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Forensic Science, Medicine,and Pathology ISSN 1547-769XVolume 7Number 3 Forensic Sci Med Pathol (2011)7:233-247DOI 10.1007/s12024-010-9204-7

Investigation on the utility of permanentmaxillary molar cusp areas for sexestimation

P. James Macaluso

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ORIGINAL ARTICLE

Investigation on the utility of permanent maxillary molar cuspareas for sex estimation

P. James Macaluso Jr.

Accepted: 30 October 2010 / Published online: 16 November 2010

� Springer Science+Business Media, LLC 2010

Abstract Digital photogrammetric methods were

employed to assess the level of sexual dimorphism present

in permanent maxillary molar cusp areas of black South

Africans (130 males, 105 females). Odontometric standards

were then developed for diagnosing sex, based on the cusp

area data derived for these teeth. Results demonstrated that

all cusp area measurements of both the first and second

maxillary molars were significantly dimorphic (P \0.0001)

in this group. Univariate and multivariate discriminant

function analyses yielded overall sex prediction accuracy

rates between 59.6 and 74.5%. Comparable allocation

results were also obtained for binary logistic regression

analyses, but with larger classification sex biases. The

highest classification accuracies were observed for different

combinations of just two cusp areas for the first molar.

Allocation rates of formulae derived for second molar

dimensions were on average 4.3% lower than those obtained

for the first molar. Analyses incorporating cusp areas of both

maxillary molars did not improve classification accuracies

achieved when only using first molar measurements. The

classification rates are below the suggested minimum

accuracy of 75–80% for reliable forensic application of a

method; however, the derived formulae may provide a

useful statistical indication as to the sex of fragmentary

remains in which complete or even partial tooth crowns are

the only materials available for examination. Furthermore,

the formulae can be applied not only to adults but also to

subadults (above the age of 3 years) in which the more

accurate sex discriminating features of the pelvis and skull

are yet to develop.

Keywords Discriminant analysis � Photogrammetry � Sex

discrimination � Dentition � South Africa

Introduction

The determination of sex is a primary concern in the analysis

of human skeletal remains. Sex is most often and accurately

assessed by examination of the pelvis and cranium; how-

ever, this may not always be possible in forensic or

archaeological contexts as skeletal remains are frequently

incomplete or damaged. Metric methods that employ non-

pelvic postcranial bones to estimate sex can be useful in

such cases where the hip bone and skull are not available for

study. In addition, DNA analysis can be used to determine

sex, even in highly fragmentary specimens, provided

nuclear DNA is preserved; although this method is more

expensive and time-consuming [1].

A number of studies have also demonstrated the useful-

ness of the permanent dentition in sex assessment of human

skeletal remains. Odontometric analyses have traditionally

relied on linear measurements of whole tooth crowns using

sliding calipers. The most widely used dimensions in sex

determination studies have been mesiodistal and buccolin-

gual crown diameters [2–6]. However, diagonal crown

measurements, such as mesiobuccal-distolingual and dis-

tobuccal-mesiolingual diameters [7–9], and root lengths

[10–12] have also been employed.

Various researchers have devised alternative approaches

for measuring tooth size in which intra-coronal components

(e.g., intercusp distances, cusp areas) are studied instead of

the whole crown [13–20]. Earlier efforts received limited

attention given the labor-intensive methods required

to collect and analyze the data. However, the advent of

digital photography and the availability of image-analysis

P. J. Macaluso Jr. (&)

Department of Anthropology, Binghamton University (SUNY),

P.O. Box 6000, Binghamton, NY 13902-6000, USA

e-mail: p.james.macaluso@hotmail.com

123

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DOI 10.1007/s12024-010-9204-7

Author's personal copy

computer software programs now permit crown components

to be measured with relative ease.

Recently, standardized digital occlusal photographs have

been used to measure intercusp distances and basal cusp

areas of the postcanine teeth among modern humans

[17–21]. Although several of the above mentioned studies

have demonstrated that cusp areas of the maxillary molars

display greater sexual dimorphism than conventional crown

length and breadth dimensions [20, 21], they do not attempt

to apply classificatory procedures for separating the sexes.

Therefore, the purpose of this preliminary investigation is to

explore the potential utility of cusp area measurements of

the permanent maxillary molars for sex determination of

unidentified human remains from medicolegal or archaeo-

logical contexts. To this end, digital photogrammetric

methods were employed to assess the level of sexual

dimorphism present in cusp areas of the maxillary molars of

a documented skeletal series. Odontometric standards were

then developed for determining sex, based on the cusp area

measurements derived for these teeth.

Materials and methods

Sample

Dental measurements were collected from 235 black South

Africans drawn from the Raymond A. Dart Collection of

Human Skeletons (School of Anatomical Sciences, Uni-

versity of the Witwatersrand) and the Pretoria Bone Col-

lection (Department of Anatomy, School of Medicine,

Faculty of Health Sciences, University of Pretoria). The

specimens in these documented skeletal series largely

derive from unclaimed bodies at public hospitals which

were used in medical training and research [22, 23]. The

selected sample comprised the permanent maxillary molars

of 130 males and 105 females between the ages-at-death of

12 and 78 years. Although different indigenous population

groups constitute the South African black sample, in this

study they were regarded as a single group given that

previous analyses showed no significant inter-populational

differences in most of the metric and morphological char-

acteristics of their skulls [24] and dentition [25]. In addi-

tion, in many forensic situations the local population is not

known, and thus the use of a general model which incor-

porates the various ethnic groups is more appropriate [26].

