Boards and Cords: Discriminating Types of Artificial Cranial Deformation in Prehispanic South Central Andean Populations

Boards and Cords: Discriminating Typesof Artificial Cranial Deformation inPrehispanic South Central AndeanPopulationsT. G. O’BRIENa* AND A. M. STANLEYb

a Department of Sociology, Anthropology and Criminology, University of Northern Iowa, Cedar Falls, IA50614, USAb Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614, USA

ABSTRACT For over a century, a number of ambiguous typologies have been employed to distinctly categorise types ofartificial cranial deformation. This paper provides a quantitative method, based on multiple dimensionsand discriminant function analysis, by which to assign skulls not only into discrete categories: deformed ornot, but also by type: annular or tabular. A series of prehispanic, adult, human crania (n=469) fromarchaeological sites in Argentina, Bolivia, Chile and Peru represented by both normal and artificiallydeformed specimens, provide craniometric data for four measurements across the vault: maximum craniallength, breadth and height and the frontal chord. These data are used to develop three indices which in turnare used to compute two discriminant functions. Results are plotted on a territorial map whereby the type ofdeformity can be determined. When these methods were applied to a comparative cranial sample ofnondeformed skulls from South America, 100% of the samples was found to be nondeformed. Whenthese methods were applied to the samples which were subjectively classified a priori by the first author asnondeformed, 81.3% of the samples were found to be nondeformed. This study demonstrates the value ofa more objective and quantitative method by which to classify artificial cranial deformation, and thus providesa new approach. Copyright © 2011 John Wiley & Sons, Ltd.

Key words: annular; craniometrics; cultural cranial modification; discriminant function; head moulding; SouthAmerica; tabular

In physical anthropology, the skull is traditionally thebest part of the skeleton by which to determine sexand/or ancestry for either forensic identification pur-poses or for computing ancient group connections,such as with biodistances. To do this, a plethora ofcraniometric data is usually collected and subjectedto multivariate statistical analysis. However, if a skullshows signs of being intentionally altered, it is oftendeemed unusable from a strict craniometric perspective(Cocilovo, 1975). Therefore, it is often that such skullsare discarded from analysis. There are two problemswith this tacit dismissal of valuable cranial information:first, interpreting whether or not a cranial vault hasbeen intentionally altered has been and continues tobe an extremely qualitative decision; and second, if

the skull is judged to be altered, then it is often classi-fied into a certain style based, once again on ambiguoustypological systems; such systems will be describedlater. The objectives of this paper are to resolve theseproblems by providing a quantitative approach to de-termining the metric limitations to whether or not askull has been artificially deformed, and if so, then todiscretely categorise its type; at least for this regionof the south central Andes from which the samplesused herein originate. For this paper, the phrase artifi-cial cranial deformation (ACD) is used to denote whatothers have called cultural cranial modification, headbinding, skull moulding or variants thereof (EllenFitzSimmons & Prost, 1998; Blom, 2005; Torres-Rouff& Yablonsky, 2005; Perez, 2007).

Archaeological evidence and ethnohistoric accountsdocument ACD as a human cultural phenomenonfound on almost every continent (Dingwall, 1931). Asa biocultural process, it is defined as the product of

* Correspondence to: Department of Sociology, Anthropology andCriminology, University of Northern Iowa, Cedar Falls, IA. 50614–0513 USA.e-mail: [email protected]

Copyright © 2011 John Wiley & Sons, Ltd. Received 15 December 2010Revised 12 May 2011Accepted 5 July 2011

International Journal of OsteoarchaeologyInt. J. Osteoarchaeol. (2011)Published online in Wiley Online Library(wileyonlinelibrary.com) DOI: 10.1002/oa.1269

dynamically distorting the normal patterns of neurocra-nial growth in the infant through the agency of exter-nally applied forces (Moss, 1958:275). Deformationcan be produced unintentionally through the inadvert-ent effects of tying the child’s head to a cradleboard, asseen in some native North American Indian groups(Kohn et al., 1995; Piper, 2002). Yet, the most dramaticeffects come from the intentional process of ACD. Ingeneral, ancient groups from around the world have prac-tised the act of binding the head in basically one of twostyles (see Figure 1): soon after birth, they would eitherstrap hard, flat devices like boards, to both the frontand back of the infant’s head or wrap the infant’shead with tight bandages like cords. By leaving theseapparati on the head for a period of time ranging from3 to 5years, and being occasionally tightened, the resul-tant growth processes of the brain and cranium wouldbe altered producing in the adult a more upright, boxyshaped skull in the first (referred to as tabular) anda more conical shaped skull in the second style (referredto as annular) (Dembo & Imbelloni, 1938). The endresult is a permanently altered, adult head that somehave speculated improved a person’s beauty, socialstatus or class; but most widely accept that head

shaping marked an individual as belonging to a certainregion, ethnic or kin group or segment of society(Gerszten & Gerszten, 1995; Blom, 1999).

