet animal bone occurs with only 0o5% of the population(2 out of 439 individuals). The allocation of such a major portion of the classification tothis relatively unimportant attribute is a totally unsatisfactory outcome.

In an attempt to solve the problems caused by the tendency of chi-square to splitoutliers off from a population, the classification was run a second time utilizing RobertWhallon's programme TYPE with the specification of a lower expected cell-value for


11/16

828.788 749.351!r

CM

743.839

658,.889

573.940

48 .990

404.040

67171t

594072 -

It

438.794- -

361.155 -

283-516

205.87734.ql -

149.192

64.2q2

-20-707--13am = . -r w a = -W- ..64 V- y-I 4 4

Figure3 Monotheticdivisionof Klunk and Gibsondatausing Sum chi-square(CLUSTAN)

128.238

50.ig9

-27.041 -

cq 14i 0

-< 4to .0

fn4 n '

Figure4 Monotheticdivision of Klunk andGibson datausing Sum chi-square(TYPE)

-4t

f

-

I

rr

4*s

I

Is

i

i

Ir

I

I

I

I

I

r ,*


12/16

Social inferenceand mortuarypractices: an experiment n numericalclassification I

eliminating tables from the calculations. Whallon's (I971: 18-19) experimental work withthe chi-square algorithm indicates that setting very low expected cell-frequency valueswill still provide a solution to the problem of isolating individuals possessing idiosyncraticattributes. Accordingly, the second sum of chi-squares classification run on the Klunkand Gibson data utilized an expected cell-frequency of I.o as a lower limit for excludingtables from the computations. The results of this second run are illustrated in fig. 4. Atotal of eleven clusters was derived at the cut-off point. These clusters did not prove to besusceptible to the problem evident in the previous classification, but this analysis did inturn produce its own peculiar set of undesirable features. The final solution of I I clusterssucceeded in making a number of discriminations on the basis of such energy expenditurevariations as log coverings, earth ramps, and disarticulation, but failed to segregategroups of burials defined by the presence or absence of log-walled tombs or limestoneslabs placed over the grave. The results obtained from this classification can be consideredonly partially useful, and indicate that chi-square is not an appropriate algorithm forclassifying mortuary data.An alternative algorithm for monothetic-divisive classification is the informationstatistic, which has been successfully utilized on the Moundville burials by ChristopherPeebles (I972). The use of the information statistic in classification arises from theconcept of entropy. It can be regarded as a measure of the disorder of a group, andachieves a value of zero if all members of a cluster are identical. When applied to a2 x 2 contingency table, the information statistic is computed as 2(b+ c)log2,where b and csymbolize respectively the upper right and lower left cells of the table. (For discussionsof the use of information-theoretic measures in classification see MacNaughton-SmithI965; Williams, Lambert, and Lance 1966; Lance and Williams I968 and 197I; andOrloci I969.)

Application of the information statistic to the Klunk-Gibson data yielded a finalsolution which satisfactorily met the specified classification requirements. A total oftwenty-two clusters was derived which consistently isolated attributes reflectingdifferences in the amount of energy expended in mortuary treatment (see fig. 5). Theprocedure identified not only burials with log and slab covered graves, but also variationsin the mode of construction of central features (log walls and earthramps), and differencesin the mortuary procedures (e.g. disarticulation) accorded to persons processed throughthese features. No fragmentation of the analysis occurred, and no trivial splits were madein the divisive process. Of the entire range of classification procedures tested, theinformation statistic alone has succeeded in isolating non-trivial sets of burials accordedequivalent forms of interment. It would seem therefore to be the most useful algorithmfor isolating the structural components of a social system which are reflected in thevarying forms of mortuary ritual.

DiscussionAs a conclusion to this investigation, we may consider the implications of these findingsin a general framework which can serve to indicate the utility of the classification pro-cedures evaluated here for the analysis of other sets of mortuary data.