This study focuses on the first and second maxillary

molars, given that the third molar is frequently absent

among modern humans due to incomplete maturation,

extraction or agenesis [18, 19, 27–30]. In addition, the

occlusal surface of the third molar is more variable than the

mesial two molars [30–32], and therefore interpretation of

detailed crown morphology, including cusp boundaries, is

often difficult. Individuals possessing tooth crowns in which

the fissures separating the cusps could not be identified, due

to pathology, dental restorations or marked occlusal wear,

were excluded from the analysis. Only molars possessing

all four principal cusps (paracone, protocone, metacone,

hypocone) were utilized. This included teeth exhibiting

hypocone (cusp 4) expression consistent with grade 3.5

(moderate-sized cusp) or higher according to the Arizona

State University Dental Anthropology System [33]. Given

that asymmetry in dental metrics and morphological traits,

including cusp configurations, tends to be minor [30, 32, 34,

35], only teeth on the left side of the dental arch were

measured; but in cases where this was not possible, the

corresponding tooth on the right side was utilized.

Data acquisition

Standardized high-resolution photographs of the occlusal

surfaces of maxillary first and second molars were obtained

for each specimen using a Nikon Coolpix S610 digital

camera. The camera was mounted on a tripod and a lev-

eling device was used to ensure a consistent camera angle.

Several different crown orientation systems have been

employed in studies based on occlusal surface photographs

[36 and references therein]. Although a recent study has

demonstrated that inter-observer error due to orientation

method when measuring cusp areas is insignificant [37],

not all orientation systems are applicable to dental remains

from forensic and archaeological contexts due to occlusal

wear. Therefore, in this study each tooth was oriented such

that the buccal and, where possible, mesial and distal cer-

vical enamel line was perpendicular to the optical axis of

the camera, given that this method does not rely on the

preservation on cusps apices. A millimeter scale, placed

parallel to the tooth and in approximately the same hori-

zontal plane as the occlusal surface, was included in each

photograph for calibration.

The digital photographs were then transferred to a per-

sonal computer, calibrated, and measured on-screen using

the NIH ImageJ software program developed and freely

distributed by the National Institutes of Health, USA

(http://rsb.info.nih.gov/ij/). Calibration was accomplished

by using the program’s set scale function and the milli-

meter scale present in each image. The polygon, straight

line, and freehand line tools within the NIH ImageJ pro-

gram were used to take measurements.

Individual cusp areas were measured by tracing the

tooth perimeter and the course of the primary fissures

separating the four principal cusps. When a fissure did not

extend to the crown margin, its course was projected by

following the direction of the fissure before it became

obscure [37]. Following the protocol of Wood and Engl-

eman [38], when an additional cuspule was present (e.g.,

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metaconule, mesial marginal accessory tubercle) the pri-

mary fissure was extended to the crown margin and the

appropriate proportions of the area of the additional cusp-

ule were added to the areas of the adjacent main cusps.

Where necessary, conservative corrections for interproxi-

mal wear were made by reconstructing the original mesial

and distal crown margins based on the overall crown shape

and the buccolingual extent of the wear facets [38]. The

areas of the four cusps were measured to the nearest tenth

of a square millimeter (Fig. 1). In addition to area data,

maximum mesiodistal and buccolingual crown diameters

[39] were also measured from the digital images and

recorded to the nearest tenth of a millimeter.

Statistical analyses

Previous studies have demonstrated that dental measure-

ments recorded from digital photographs utilizing image-

analysis software are comparable to those obtained using

conventional anthropometric instruments [17, 40]. In addi-

tion, Bailey et al. [37] and others [20, 21, 41] have shown

that photogrammetric methods for measuring cusp base

areas have relatively low levels of both intra- and inter-

observer error. In the present study, intra-observer mea-

surement error associated with the photogrammetric process

(crown orientation, image capture, identification of primary

fissures) was assessed by repeating the entire data recording

procedure on 30 randomly selected teeth from the original

sample. Differences between first and second determina-

tions were then analyzed by computing the absolute (TEM)

and relative (rTEM) technical errors of measurement, using

the following formulae:

TEM ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

X

D2.

2N

r

rTEM ¼ TEM�

XT

In these formulae, D2 is the squared difference between the

first and second measurements, N is the number of speci-

mens measured, and XT is the grand mean of the arithmetic

means for the first and second measurements [42]. Paired-

sample t tests were also used to detect systematic meth-

odological errors.

To investigate sexual dimorphism within the study

sample, basic descriptive statistics were computed for all

crown dimensions and the significance of mean differences

between the sexes was evaluated utilizing independent-

samples t tests. Following this, discriminant function

analysis was used to develop a set of formulae for deter-

mining sex. The use of discriminant analysis requires

meeting several assumptions concerning the data, including

multivariate normality and equality of covariance matrices

across groups. D’Agostino–Pearson omnibus tests con-

firmed that the data are distributed normally (P [ 0.05).

Box’s M tests were used to test for an equality of covari-

ance in the male and female samples. Given that Box’s M

tests are particularly sensitive to deviations from normality,

an alpha level of P \ 0.001 was used [43]. The Box’s M

tests did not attain statistical significance, indicating

homogeneity of male and female covariance matrices, and

that the assumptions of discriminant function analysis have

not been violated. As human remains recovered in forensic

and archaeological contexts are variably preserved, various

stepwise and multivariate direct discriminant analyses were

carried out on each molar crown separately (M1 or M2) to

obtain functions that could be used with fragmentary

dentitions, as well as on both teeth concurrently (M1 and

M2) for more complete remains. In addition, direct dis-

criminant function analysis was performed on individual

measurements (e.g., M1 protocone area) in an attempt to

identify demarking points that may be used for highly

fragmentary dental remains in which broken or incomplete

tooth crowns are the only materials available for study. The

discriminant equations were all cross-validated using the

jackknife (leave-one-out) classification procedure.