Historical background

In the last century, a steadily increasing trend has emergedin the study of ACD from a biological anthropologicalperspective. Such issues that have been explored include:the effects of deformation on normal patterns of growthand development (Björk & Björk, 1964; Anton, 1989;Cheverud et al., 1992; Kohn et al., 1993; Konigsberget al., 1993; Dean, 1995a, 1995b; O’Loughlin, 1996;Pomatto et al., 2006); its influence on cranial traitmorphology (Ogura et al., 2006; Rhode & Arriaza,2006; Del Papa & Perez, 2007; Durband, 2008); theeffects on sutural bone development (Ossenberg,1970; El-Najjar & Dawson, 1977; Gottlieb, 1978;Anton et al., 1992; White, 1996; O’Loughlin, 2004;O’Brien & Sensor, 2008); using ACD type distributionacross time and space to interpret migration, andcross-cultural influences (Hoshower et al., 1995; Blomet al., 1998; Anton & Weinstein, 1999; Őzbek, 2001;

1

2

3

A B C D

Figure 1. Column A: infants. Column B: adults. Column C: adult skull, lateral view. Column D: adult skull, superior view. Row 1: tabular style. Row 2:normal. Row 3: annular style. (Drawing by TGO, modified after Imbelloni, 1938 and Anton, 1989).

T. G. O’Brien and A. M. Stanley

Copyright © 2011 John Wiley & Sons, Ltd. Int. J. Osteoarchaeol. (2011)

Blom, 2005; Torres-Rouff & Yablonsky, 2005); andmathematical analysis (Shapiro, 1928; Watson, 1999;Frieb & Baylac, 2003; Perez, 2007).For over a century assessing, classifying or scoring

forms, types, methods, or techniques of ACD on thehuman skull has remained ambiguous and inconsistent.There are a number of classical works that showthis diversity (Dingwall, 1931; Neumann, 1942; Moss,1958; McNeill & Newton, 1965; Rogers, 1975;Munizaga, 1976; Allison et al., 1981; Cheverud et al.,1992; Gerszten, 1993; Buikstra & Ubelaker, 1994). Pre-vious scholars in the fields of craniology and anthro-pometry recognised from as few as two or three typesto as many as 16 types of ACD (see O’Brien & Sensor,2004). Some made distinctions between unintentionaland intentional, whereas others tended to constructtheir classification by describing cranial shape andform, or by applying geographic distribution, like thenorthwest Pacific Coast type, or by use of tribal no-menclature, like the Aymara type or the Chinook type(Dingwall, 1931). However, many typological schemestoday tend to favour a stylistic approach defined by thedeforming apparatus employed (Buikstra & Ubelaker,1994). Other contemporary approaches continue tocloud the issue by presenting new names for old styles(Munizaga, 1976; Anton, 1989). Previous discussionson the history of the typological study of ACD havetended to ignore the ambiguity in the various classifica-tion schemes presented over time (Rogers, 1975; Dean,1995b). Today, we still struggle with defining ACDtypes (O’Brien & Sensor, 2004). Therefore, a methodby which to quantitatively determine ACD is needed.It is important to be able to categorise ACD by typebecause of its regional variation, especially as it pertainsto prehispanic, human groups in the Andes, but further-more to see how that variation contributes to culturaland archaeological interpretations of such populations.Although the system for assessing types of artificially

deformed crania may be interpreted as seeming sub-jective (Blom, 1999:144), it was Dembo & Imbelloni(1938:240; translated by TGO) who said, “. . . in theclassification of intentionally deformed types and theuse of their respective terminology, the large numberof researchers who study this subject do not agree onany unified vision or system; thereby leaving this mat-ter to be dominated bymassive confusion.”Nevertheless,previous classification schemes of ACD, regardless of thevariety of types they have produced, seem to agree onone common trait – that intentional deformation can beperformed in basically one of two manners: either withboards or cords. Argentine physical anthropologist JoséImbelloni (1938, 1963) was certainly one of the firstto note this duality. It was modified slightly by Anton