13/16

S28.-63

68.573 -

408.682 -

348-791

288-.900

229.010 -

0 0169.119 -l N

r-


14/16

Social inferenceand mortuarypractices: an experiment n numericalclassification 13Polythetic classificationproceduresOf the polythetic-classification methods tested in this experiment, both the average- andcomplete-linkage cluster-analyses produced totally inappropriate results. Theseprocedures proved incapable of segregating the data set into groups of burials accordedequivalent forms of interment. The factor analysis on the other hand produced far moreacceptable results. Energy expenditure variations were consistently distinguished in theclassification, in contrast to the polythetic cluster-analyses. Yet even with these positiveresults, it is difficult to recommend the use of factor analysis for the classification of burialdata. For any set of mortuary data coded on a binary scale, the suitability of polythetic-classification procedures will be dictated by the amount of redundancy in attributecombinations. Perfectly redundant attribute-states represent situations in which clustersof burials are defined by the values of variables which are not present in any other cluster(cf. Clarke I968: 90-2). When such an ideal pattern is present, polythetic measures ofco-variation will produce sets of burials which are clearly distinct, and which possessnone of the draw-backs apparent in the average- and complete-linkage analyses reportedhere. In theory both factor and polythetic cluster-analyses could potentially be used formortuary data. But in practice few or nQ sets of burials will ever display perfectlyredundant attribute-combinations (cf. Saxe 1970: 102-9, 230-I). As a consequence,polythetic classification of mortuary data cannot be expected consistently to yieldsatisfactory and distinct burial clusters.Monothetic-divisiveproceduresMonothetic-divisive procedures are far more appropriate for mortuary data which canbe coded binarily. The choice of an appropriate algorithm for hierarchial subdivision iscrucial, for certain divisive methods have been shown in this paper to yield very poorresults with mortuary data. The use of chi-square in this regard seems particularlyinappropriate, in part because this statistic tends to split outliers off from the population.It is possible to overcome this difficulty by employing a lower expected cell-value foreliminating tables from the classification. Yet there is a more fundamental draw-back tothe use of chi-square which cannot be circumvented. This is the inclusion of negativematches in the chi-square formula. The measurement of negative association is notconsidered desirable for mortuary studies, especially when the data set is composed of alarge number of attributes, few of which occur positively with any single burial. In suchsituations, the inclusion of negative matches in the computation of an associationalgorithm will tend to produce a highly skewed sequence of subdivisions. Such aconsideration indicates that the sum-of-chi-squares criterion should not be employed inthe classification of mortuary data. Yet it should be pointed out that this discussion isintended only to indicate that chi-square is not appropriatefor mortuary remains. Otherforms of archaeological data might conceivably be amenable to the use of chi-square,as Robert Whallon's (I972) analysis of Owasco pottery indicates.The information statistic appears susceptible to none of the draw-backs of chi-square.This measure is highly sensitive to cluster size, does not fragment the final solution, andexcludes negative matches from the computation. The information statistic was foundin this experiment to yield the greatest number of interment clusters, and to isolate sets of

BWA


15/16

14 Joseph A. Tainterburials which can confidently be interpreted as socially distinctive. Among theprocedures considered in this paper, monothetic division utilizing the informationstatistic appears to be the most suitable technique for classifying mortuary data for thepurpose of social inference.

AcknowledgementsThe data sets utilized in this study were graciously provided to the author by MrGregory Perino and the Thomas Gilcrease Institute of Tulsa, Oklahoma, and byProfessor Jane Buikstra, Northwestern University. The project was financially supportedby the Foundation for Illinois Archaeology, while funding for computer utilization wassupplied through the Department of Anthropology, Northwestern University. I wouldlike to express my appreciation to Christopher Peebles for providing valuable commentson an earlier version of the research reported in this paper.25.V. I974 Departmentof AnthropologyNorthwestern UniversityReferencesBinford,L. R. I962. Archaeologyas anthropology.AmericanAntiquity.28:217-25.Binford, R. I97I. Mortuary practices:their study and their potential. In Approacheso theSocial Dimensions f MortuaryPractices,ed. J. A. Brown. 6-20. Memoirsof the Society forAmericanArchaeology. 5.Brown,J. A. 1971.The dimensionsof status in the burialsat Spiro. In Approacheso the SocialDimensionsf MortuaryPractices, d. J. A. Brown.92-112. Memoirsof theSociety or AmericanArchaeology. 5.Buikstra,J. E. 1972. Hopewelln the ower llinoisRivervalley:a regionalapproach o thestudyofbiological ariabilityandmortuary ctivity.M.S., Ph.D. dissertation,Universityof Chicago.Clarke,D. L. I968. AnalyticalArchaeology.London.Decker, D. A. I969. Earlyarchaeologyon CatalinaIsland: potentialand problems.Archaeo-logicalSurveyAnnualReport.1 :69-84. Los Angeles: Universityof California.Finnerty,P., Decker, D., LeonardIII, N., King, T., King, C., and King, L. I970. Communitystructureand trade at Isthmus Cove: a salvageexcavation on Catalina Island. Pacific CoastArchaeologicalociety,OccasionalPaper i. Costa Mesa.Goodenough,W. H. I965. Rethinking status' and 'role':toward ageneralmodel of the culturalorganizationof social relationships.In The Relevanceof Modelsin Social Anthropology,ed.M. Banton. I-24. London.Kay, P. I966. Commentson 'Ethnographic emantics:a preliminary urvey', by B. N. Colby.CurrentAnthropology.:20-3.King, F. 1970. Thedead at Tiburon:mortuary ustoms ndsocialorganizationonnorthern SanFranciscoBay. NorthwesternCaliforniaArchaeologicalociety,OccasionalPaper2. Santa Rosa.Lance, G. N. and Williams, W. T. I965. Computerprogramsfor monothetic classification('associationanalysis').TheComputer ournal.8:246-9.