In addition to discriminant function analysis, the data

was subjected to binary logistic regression analysis as

previous studies [44–48], including a recent dental inves-

tigation [49], have suggested that it may be advantageous

to use both statistical methods to estimate sex. As pointed

out by these authors, the benefits of binary logistic

regression are that this technique generally performs as

well as or better than discriminant function analysis with

Fig. 1 Photograph of a permanent maxillary second molar. Outlinesillustrate individual cusp areas and how worn teeth were corrected for

interproximal wear

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fewer statistical assumptions when predicting dichotomous

variables such as sex, and the resulting score used to

classify an unknown individual also provides a probability

value for the allocation. A set of univariate and multivar-

iate formulae for predicting sex, comparable to that gen-

erated using discriminant function analysis, was developed

utilizing logistical regression methods. All statistical

analyses were conducted using various subroutines of the

SPSS 14.0 statistical software package.

Results

Assessment of methodological error

The results of the paired-sample t tests demonstrate that

there were no statistically significant differences between

repeated measurements (P [ 0.05 for all variables), sug-

gesting that methodological errors associated with the

photogrammetric process were small and unlikely to have

unduly influenced the results (Table 1). The values

observed for the relative technical error of measurement

(rTEM) reveal that mesiodistal and buccolingual dimen-

sions are very reliable (1.01 and 0.79%, respectively),

while cusp area measurements are slightly more difficult to

replicate with error rates between 1.53 and 3.02%.

Assessment of sexual dimorphism

Descriptive statistics for crown diameters and cusp area

measurements recorded in both males and females are

provided in Table 2. Results of the independent-sample

t tests show that mean values for males are significantly

larger than those of females (P \ 0.0001) for all dental

dimensions. As indicated by t values, dimensions of the first

molar generally displayed greater sexual dimorphism than

the second molar. Mesiodistal and buccolingual diameters

were by and large more dimorphic than individual cusp area

measurements, particularly for the M2. Among cusp areas,

the two mesial cusps (paracone and protocone) showed

greater sex dimorphism than the distal cusps (metacone and

hypocone) in both maxillary molars. The paracone area of

the M1 displayed the greatest dimorphism among all vari-

ables examined in this study. Metacone area was the least

dimorphic measurement in both teeth.

Discriminant function analysis

The discriminant function coefficients of the sex predicting

formulae generated for dimensions of the maxillary first

Table 1 Intraobserver error test results

P-value TEM (mm) rTEM (%)

MD 0.130 0.1103 1.0066

BL 0.475 0.0885 0.7859

Pr area 0.370 0.4806 1.5294

Pa area 0.105 0.4919 1.8793

Me area 0.914 0.5850 2.8770

Hy area 0.210 0.6214 3.0222

MD mesiodistal diameter, BL buccolingual diameter, Pr protocone,

Pa paracone, Me metacone, Hy hypocone

Table 2 Descriptive statistics and t values for first and second maxillary molar variables

Variables Males (n = 130) Females (n = 105) t Values*

Mean ± SD Range CV Mean ± SD Range CV

M1

MD 11.09 ± 0.57 9.5–12.6 5.16 10.63 ± 0.53 9.4–12.4 5.01 6.383

BL 11.50 ± 0.59 10.1–13.4 5.13 10.89 ± 0.52 9.6–12.3 4.75 8.367

Pr area 32.70 ± 3.55 25.5–43.9 10.84 29.40 ± 3.19 23.6–37.5 10.86 7.429

Pa area 26.47 ± 2.75 20.0–34.4 10.38 23.68 ± 2.08 19.3–28.8 8.77 8.856

Me area 22.35 ± 2.80 16.1–29.0 12.54 20.79 ± 2.33 15.4–26.0 11.22 4.568

Hy area 23.75 ± 3.44 13.5–31.1 14.47 21.57 ± 2.90 14.8–28.7 13.43 5.169

M2

MD 10.94 ± 0.76 9.3–12.6 6.94 10.38 ± 0.57 9.1–12.0 5.54 6.526

BL 11.70 ± 0.71 10.0–13.5 5.99 11.18 ± 0.61 9.6–12.6 5.46 6.967

Pr area 34.61 ± 4.68 24.6–47.3 13.53 31.44 ± 3.44 24.6–40.0 10.94 5.982

Pa area 28.38 ± 3.68 19.2–39.1 12.99 25.90 ± 2.99 19.4–34.4 11.54 5.566

Me area 20.07 ± 2.84 12.5–27.8 14.15 18.47 ± 2.48 12.0–27.1 13.44 4.522

Hy area 21.04 ± 4.46 10.5–32.9 22.05 18.02 ± 3.85 10.1–26.4 21.37 5.351

Abbreviations of crown dimensions are the same as in Table 1

* All significant at P \ 0.0001

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molar, second molar, and both molars combined are pre-

sented in Tables 3, 4, and 5, respectively. The cross-vali-

dated classification accuracy rates for all these functions

are provided in Table 6. In the stepwise analysis of all six

M1 crown and cusp area measurements (Function 1), the

selected variables included the paracone area and proto-

cone area, producing an overall classification accuracy of

72.8%. For a similar procedure incorporating M2 dimen-

sions (Function 13), only buccolingual and mesiodistal

crown diameters were selected, which correctly assigned

69.4% of the study sample. Direct analyses incorporating

mesiodistal and buccolingual crown diameters for either

the M1 (Function 2) or M2 (Function 14) yielded accuracy

rates of 73.6 and 69.4%, respectively.

Additional functions generated by the direct approach

were designed for less complete remains in which only a

portion of the tooth crown is available for examination.

The combination of protocone area and hypocone area

(lingual cusps) for the M1 (Function 5), achieved an overall

correct sex classification rate of 74.0%. Similar, but

slightly lower, sex prediction accuracies were obtained for

the combination of the paracone area and protocone area

(Function 3, 72.8%), as well as the paracone area and

metacone area (Function 6, 72.3%). Classification accuracy

dropped to 66.8% when only the distal cusp areas (meta-

cone and hypocone) were used (Function 4). Appreciable

lower accuracies were obtained for similar functions

derived for M2 dimensions. The percentage correctly

allocated ranged from 62.6% for the combination of par-

acone and metacone (Function 18) to 65.5% for the com-

bination of protocone and hypocone (Function 17).