(1989) and subsequently adopted for ACD documenta-tion and recording by Buikstra and Ubelaker (1994).Imbelloni (1923; 1924–25) sought to interpret the

ranges of cranial deformity that were artificially inducedby utilising geometric and trigonometric techniques.The methods that he utilised were never widely accepted,most likely because his work was published in museumannals or as research reports. But he eventually created asimple and useful typology for describing South Americanskulls (Imbelloni, 1938; see also Dembo & Imbelloni,1938) (see Figure 1). For his first type he renames the‘highland’ or ‘Aymara’ style (Hrdlička, 1922, 1923) asthe annular form, characterised by bandages, belts orcords wrapped around the infant’s head. The deformingapparatus would pass across the individual’s foreheadtransversely, run above the ears and be bound at oraround the lower back of the head. The result of thisdeformation technique would produce a skull shapethat was obliquely conical when viewed in profile. Forhis second type, Imbelloni names the utilisation ofboards or hard flat surfaces bound to the child’s headas the tabular form. The deforming apparatus wastypically a thin, flat board placed across the foreheadand tied laterally to another board placed across theback of the head. The stronger forces of deformationwould produce a nearly box-like vault shape, that is,high and short).Imbelloni supports a more geometric approach in

craniomorphologicla assessment of ACD when hestates that: (translated by TGO from original: Imbelloni,1923:32):

. . . an exact or mathematical morphology should beemployed to reduce the synthetic expression of theskull to a group of geometric formulas, that repre-sent the most significant analytical relationships be-tween points, lines and planes; relationships that indefining geometric notation appear in the form ofarcs, angles and chords.

This observation by Imbelloni is applied within thispaper; such that, in normal (nondeformed) skulls, thelength of the frontal, parietal or occipital chords varybetween and within populations. However, when com-pared with individuals exhibiting signs of ACD, such asannular or tabular, the chord lengths and vault shape,in general, are more greatly altered (Anton, 1989).For example, in an annular deformed skull, the poster-ior parietals extend superiorly and posteriorly, and thebones of the frontal, occipital and cranial base arelengthened (Anton, 1989; Kohn et al., 1993). In a tabu-lar deformed skull, the postero-lateral parietals (thebosses) are often widened laterally becoming somewhat

Discriminating Types of Artificial Cranial Deformation


bilobular and more vertical, whereas the frontal bone islengthened and widened (Cheverud et al., 1992).The main problem for any assessment procedure out

there today is the lack of discrete boundaries betweendeformation types. What is the deciding factor betweena normal, nondeformed skull and one that shows, forexample, tabular deformation? Above and beyond theissues of typological nomenclature (see O’Brien & Sensor,2004), there is a real problem with figuring out exactlywhether the observed cranium is actually deformedor just on the periphery of the population’s normalrange of variation. Where are the measurable, typo-logical limits? The recent contribution by Perez(2007) of approximating ACD in South America usinggeometric morphometrics is a well-needed addition tosolving the dilemma, but produces a complicated ap-proach that might be difficult to reproduce in the fieldcontext.If one can construct a population’s normal range of

cranial microvariation from multiple dimensions, chordlengths, or other indices and then use that informationin comparison with similar data taken from artificiallydeformed skulls, then it might just be possible to quan-tify the variation seen in patterns of ACD. Our goal isto produce an analytical tool for objectively determin-ing ACD by applying standardised craniometric tech-niques and a mathematical approach as they apply toa series of skulls from prehispanic Andean groups.The results can be used in the field or laboratory apply-ing simple computation. By taking a few recognisedcranial measurements, developing the relevant indicesand plotting them into the appropriate formulas, oneis be able to say with a certain level of confidence thatthe skull measured is either normal (not deformed),tabular (deformed), or annular (deformed).

Materials

Three collections of crania are combined and examinedfor this study. The first is from the Museo Arqueológicode San Simon in Cochabamba, Bolivia (O’Brien &Sanzetenea, 2002; O’Brien, 2003). The second is fromthe Museo de La Plata in La Plata, Argentina. Finally,the third is from the Museo Etnográfico de JuanAmbrosetti in Buenos Aires, Argentina. All crania inthe three collections originate from prehispanic, archaeo-logical sites in: Argentina (n=92), Bolivia (n=301),Chile (n=7) and Peru (n=69). The crania vary in theirtemporal provenience but date roughly to the MiddleHorizon (AD ~500–1000) for the south central Andeanregion. The data from the three combined collectionsis be referred to as the O’Brien dataset (n=469).