16/16

Social inferenceand mortuarypractices: an experiment n numericalclassification 15Lance, G. N. and Williams, W. T. 1968. Note on a new information-statisticclassificationprogram.TheComputerournal.11:95.Lance, G. N. and Williams,W. T. 197I. A note on a new divisive classificatoryprogramformixed data. TheComputerournal.I4:I54-5.MacNaughton-Smith,P. I965. Some Statistical and otherNumericalTechniquesforClassifyingIndividuals.London.Miller,J. G. 1965. Living systems: basic concepts.BehavioralScience.10:I93-237.Orloci, L. I969. Informationtheory models for hierarchicand non-hierarchicclassifications.In NumericalTaxonomy, d. A. J. Cole. 148-64. London.Peebles, C. S. 1972. Monothetic-divisiveanalysisof the Moundville burials: an initial report.Newsletter of ComputerArchaeology. 8(2):I--3.Perino,G. H. 1968.The Pete KlunkMoundGroup,CalhounCounty,Illinois: the ArchaicandHopewelloccupations.In Hopewelland Woodland ite archaeologyn Illinois, ed. J. A. Brown.9-124. IllinoisArchaeological urvey,Bulletin 6. Urbana.Rodeffer,M. J. I973. A classificationof burials in the lower Snake River region. NorthwestAnthropological esearchNotes.7:IoI-3I.Rothstein,J. I958. Communication,rganization, nd Science.Indian Hills.Saxe,A. A. I970. Socialdimensionsfmortuary ractices.M.S., Ph.D. dissertation,UniversityofMichigan.Sokal, R. R. and Sneath, P. H. A. I963. Principlesof NumericalTaxonomy.San Francisco.Whallon,R. Jr. 1971. A computerrogramor monotheticubdisive lassificationn archaeology.Museumof Anthropology,Universityof Michigan,TechnicalReportsI.Whallon,R. Jr. 1972. A new approach o potterytypology. AmericanAntiquity.37:13-33.Williams, W. T., Lambert, J. M., and Lance, G. N. I966. Multivariate methods in plantecology, V: Similarityanalysesand information-analysis.TheJournal of Ecology.54:427-45.Wishart D. I969. CLUSTAN IA User Manual. Computing Laboratory,University of StAndrew's,Fife.

AbstractTainter,J. A.Social inference and mortuary practices: an experiment in numericalclassificationRecent cross-cultural tudies of ethnographicallyrecordedmortuary procedures ndicate thatvariations n the form of mortuaryritualsymbolizeand reflect the membershipof the deceasedin the componentsof a social system. Such formalpatternsof burial procedurecan best beidentifiedarchaeologicallyhroughthe numericalclassification f mortuaryattributes.A generalinterpretiveorientation owards the study of mortuarypractices s developedin this paperas abasis for testing the relative utility of average-and complete-linkage cluster-analyses,fact-analysis,andmonotheticdivisionusingthe sumofchi-squaresand he information tatistic, ortheclassificationof mortuarydata.The results of this experiment ndicate hatclassificationwiththeinformation tatistic s most suitable for analysisof the socialdimensionsof mortuarypractices.

Social Inference and Mortuary Practices an Experiment in Numerical Classification

Documents

Transcript of Social Inference and Mortuary Practices an Experiment in Numerical Classification