The direct method was also employed to develop

functions for single dimensions of either the M1 (Functions

7–12) or M2 (Functions 19–24), which may be used with

highly fractured tooth crowns. Classification accuracies for

M1 dimensions ranged from a low of 62.1% for metacone

area (Function 11) to a high of 73.6% for buccolingual

diameter (Function 8). The most effective cusp area for the

first molar was that of the paracone (Function 10) with

72.3% of the study sample correctly classified. The clas-

sification accuracies for maxillary second molar dimen-

sions were again lower than those for the first molar. The

highest accuracy rate was obtained for the buccolingual

diameter (Function 20) at 68.1%, while the paracone area

(Function 22) provided the lowest accuracy (59.6%) for a

single variable. The best discriminating cusp area for the

M2 was that of the protocone (Function 21) with an overall

sex prediction percentage of 64.7%.

The remaining functions, derived by the stepwise

method, were designed for better preserved remains in

which both maxillary molars are available for study. For

Function 25, which incorporated all 12 crown and cusp

area dimensions of both teeth, paracone area and protocone

area of the M1, as well as hypocone area of the M2 were

selected. This combination of variables provided a classi-

fication accuracy rate of 73.2%. When the four crown

diameters were entered into a stepwise procedure (Function

26), the buccolingual width of the M1 and mesiodistal

length of the M2 were the variables chosen, producing

74.0% accuracy of correctly identifying sex. As with

Function 25, a stepwise analysis of all cusp areas from both

maxillary molars, in which paracone and protocone areas

of the M1 and hypocone area of the M2 were selected

(Function 27), correctly assigned 73.2% of individuals in

the study sample. When lingual cusp areas of both the first

and second molars were entered into a stepwise procedure

(Function 28), the selected variables included protocone

area of the M1 and hypocone area of the M2. This com-

bination of dimensions yielded 70.2% accuracy in identi-

fying sex, a level only slightly lower than that obtained for

Function 27, which also included M1 paracone area. For a

similar procedure conducted for buccal cusp areas of both

teeth (Function 29), only the paracone area of the M1 was

chosen, providing a classification accuracy of 72.3%.

Logistical regression analysis

The logistic regression equations and associated classifi-

cation accuracy rates derived for dimensions of the max-

illary first molar, second molar, and both molars combined

are presented in Tables 7, 8, and 9, respectively. In general,

the regression analyses yielded slightly higher overall sex

prediction accuracies compared to those provided by the

discriminant function analyses. The same variables were

selected in all stepwise regression analyses as those chosen

for the corresponding discriminant functions discussed

above. Therefore, for Equation 1, in which all six M1

crown and cusp area dimensions were entered into a

stepwise procedure, the selected variables included the

protocone area and paracone area. This combination of

measurements achieved a correct sex classification rate of

71.9%. For a similar procedure incorporating M2 dimen-

sions (Equation 13), again only buccolingual and mesio-

distal crown diameters were selected, which correctly

allocated 69.4% of individuals in the study sample. When

mesiodistal and buccolingual crown diameters are entered

into an equation, using the direct method, similar classifi-

cation accuracies were observed: 74.0% for the M1

(Equation 2) and 69.4% for the M2 (Equation 14). As these

abovementioned classification rates demonstrate, appre-

ciable lower accuracies were obtained for logistic regres-

sion equations derived for dimensions of the second molar

than for the first molar, similar to the results provided in the

discriminant function analyses.

The combination of paracone area and metacone area

(buccal cusps) provided the best separation among M1 cusp

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Table 3 Canonical discriminant function coefficients of the derived equations for maxillary first molar

Functions and selected

variablesaUnstandardized

coefficient

Standardized

coefficient

Structure point Group

centroids

Sectioning

point

Function 1: all six variables

M1 Pa area 0.283 0.699 0.923 M = 0.546 -0.066

M1 Pr area 0.131 0.445 0.797 F = -0.677

Constant -11.236

Function 2: crown diameters

M1 BL 1.427 0.797 0.963 M = 0.509 -0.061

M1 MD 0.570 0.316 0.735 F = -0.631

Constant -22.223

Function 3: mesial cusps

M1 Pa area 0.283 0.699 0.923 M = 0.546 -0.066

M1 Pr area 0.131 0.445 0.797 F = -0.677

Constant -11.236

Function 4: distal cusps

M1 Hy area 0.216 0.692 0.845 M = 0.359 -0.043

M1 Me area 0.214 0.556 0.797 F = -0.444

Constant -9.543

Function 5: lingual cusps

M1 Pr area 0.240 0.814 0.947 M = 0.740 -0.185

M1 Hy area 0.108 0.347 0.659 F = -1.110

Constant -9.543

Function 6: buccal cusps

M1 Pa area 0.421 1.041 0.998 M = 0.505 -0.060

M1 Me area -0.028 -0.074 0.530 F = -0.625

Constant -10.014

Function 7

M1 MD 1.802 M = 0.374 -0.045

Constant -19.619 F = -0.463

Demarking point Females \ 10.86 mm \ males

Function 8

M1 BL 1.790 M = 0.491 -0.058

Constant -20.099 F = -0.607

Demarking point Females \ 11.20 mm \ males

Function 9

M1 Pr area 0.295 M = 0.436 -0.052

Constant -9.207 F = -0.539

Demarking point Females \ 31.05 mm2 \ males

Function 10

M1 Pa area 0.405 M = 0.504 -0.060

Constant -10.209 F = -0.624

Demarking point Females \ 25.08 mm2 \ males

Function 11

M1 Me area 0.384 M = 0.268 -0.032

Constant -8.320 F = -0.332

Demarking point Females \ 21.57 mm2 \ males

Function 12

m1 hy area 0.312 M = 0.303 -0.036

Constant -7.012 F = -0.375

Demarking point Females \ 22.66 mm2 \ males

a Function 1 was derived by means of stepwise analysis, all others by direct analysis. Abbreviations of crown dimensions are the same as in Table 1