Demographics and sample sizes for this dataset arepresented in Table 1.The Howells database is used totest our methods developed from the South Americancranial data in O’Brien’s dataset. This database includes57 measurements taken from over 1200 crania groupedinto about 28 specific populations from around theworld. Further information regarding this collectioncan be found in three principal monographs (Howells,1973, 1989, 1995, 1996) and the data itself can bedownloaded from: http://konig.la.utk.edu/howells.htm.However, for this study, only the Peruvian sample(n=110), from the old province of Yauyos, is utilisedbecause, as a comparative sample, it was the mosttemporally and spatially relevant. Howells (1973:30)states in respect to this particular collection that itwas originally developed by Dr. J. C. Tello and wascomprised of 536 crania, but the crania selected byHowells were ones that showed ‘. . .no evidence ofartificial or natural shaping or distortion of the vault(uncommon in this population in any case).’ Thus, only150 nondeformed crania became available; from whichhe attempted to get an unbiased geographically distrib-uted series. Hence, 55 males and 55 females constructthe 110 crania used in the present study. Therefore, itis argued that the series of undeformed crania selectedby Howells is suitable to function as a control in thisstudy (Ross et al., 2008).

Methods

For a cranium to be included in this study, it needed tobe an adult and generally complete. The minimal signsused to assess whether a skull was of adult statusincluded the following: full eruption and use of thirdmolar(s), moderate signs of attrition patterns andcranial suture obliteration (Lovejoy, 1985; Meindl &Lovejoy, 1985; Masset, 1989; Buikstra & Ubelaker,1994; O’Brien & Sensor, 2008). Of course, advancedsigns of these factors guaranteed adult status. Further-more, the following cranial landmarks were required

Table 1. Demographics of the O’Brien dataset

Region

Type of deformation

NAnnular None Tabular

Argentina 5 39 48 92Bolivia 56 203 42 301Chile 2 4 1 7Peru 14 34 21 69Total 77 280 112 469



to be present: basion, nasion, glabella, bregma, euryon,opisthocranion and opisthion.Each cranium was subjected to a battery of 33 trad-

itional craniometric observations. Data were collectedby the first author (TGO) using standardised measuringprocedures with spreading, sliding and coordinate calli-pers (see Howells, 1973, 1989; Moore-Jansen et al.,1994; Buikstra & Ubelaker, 1994). Incidentally, cranialcircumference was not recorded because we felt thatthese data would not contribute adequately to the de-velopment of the specific indices. From the craniomet-ric observations, four major dimensions (recorded inmillimetres) are utilised as variables in this study: max-imum cranial length [glabella – opisthocranion] (L),maximum cranial height [basion – bregma] (H), max-imum cranial breadth [euryon – euryon] (B) and thefrontal chord [nasion – bregma] (F) (see Figure 2).These four measurements were selected because theyencompass the entire cranial vault and facilitate compu-tation. More dimensions might complicate calculationsand reduce potential sample sizes by eliminating in-complete skulls. Future work could examine the effects

of adding more dimensions, but for now we believethese four dimensions to be suitable for analysis.Imbelloni’s nomenclature for ACD types (1938;

Dembo & Imbelloni, 1938) is favoured in this studydespite the abundance of various cranial deformationtypologies (see O’Brien & Sensor, 2004 for a thoroughreview). Our reasoning behind this is because the cra-nial materials used in this study originated from Argen-tina, Bolivia, Chile and Peru, and Imbelloni’s ACDtypology was developed from observing South Americancranial samples. It is understood that Imbelloni expandedhis binomial typology into subdivisions, like the erect,oblique and pseudo-circular forms. For this study, though,those subdivisions are not employed.Each of the crania was observed visually for signs of

intentional deformation by the first author. Craniawere assigned a priori, without any measuring, to a de-formation category based on morphological traits con-sistent with what is described by Imbelloni (1938; seealso Dembo & Imbelloni, 1938). This qualitative, non-metric approach to ACD typing classified those skullsthat exhibited an obliquely elongated and conical-shaped vault as the annular type; those skulls thatexhibited a vertically boxy-shaped or slightly bilobularvault as tabular; and those that showed neither asnormal.The deformation of the skull involves major shape

changes in multiple dimensions. We, therefore, aremainly concerned with major skull measurements:length, breadth, height and chords. In order to avoidthe relative size of any given skull, we use self-referentialratios.

Results

Cranial dimensions and their relationships

In order to better understand the indices, we discussthe relationships among the measurements as theyapply to the two deformation types and normal skulls(please refer to Figures 1 and 2). We first begin withcranial breadth (B). When viewed from above, annularskulls are conical, or elongated, in shape. Thus, we ex-pect a smaller cranial breadth for annular skulls as com-pared with normal skulls (Figure 2). Further, thetriangular, or bilobular, shape of the tabular skulls leadsus to expect the cranial breadth of tabular skulls to belarger than that for normal skulls (Figure 2). We com-puted the means of the cranial breadths for each of ourdata sets. The results are in Table 2. Using a t-statisticwith a p-value of 0.05, we conclude that in general,the annular cranial breadth (BA) is less than the normal

B

B

B

B

B

B

H

F, H

F, H

F, H

F

F

F

L

L

L

L

L

L

H

H

A

B

C

Figure 2. Four measurements recorded for this study. Row A: tabularskull. Row B: normal skull. Row C: annular skull. Left side is lateral viewand right side is superior view. Maximum cranial height (H), Maximumcranial length (L), Frontal chord (F) and Maximum cranial breadth (B).



cranial breadth (BN) which in turn should be less thanthe tabular cranial breadth (BT). Therefore, for CranialBreadth, we have the relationship BA<BN<BT.We now look at cranial length (see Figure 2). The

conical shape of the annular skulls tends upwards at anangle from the Frankfort horizontal. Thus, we expectthe cranial length of annular to skulls to be larger thannormal skulls but not significantly larger. The shape ofthe boxy tabular skulls leads us to expect that the craniallength should be smaller for tabular skulls than for nor-mal skulls. We computed the means of the craniallengths for each of our data sets (see Table 2). Using at-statistic with a p-value of 0.05, we concluded that ingeneral, the tabular cranial length (LT) is less than thenormal cranial length (LN) which should be similar orslightly smaller than the annular cranial length (LA).Therefore, for Cranial Length, we have the relationshipLT<LN�LA.Now, consider cranial height (see Figure 2). The pos-

ition for the bregma in annular skulls often falls roughlybehind the placement of the external auditory meatus(or porion). This causes the cranial height of the con-ical annular skulls to be larger than that of normalskulls. The boxy tabular skulls should also tend to havea larger cranial height than normal skulls because of theraised vault. We computed the means of the cranialheights for each of our data sets (see Table 2). Usinga t-statistic with a p-value of 0.05, we are able to con-clude that in general, the normal cranial height (HN)is less than the tabular cranial height (HT) which inturn should be similar to the annular cranial height(HA). Therefore, for Cranial Height, we have the rela-tionship HN<HT�HA.Finally, we consider the frontal chord (see Figure 2). In

tabular skulls, the higher cranial vault leads us to expecta larger frontal chord for tabular skulls than for normalskulls. Furthermore, the position for bregma in annularskulls also leads us to expect the frontal chord to beconsiderably larger in annular skulls than in normalskulls. Therefore, we expect the frontal chord of annu-lar skulls to be larger than that of tabular skulls as well.We computed the means for frontal chords for our data

sets (see Table 2). Using a t-statistic with a p-value of0.05, we are able to conclude that in general, the nor-mal frontal chord (FN) is less than the tabular frontalchord (FT) which in turn should be less than the annu-lar frontal chord (FA). Therefore, for Frontal Chord, wehave the relationship FN<FT<FA.We now use this information to define indices that

differentiate between the two types of deformationsand normal skulls. We define the annular index as B/H,the tabular index as H/L and the normal index as F/Land their respective means in Table 3. Following eachindex’s description and verification, we show how theseindices discriminate between the types of deformationand normal skulls.

Calculating index values

Annular index (B/H): Because HA>HN>0, we canconclude that 1/HA<1/HN. This, together with thefact that BA<BN tells us that BA/HA<BN/HN. BecauseHA�HT, we can conclude that 1/HA�1/HT. This,together with the fact BA<BT tells us that BA/HA<BT/HT.Thus, we expect the value for the annular index in

annular skulls to be less than the values for the sameindex in normal and tabular skulls, respectively; or inmathematical terms: BA/HA<BN/HN, BT/HT. In Table 3,, we demonstrate the observed means for the annularindex across our populations. This corroborated ourexpectations that the annular index would indicatewhether or not a given skull had a tendency towardsan annular deformation.Tabular index (H/L): Because 0<LT<LN, we can con-

clude that 1/LN<1/LT. This, together with the factthat HN<HT gives us that HN/LN<HT/LT. Because0<LT<LA, we can conclude that 1/LA<1/LT. This, to-gether with the fact that HA�HT tells us that HA/LA<HT/LT.Thus, we expect the value for the tabular index

in tabular skulls to be greater than the values for thesame index in normal and annular skulls, respectively;or in mathematical terms: HA/LA, HN/LN<HT/LT. InTable 3, we demonstrate the observed means for the