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Table 4 Canonical discriminant function coefficients of the derived equations for maxillary second molar

Functions and selected

variablesaUnstandardized

coefficient

Standardized

coefficient

Structure

point

Group

centroids

Sectioning

point

Function 13: all six variables

M2 BL 0.988 0.657 0.902 M = 0.453 -0.054

M2 MD 0.727 0.497 0.321 F = -0.561

Constant -19.147

Function 14: crown diameters

M2 BL 0.988 0.657 0.902 M = 0.453 -0.054

M2 MD 0.727 0.497 0.321 F = -0.561

Constant -19.147

Function 15: mesial cusps

M2 Pa area 0.144 0.602 0.923 M = 0.368 -0.044

M2 Pr area 0.148 0.501 0.886 F = -0.456

Constant -8.819

Function 16: distal cusps

M2 Hy area 0.165 0.712 0.869 M = 0.361 -0.043

M2 Me area 0.193 0.519 0.735 F = -0.447

Constant -6.993

Function 17: lingual cusps

M2 Pr area 0.159 0.664 0.839 M = 0.405 -0.048

M2 Hy area 0.133 0.572 0.775 F = -0.501

Constant -7.898

Function 18: buccal cusps

M2 Pa area 0.218 0.738 0.930 M = 0.351 -0.042

M2 Me area 0.154 0.415 0.756 F = -0.434

Constant -8.926

Function 19

M2 MD 1.463 M = 0.372 -0.044

Constant -15.642 F = -0.460

Demarking point Females \ 10.66 mm \ males

Function 20

M2 BL 1.504 M = 0.408 -0.049

Constant -17.318 F = -0.506

Demarking point Females \ 11.48 mm \ males

Function 21

M2 Pr area 0.240 M = 0.340 -0.041

Constant -7.953 F = -0.421

Demarking point Females \ 33.03 mm2 \ males

Function 22

M2 Pa area 0.295 M = 0.326 -0.039

Constant -8.041 F = -0.404

Demarking point Females \ 27.14 mm2 \ males

Function 23

M2 Me area 0.372 M = 0.265 -0.032

Constant -7.205 F = -0.328

Demarking point Females \ 19.27 mm2 \ males

Function 24

M2 Hy area 0.232 M = 0.314 -0.037

Constant -4.573 F = -0.388

Demarking point Females \ 19.53 mm2 \ males

a Function 13 was derived by means of stepwise analysis, all others by direct analysis. Abbreviations of crown dimensions are the same as in Table 1

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dimensions (Equation 6) with an overall sex prediction

percentage of 73.2%. Slightly lower accuracies were

obtained for other cusp area combinations: paracone area

and protocone area (Equation 3, 71.9%), hypocone area

and metacone area (Equation 4, 69.8%), protocone and

hypocone (Equation 5, 71.5%). For the M2, the combina-

tion of protocone area and hypocone area (Equation 17,

68.1%) provided the highest accuracy rate, followed by the

protocone area and paracone area (Equation 15, 66.0%)

and paracone area and metacone area (Equation 18,

64.7%). The lowest accuracy was observed for the com-

bination of hypocone and metacone (Equation 16), with

only 64.3% of the study sample correctly assigned.

Overall classification accuracies for individual M1

dimensions ranged from a low of 61.7% for metacone area

(Equation 12) to a high of 73.2% for the paracone area

(Equation 10). For the M2, buccolingual diameter yielded

the highest allocation accuracy for a single variable

(Equation 20, 67.7%), while the lowest accuracy was

obtained for metacone area (Equation 25, 62.1%). The

highest accuracy rate for individual M2 cusp areas was

observed for the protocone (Equation 21) and hypocone

(Function 24), as both correctly assigned 65.1% of the

study sample.

The stepwise analyses incorporating both first and second

maxillary molar dimensions provided classification accu-

racy rates ranging from 68.5 to 74.5%. The highest accuracy

was observed for Equation 25 in which all 12 dental

dimensions of the M1 and M2 were entered into the procedure

and only the paracone area and metacone area of the first

molar and hypocone area of the second molar were selected.

Likewise, a stepwise analysis of all cusp areas from both

maxillary molars, in which paracone and protocone areas of

the M1 and hypocone area of the M2 were selected (Equa-

tion 27), correctly allocated 74.5% of the study sample. As

with the discriminant function analysis, when the four crown

diameters were entered into a stepwise procedure (Equa-

tion 26), the buccolingual width of the M1 and mesiodistal

length of the M2 were the variables chosen, producing 72.3%

accuracy of correctly identifying sex. The paracone area of

the M1 was the only variable selected in the stepwise analysis

incorporating the buccal cusp areas of both molars (Equa-

tion 29), yielding a prediction percentage of 73.2%. Finally,

when lingual cusp areas of both the first and second molars

were entered into a stepwise procedure (Function 28), the

selected variables included the protocone area of the M1 and

hypocone area of the M2. This combination of cusp dimen-

sions provided 68.5% accuracy in correct sex assignment.

Table 5 Canonical discriminant function coefficients of the derived equations for maxillary first and second molars combined

Functions and selected

variablesaUnstandardized

coefficient

Standardized

coefficient

Structure

point

Group

centroids

Sectioning

point

Function 25: all 12 variables

M1 Pa area 0.257 0.635 0.881 M = 0.572 -0.068

M1 Pr area 0.105 0.355 0.761 F = -0.708

M2 Hy area 0.072 0.310 0.548

Constant -11.169

Function 26: crown diameters

M1 BL 1.404 0.784 0.949 M = 0.517 -0.062

M2 MD 0.502 0.356 0.719 F = -0.640

Constant -21.325

Function 27: cusp areas

M1 Pa area 0.257 0.635 0.881 M = 0.572 -0.068

M1 Pr area 0.105 0.355 0.761 F = -0.708

M2 Hy area 0.072 0.310 0.548

Constant -11.169

Function 28: lingual cusps

M1 Pr area 0.232 0.787 0.909 M = 0.479 -0.057

M2 Hy area 0.101 0.434 0.655 F = -0.593

Constant -9.234

Function 29: buccal cusps

M1 Pa area 0.405 1.000 1.000 M = 0.504 -0.060

Constant -10.209 F = -0.624

a All functions derived by means of stepwise analysis. Abbreviations of crown dimensions are the same as in Table 1