Table 2. Computed means for each cranial dimension by typeof deformation

Deformation type

Annular Normal Tabular

Cranial breadth 127.46 136.44 143.89Cranial length 174.33 173.46 163.11Cranial height 134.94 127.72 134.09Frontal chord 117.94 107.40 115.15

Table 3. Observed means for each index by type acrosspopulations

Deformation type


Annular index B/H mean 0.95 1.07 1.08Tabular index H/L mean 0.77 0.74 0.82Normal index F/L mean 0.67 0.62 0.68



tabular index across our populations. This corroboratedour expectations that the tabular index would indicatewhether or not a given skull had a tendency towardsa tabular deformation.Normal index (F/L): Because 0<LT<LN, we can

conclude that 1/LN<1/LT. This, together with thefact that FN<FT tells us that FN/LN<FT/LT. BecauseLN�LA, we can conclude that 1/LN�1/LA. This, to-gether with the fact that FN<FA gives us that FN/LN<FA/LA.Thus, we expect the value for the normal index in

normal skulls to be less than the values for the sameindex in annular or tabular skulls, or in mathematicalterms: FN/LN<FA/LA, FT/LT. In Table 3, we demon-strate the observed means for the normal index acrossour populations. This corroborated our expectationsthat the normal index would indicate whether or nota given skull had a tendency towards deformation.We summarise the indices in Table 4.Before discussing the formula for determining the de-

formation and the likelihood of success, the need for theformula is discussed. Prior to developing the techniquedescribed in this paper, O’Brien classified 280 skulls, inthe data set of 469 skulls, as nondeformed through visualassessment only. The average normal index for this set is0.64. Taking Howells’ data set as our control group, theaverage normal index for nondeformed skulls in this re-gion is 0.62. Using the normal distribution for randomsamples, the probability that a random collection of280 skulls could have an average normal index of 0.64,when the true average for the population is 0.62, is lessthan 2x10-68 (or essentially zero). Therefore, it is con-cluded that there is a significant number of deformed

skulls that were inaccurately classified by O’Brien. Thisattests to the inaccuracy of a visual and qualitative formof ACD type classification system. O’Brien’s methodsof interpretation are based on the conflicted and am-biguous typological systems that currently exist (seeO’Brien & Sensor, 2004). Therefore, it is not surprisingthat classifications would differ. We suspect that manyof the studies that have been conducted on skull de-formation may produce similar results of inaccuracy.Thus, we offer a more objective classification system.

Discriminant function analysis

Discriminant function analysis has been used manytimes before to analyse craniometric data as it pertainsto differentiating groups (Giles & Elliot, 1962; Birkby,1966; Keita, 1988; Clark et al., 2007; Kranioti et al.,2008; Robinson & Bidmos, 2009). Therefore, we deemit appropriate to use in this study to find functionsthat best separate our data into distinct categories:normal, annular, or tabular (Tabachnick & Fidell,2001). A Shapiro–Wilks test was performed with thestatistical software package SAS (SAS, Institute, Inc.,NC, USA) (SAS, 2009). The p-values are separatedinto O’Brien annular, O’Brien tabular and Howells’ nor-mal (see Table 5).As all the p-values for the univariate test are greater

than 0.05, there is a 95% confidence interval that theseare all normal distributions. Notice that both thetabular population (p=0.277) and the normal popula-tion (p=0.201) are also multivariate normal. Whenperforming the discriminant analysis, the prior prob-abilities used were: 90% for normal, 5% for annularand 5% for tabular.Second, it was necessary to verify the existence of

a low multicollinearity of the independent variables.This is verified by examining the pooled within-groupscorrelation matrix using the statistical software packageSPSS (1989–2001) (SPSS, IBM Corporation, NY, USA).The desired low multicollinearity of the independentsexists if all the entries not on the diagonal are below

Table 4. Index tendency by deformation type across populations

Annular index(B/H)

Tabular index(H/L)

Normal index(F/L)

Annular Low Low HighTabular High High HighNormal High Low Low

Table 5. The p-values for univariate and multivariate normality of the annular, tabular and normal indices

p-values forunivariate normality p-values for

multivariatenormalityData collection Deformation type B/H annular index F/L normal index H/L tabular index

O’Brien Annular 0.112 0.798 0.250 0.041Tabular 0.939 0.582 0.914 0.277

Howells Normal 0.645 0.682 0.840 0.201



0.8. The results displayed in Table 6 clearly demonstratethat this requirement to use discriminant analysis issatisfied.Third, it was needed to determine whether or not

the covariance matrices were statistically different. ABox’sM test was performed which returned a p-valueless than 0.0005. Thus, the covariance matrices werestatistically different. Therefore, covariance matriceswere used as separated by groups.Using SPSS (1989–2001), the coefficients for the

discriminant functions were computed. The coeffi-cients and constants are listed in Table 7 and appliedin the following two functions:

Function 1 ¼ 4:997�B=Hþ 29:179�F=Lþ 19:551�H=L� 38:311

Function 2¼ 21:466�B=H� 28:719�F=Lþ 24:521�H=L� 23:115

When computed, these functions give the greatestseparation of our data. To compute these functions,the data used were O’Brien’s for annular and tabularskulls and Howell’s for the normal skulls. A territorialmap was constructed to help with future classifications.Thus, given a skull’s four measurements (i.e., L, H, B

and F), each index can be computed, their values placedinto the functions, and a skull’s location plotted on theterritorial map (see Figure 3). The skull is classified asdetermined by the zone, or region, into which it fallson the map (i.e., the annular, tabular or normal zone).The territorial map also displays the severity of the

deformation. For example, if the skull gets plotted inthe annular zone but is near the border to the normalzone, it indicates a less moderate degree of deformation.To illustrate how to use these functions and the ter-

ritorial map, consider the example of skull 1380 fromO’Brien’s data set in which the following measurementsare applied: B=120, F=110, H=123 and L=173 (seeTable 8). Next, the index values are computed: B/H=0.98, F/L=0.64 and H/L=0.71. But before computingthe discriminant function values, consider what out-come could be expected by comparing these indexvalues to the known means for annular, normal andtabular skulls (see Table 9). The standard deviations

Table 6. Correlation matrix for the annular, tabular and normalindices

Correlationmatrix

B/H annularindex

F/L normalindex

H/L tabularindex

B/H 1.000 �0.016 �0.308F/L �0.016 1.000 0.478H/L �0.308 0.478 1.000

Table 7. Canonical discriminant function coefficients

Function

1 2

B/H 4.997 21.466F/L 29.179 �28.719H/L 19.551 24.521Constant �38.311 �23.115

Figure 3. Territorial map.

Table 8. Measurements and associated indices for exampleskull #1380

Skull #1380 Cranial measurement (mm) Index values

L B H F B/H F/L H/L173 120 123 110 0.98 0.64 0.71

Table 9. Means and standard deviations for the annular, tabularand normal indices

Means (s.d.)

B/H annularindex

F/L normalindex

H/L tabularindex

Annular – O’Brien 0.95 (0.052) 0.68 (0.028) 0.78 (0.042)Normal – Howells 1.07 (0.045) 0.62 (0.019) 0.74 (0.026)Tabular – O’Brien 1.10 (0.081) 0.69 (0.032) 0.83 (0.045)



can be used to help determine the strength of anygiven tendency (see Table 9). Initially, without com-puting the functions, the standard deviations can beused as early indicators for classification.For example, first consider just the annular index for

skull 1380. To determine its tendency towards beingan annular skull, the z-score for the annular index iscomputed assuming it is an annular skull (z-score=0.58); assuming it is a normal skull (z-score=1.96);and finally assuming it is a tabular skull (z-score=1.5).The lower the z-score, the stronger the tendency askull has towards a certain classification. Thus, skull1380 has a strong tendency towards being classifiedas having annular deformation.Now consider only the normal index. Again, the z-

scores are computed assuming that this skull is a mem-ber of a certain population: annular (z-score=1.43),normal (z-score=1.05) and tabular (z-score=1.56).Thus, this skull tends to be normal but not strongly so.Finally, consider only the tabular index. Again, the

z-scores are computed assuming that this skull is amember of a certain population: annular (z-score=1.67), normal (z-score=1.15) and tabular (z-score=2.67). Thus, this skull leans weakly towards normal,whereas it strongly indicates that this is not a tabularskull, because of the high z-score. Therefore, it canbe assumed that this is not a tabular skull. Furthermore,because it only has one strong tendency, it is predictedthat this skull is classified as annular, but also, that theplotted point on the territorial map is located veryclose to the border of the normal zone.Thus, when the indices for skull, 1380 are applied to

the two discriminant functions, the results are: –0.86 forFunction 1 and �3.05 for Function 2. These values areplotted as points on the territorial map (see Figure 4),and as expected, the skull is classified as annular but isalmost on the border of the zone for nondeformedskulls. Incidentally, O’Brien also classified this as an an-nular skull. Thus, through this relatively straightforwardprocedure of measuring four craniometric dimensions,computing the indices, performing the functions andplotting the points, an unknown skull can be objectivelydetermined to have been modified or not. It has beenshown in this paper that a visual, qualitative assessmentof ACD type employing practised techniques results inrelatively poor results when tested on an unknown sam-ple (see Table 10) – being able to correctly identify an-nular deformation 83.1% of the time, tabular deformation87.5% of the time and no deformation 73.2% of the time(according to the newer quantitative methods presentedhere). However, it is much more acceptable to be correctin ACD typing 100% of the time, as demonstrated in ourtest on the Howells dataset, a known sample. To explain