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Discussion

Digital photogrammetric methods were used to collect

odontometric data for a documented sample of black South

Africans. All recorded dental dimensions for the permanent

maxillary first and second molars were sexually dimorphic,

with significantly larger mean values observed in males

than in females. Individual cusp area measurements of the

first molar generally displayed greater dimorphism than the

second molar. In addition, the mesial cusps were more

sexually dimorphic than the distal cusps in both the M1 and

M2. Furthermore, the greatest degree of sexual dimorphism

in cusp size was observed for the paracone area of the first

molar. These results are inconsistent, in part, with previous

cusp area studies by Kondo and Townsend [21] and

Takahashi et al. [20] in which the paracone, the first cusp to

form ontogenetically, was the least sexually dimorphic

cusp in the first maxillary molar. Likewise, these authors

found that the later-formed second molar exhibited greater

sex differences than the earlier-formed first molar. The

apparent differences in the pattern of sexual dimorphism

may be population based, as the prior studies were con-

ducted on non-African groups. However, these compari-

sons must be viewed with caution as they are based on

percentages of sexual dimorphism provided in the above-

mentioned studies and not corresponding t values, which

were not reported.

Although sexually dimorphic, cusp area measurements

of the first and second maxillary molars are only low to

moderate sex discriminators. Univariate and multivariate

discriminant function and binary logistic regression anal-

yses yielded overall classification accuracy rates ranging

from 59.6 to 74.5%. The logistic regression equations

derived in this study yielded higher sex prediction accu-

racies compared to those provided by the discriminant

functions; however, the difference between allocation rates

was generally below 2.0%. In addition, these slightly

improved classification rates were often associated with

larger sex biases, in which males were classified more

accurately than females. The sex bias percentages for the

binary logistic regression equations ranged from 2.8 to

29.5%. In contrast, the classification sex biases for all of

the derived discriminant functions were between 2.9 and

10.1%, with greater accuracy in females than in males for

nearly all formulae. Therefore, discriminant function

analysis appears to be the better statistical method for the

present dataset given its ability to make sex predictions that

have both high classification accuracies and low sex bias

percentages. Nonetheless, given the relative success of the

binary logistic regression analyses observed in the present

research, as well as previous investigations [e.g., 49], it is

further recommended that both methods be utilized in

future dental studies to determine which statistical

approach provides the best overall sex allocation results.

The classification results obtained in the present study

are comparable to those reported in a previous dental

investigation concerning sex determination in black South

Africans. Examining crown diameters of the maxillary

teeth, Kieser and Groeneveld [50] reported sex prediction

accuracy rates of 70.2 and 66.7% for males and females,

respectively, using multivariate discriminant function

analysis. In comparison, the current study revealed overall

allocation accuracies that ranged from 63.4 to 74.0% for

Table 6 Classification accuracy rates of the derived discriminant

functions for maxillary molar dimensions

Functionsa Cross-validated %

Males Females Overall Sex

biasb

M1

Function 1: all six variables 69.2 77.1 72.8 -7.9

Function 2: crown diameters 72.3 75.2 73.6 -2.9

Function 3: mesial cusps 69.2 77.1 72.8 -7.9

Function 4: distal cusps 65.4 68.6 66.8 -3.2

Function 5: lingual cusps 70.8 78.1 74.0 -7.3

Function 6: buccal cusps 70.8 74.3 72.3 -3.5

Function 7: MD 60.0 67.6 63.4 -6.7

Function 8: BL 76.2 70.5 73.6 5.7

Function 9: Pr area 63.8 68.6 66.0 -4.8

Function 10: Pa area 70.8 74.3 72.3 -3.5

Function 11: Me area 58.5 66.7 62.1 -8.2

Function 12: Hy area 67.7 61.0 64.7 6.7

M2

Function 13: all six variables 67.7 71.4 69.4 -3.7

Function 14: crown diameters 67.7 71.4 69.4 -3.7

Function 15: mesial cusps 62.3 66.7 64.3 -4.4

Function 16: distal cusps 58.5 68.6 63.0 -10.1

Function 17: lingual cusps 63.1 68.5 65.5 -5.4

Function 18: buccal cusps 59.2 66.7 62.6 -7.5

Function 19: MD 62.3 70.5 66.0 -8.2

Function 20: BL 70.0 65.7 68.1 4.3

Function 21: Pr area 62.3 67.6 64.7 -5.3

Function 22: Pa area 56.9 62.9 59.6 -6.0

Function 23: Me area 60.0 63.8 61.7 -3.8

Function 24: Hy area 60.0 69.5 64.3 -9.5

M1 and M2

Function 25: all 12 variables 70.8 76.2 73.2 -5.4

Function 26: crown diameters 72.3 76.2 74.0 -5.1

Function 27: cusp areas 70.8 76.2 73.2 -5.4

Function 28: lingual cusps 66.9 74.3 70.2 -7.4

Function 29: buccal cusps 70.8 74.3 72.3 -3.7

a Abbreviations of crown dimensions are the same as in Table 1b Sex bias = % males correctly classified - % females correctly

classified

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Table 7 Logistic regression equations and classification accuracies for maxillary first molar variables

Selected variablesa ß coefficient Standard error Sectioning point Correctly classified (%) Sex biasb

Male Female Overall

Equation 1: all six variables

M1 Pr area 0.172 0.056 0.5 75.4 67.6 71.9 7.8

M1 Pa area 0.391 0.083

Constant -14.844 2.178

Equation 2: crown diameters

M1 BL 1.734 0.351 0.5 79.2 67.6 74.0 11.6

M1 MD 0.699 0.332

Constant -26.767 4.113

Equation 3: mesial cusps

M1 Pa area 0.172 0.056 0.5 75.4 67.6 71.9 7.8

M1 Pr area 0.391 0.083

Constant -14.844 2.178

Equation 4: distal cusps

M1 Hy area 0.178 0.058

M1 Me area 0.173 0.047 0.5 78.5 59.0 69.8 19.5

Constant -7.541 1.476

Equation 5: lingual cusps

M1 Pr area 0.260 0.052

M1 Hy area 0.110 0.050 0.5 76.2 65.7 71.5 10.5

Constant -10.342 1.671

Equation 6: buccal cusps

M1 Pa area 0.524 0.089 0.5 77.7 67.6 73.2 10.1

M1 Me area -0.032 0.072

Constant -12.17 1.948

Equation 7

M1 MD 1.564 0.286 0.5 68.5 65.7 67.2 2.8

Constant -16.75 3.099

Equation 8

M1 BL 2.081 0.317 0.5 79.2 63.8 72.3 15.4

Constant -23.068 3.546

Equation 9

M1 Pr area 0.302 0.050 0.5 72.3 61.9 67.7 10.4

Constant -9.131 1.539

Equation 10

M1 Pa area 0.504 0.076 0.5 77.7 67.6 73.2 10.1

Constant -12.369 1.900

Equation 11

M1 Me area 0.234 0.055 0.5 70.8 50.5 61.7 20.3

Constant -4.828 1.196

Equation 12

M1 Hy area 0.210 0.045 0.5 76.2 46.7 63.0 29.5

Constant -4.557 1.025

a Equation 1 was derived by means of stepwise analysis, all others by direct analysis. Abbreviations of crown dimensions are the same as in

Table 1b Sex bias = % males correctly classified - % females correctly classified

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Table 8 Logistic regression equations and classification accuracies for maxillary second molar variables

Selected variablesa ß coefficient Standard error Sectioning point Correctly classified (%) Sex biasb

Male Female Overall

Equation 13: all six variables

M2 BL 1.013 0.265 0.5 73.8 63.8 69.4 10.0

M2 MD 0.762 0.256

Constant -19.507 3.134

Equation 14: crown diameters

M2 BL 1.013 0.265 0.5 73.8 63.8 69.4 10.0

M2 MD 0.762 0.256

Constant -19.507 3.134

Equation 15: mesial cusps

M2 Pr area 0.127 0.056 0.5 76.2 53.3 66.0 22.9

M2 Pa area 0.124 0.046

Constant -7.320 1.384

Equation 16: distal cusps

M2 Hy area 0.156 0.058

m2 me area 0.134 0.036 0.5 69.2 58.1 64.3 11.1

Constant -5.404 1.137

Equation 17: lingual cusps

M2 Pr area 0.149 0.039

M2 Hy area 0.122 0.036 0.5 70.8 64.8 68.1 6.0

Constant -7.068 1.294

Equation 18: buccal cusps

M2 Pa area 0.177 0.049 0.5 72.3 55.2 64.7 17.1

M2 Me area 0.129 0.062

Constant -7.058 1.395

Equation 19

M2 MD 1.249 0.229 0.5 70.8 57.1 64.7 13.7

Constant -13.078 2.429

Equation 20

M2 BL 1.387 0.237 0.5 74.6 59.0 67.7 15.6

Constant -15.708 2.717

Equation 21

M2 Pr area 0.189 0.037 0.5 73.8 54.3 65.1 19.5

Constant -6.023 1.219

Equation 22

M2 Pa area 0.222 0.045 0.5 73.8 50.5 63.4 23.3

Constant -5.799 1.213

Equation 23

M2 Me area 0.228 0.055 0.5 70.8 51.4 62.1 19.4

Constant -4.181 1.058

Equation 24

M2 Hy area 0.167 0.035 0.5 73.1 55.2 65.1 17.9

Constant -3.029 0.682

a Equation 13 was derived by means of stepwise analysis, all others by direct analysis. Abbreviations of crown dimensions are the same as in

Table 1b Sex bias = % males correctly classified - % females correctly classified

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formulae utilizing only mesiodistal and buccolingual

dimensions of the first and second maxillary molars.

Notably, the sex classification percentages obtained for

cusp area measurements of the maxillary molars did not

differ appreciably from those observed for traditional

crown diameters in black South Africans. The combination

of just two cusp areas for the first molar, including mesial

(paracone and protocone), buccal (paracone and meta-

cone), and lingual (protocone and hypocone) cusps, yielded

overall allocation rates between 71.5 and 74.0%. Cusp area

classification accuracies were generally reduced for single

variable models; however, the paracone area of the M1

when used in isolation provided a sex prediction success

rate of 72.3 and 73.2%, employing discriminant function

analysis and binary logistic regression analysis, respec-

tively. The allocation accuracies for comparable sex

prediction models derived for maxillary second molar

dimensions were on average 4.3% lower than those

obtained for the first molar. Furthermore, the classification

models developed in this study incorporating dimensions

for both maxillary molars did not improve allocation

accuracies achieved when only using M1 measurements.

Therefore, if both maxillary teeth are preserved, it is

merely necessary to examine the first molar in order to

make full use of the sex discriminating ability of cusp area

measurements in this population group.