O’Brien’s relatively low percentage for correctly classify-ing skulls into the right ACD category, we hypothesisethat one’s visual objectivity may become skewed whenworking with or seeing so many deformed skulls in a la-boratory context; such that one tends to classify manydeformed skulls as normal.

Discussion and conclusions

Techniques vary considerably on the interpretation andassignment of ACD type. The procedure is complicatedfurther with multiple typologies or styles. For instance,the terms circular, Aymara, highland, circumferential andannular all tend to refer to the same form. This only servesto confuse the investigator and complicate the discretecategorization of deformation type. Therefore, with thisnew method, only three names are used: normal, annularand tabular.Very few studies actually consider ACD in more

than one plane. For example, recent work offers a

Figure 4. Territorial map with skull 1380 identified by the symbol: ♦.

Table 10. Predicted membership for deformation type

Datagroup

Deformationtype asclassifiedby the

investigator

Predicted membership bydeformation type (number of crania)


O’Brien Annular 83.1% (66) 14.3% (11) 2.6% (2)Normal 11.8% (33) 73.2% (205) 15.0% (42)Tabular 3.6% (4) 8.9% (10) 87.5% (98)

Howell Normal 0% (0) 100% (110) 0% (0)



different method of ACD classification developed froma study of a small sample from Southeast Asia (Clarket al., 2007). Their approach also applies discriminantfunction analysis to cranial measurements but onlytaken in the sagittal plane. Regretfully, their techniquedoes not seem to isolate type but simply whether askull is deformed or not. In contrast, we examine de-formation as it affects the whole cranium by utilisingmultiple dimensions including: height, length andbreadth. The use of a multidimensional approachgreatly increases accuracy and viability.A large sample of human crania was visually and

qualitatively sorted into groups by the first author.The two general groups included those showing no de-formity and those that exhibited signs of beingintentionally modified. The classification methodsemployed are based on well published and often-usedtechniques in the scientific literature. Not knowingfor sure if crania were being properly identified pre-sented a problem that needed a solution. The potentialanswer is presented in this paper as a mathematical ap-proach to quantifying the ranges of deformation. Thisincluded using multiple dimensions that span the cra-nial vault; developing self-referential indices and usingdiscriminant functions to determine which zone a skullfalls into on a territorial map. This simplified and ob-jective method, applicable for use in the field or labora-tory, directs this analytical procedure toward a newfuture; especially as it pertains to investigations of pre-hispanic cranial samples from the south central Andes.It is suspected that mixed methods, of both qualitativeand quantitative, may still preferred to be used but em-phasise that a more mathematical approach will dimin-ish levels of discrepancy or inter-observer error.Therefore, we argue that the quantitative approachpresented in this paper will enhance the study of artifi-cially deformed crania by placing it in a more objectivesphere of analysis. We look forward to seeing furtherdevelopment as it becomes tested on larger, temporallyand spatially diverse samples. For the time being, its ap-plication to samples from the south central Andes hasbeen demonstrated.

Acknowledgements

The authors would like to thank David Pereira [MuseoArqueológico de San Simon in Cochabamba, Bolivia],Hector M. Pucciarelli [Division Antropologia. Facultadde Ciencias Naturales y Museo de La Plata (Argentina)],Claudia Aranda, Leandro Luna and Myriam Tarrago[Museo Etnografico ‘J. B. Ambrosetti’ in Buenos Aires,Argentina], for granting access to the human skeletal

collections under their care; as well as others fortheir cooperation and support: Marien Béguelin, JoseCocilovo, Paula Gonzalez, Ivan Perez, Ramon Sanzeteneaand Hugo Varela. Furthermore, we would like to thankthe constructive and insightful critique given by IngridCarlstein, Tony Crane, Mark Ecker, Mark Jacobson, VeraRayevskaya and especially Dr. Martin and the anonymousreviewers. Much of this research was supported by aUniversity of Northern Iowa faculty fellowship.Grant sponsorship provided by: University of

Northern Iowa Faculty Fellowship

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