It is also worth noting that the classification results

reported in this investigation are also comparable to those

observed in a related study which examined the efficacy of

maxillary molar cusp diameters for sex discrimination. In

the latter study, discriminant function analyses yielded

allocation accuracies between 58.3 and 73.6% for cusp

diameter measurements obtained from the same black

South African dental sample [51]. As with the current

research, classification rates for functions generated from

first molar dimensions were higher than those for the sec-

ond molar. Likewise, discriminant functions incorporating

the lingual cusps of either the M1 or M2 yielded some of

the highest sex prediction percentages. These results are

unsurprising given that both investigations utilized datasets

which represent measures of maxillary molar cusp size for

the same set of teeth. Although in general agreement, there

are a few differences between the results of the current

study and those observed in the investigation concerning

cusp diameters. For example, the highest classification

accuracies for discriminant functions derived from M1 cusp

area measurements incorporated the paracone. In contrast,

models incorporating the protocone provided the most

Table 9 Logistic regression equations and classification accuracies for maxillary first and second molar variables

Selected variablesa ß coefficient Standard error Sectioning point Correctly classified (%) Sex biasb

Male Female Overall

Equation 25: all 12 variables

M1 Pa area 0.380 0.084 0.5 76.9 71.4 74.5 5.5

M1 Pr area 0.141 0.057

M2 Hy area 0.098 0.040

Constant -15.556 2.270

Equation 26: crown diameters

M1 BL 1.758 0.340 0.5 76.9 66.7 72.3 10.2

M2 MD 0.663 0.257

Constant -26.487 3.959

Equation 27: cusp areas

M1 Pa area 0.380 0.084 0.5 76.9 71.4 74.5 5.5

M1 Pr area 0.141 0.057

M2 Hy area 0.098 0.040

Constant -15.556 2.270

Equation 28: lingual cusps

M1 Pr area 0.260 0.051 0.5 73.1 62.9 68.5 10.2

M2 Hy area 0.108 0.037

Constant -9.935 1.595

Equation 29: buccal cusps

M1 Pa area 0.504 0.076 0.5 77.7 67.6 73.2 10.1

Constant -12.369 1.900

a All equations derived by means of stepwise analysis. Abbreviations of crown dimensions are the same as in Table 1b Sex bias = % males correctly classified - % females correctly classified

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accurate allocation results among maxillary first molar

cusp diameters.

The abovementioned sex classification accuracies for

cusp area measurements of the permanent maxillary first

and second molar are lower than those reported in previous

studies of other skeletal elements in black South Africans,

including the cranium [52, 53], mandible [26, 54], pelvis

[55], humerus [56], radius and ulna [57], femur [58, 59],

patella [60], talus [61], and calcaneus [62]. The classifi-

cation success rates obtained for maxillary molar cusp

areas were also below the suggested minimum accuracy of

75–80% for reliable application of a method for forensic

sex identification [63–66]. Therefore, the derived discrim-

inant functions and binary logistic regression equations

should be used in conjunction with other methods to assist

sex determination, if additional skeletal materials are ade-

quately preserved. Notwithstanding, the utility of these

odontometric formulae lies in the fact that the dentition is

highly resistant to postmortem insults and thus may be

employed with fragmentary remains.

Although prior dental investigations have established

sex discriminating standards with higher classification

accuracies than those observed in the current study, these

approaches require fairly complete maxillary and/or man-

dibular dentitions, or at least some portion of the anterior

tooth row, particularly the canines [8, 9, 67–69]. For

example, in a recent dental sex assessment study in the

Nepalese, up to 93% of the sample population could be

correctly allocated utilizing a stepwise discriminant func-

tion procedure, which incorporated a combination of

mesiodistal and buccolingual crown dimensions for selec-

ted teeth from both jaws [70]. However, in many forensic

situations, such as dismemberments, mass disasters and

cremations, the measurement of each tooth class in either

dental arcade is not often possible. Similarly, the anterior

dentition, including the highly dimorphic canines, may not

be available for examination given that these single-rooted

teeth are more often lost postmortem [71]. Furthermore,

various taphonomic processes and antemortem modifica-

tions, such as interproximal restorations (fillings), can

variably affect the dentition rendering overall crown size

measurements ineffective, yet still allowing individual cusp

areas to be accurately recorded. Therefore, an additional

advantage of the odontometric formulae developed in this

study is that they may be applied to isolated molar teeth or

even partial tooth crowns.

Finally, the sex discriminating standards provided in this

study can be used with the remains of immature individ-

uals, as well as adults, given that the permanent dentition

develops early in life and remains unchanged during the

growth process. The first maxillary molar crown completes

development approximately three years after birth, while

the crown of the second maxillary molar is fully formed at

around the seventh year. Therefore, cusp area measure-

ments, although not highly accurate, may provide a sta-

tistically useful indication as to the sex of an individual in

which the secondary sexual characteristics of the skeleton

are not yet developed. This is of particular importance

given that attributing sex to immature remains is one of the

most problematic observations in skeletal identification.

Key points

1. Cusp area measurements for the first and second per-

manent maxillary molars were collected for a sample

of black South Africans utilizing digital photogram-

metric methods.

2. All cusp areas of both maxillary molars were found to

be sexually dimorphic in this population group.

3. Univariate and multivariate discriminant function and

logistic regression analyses yielded overall sex classi-

fication accuracy rates between 59.6% and 74.5% for

cusp area dimensions.

4. The derived formulae, although not as accurate as

those reported for other skeletal elements in black

South Africans, can be used with fragmentary remains

in which complete or even partial tooth crowns are

preserved.

5. An added benefit is that these osteometric standards

can be applied, not only to adults, but also to subadults

in which the more accurate sex discriminating features

of the pelvis and skull are yet to develop.

Acknowledgments The author would like to thank the Department

of Anatomical Sciences, University of the Witwatersrand for per-

mission to study the Raymond A. Dart Collection of Human Skele-

tons, and Mr. Brendon Billings for his generosity and help during data

collection. The author also wishes to express his gratitude to Professor

Maryna Steyn for granting access to the Pretoria Bone Collection,

housed in the Department of Anatomy, School of Medicine, Faculty

of Health Sciences, University of Pretoria and Mr. Marius Loots and

Dr. Ericka L’Abbe of the same department for their hospitality and

assistance with the skeletal material in their care.

Conflict of interest The authors declare that they have no conflict

of interest.

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