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Dimensional variation in the proximal ulna Evaluation of a metric method for sex assessment.

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AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 135:469–478 (2008)
Dimensional Variation in the Proximal Ulna:
Evaluation of a Metric Method for Sex Assessment
Lynne S. Cowal1 and Robert F. Pastor1,2*
1
Department of Archaeological Sciences, Biological Anthropology Research Centre,
University of Bradford, Bradford, West Yorkshire, BD7 1DP, UK
2
Department of Anthropology, University of Oregon, Eugene, OR 97403-1205
KEY WORDS
anthropology
sexual dimorphism; discriminant function; Spitalfields; bioarchaeology; forensic
ABSTRACT
The determination of sex is one of the
fundamental assessments in the production of a biological
profile for human skeletal remains, and a large number of
studies have focused on evaluating sexual dimorphism
metrically. A recent study of a contemporary American
population presented high classification accuracies from
discriminant function analysis of the proximal ulna
(Grant and Jant, 2003). The present research tests this
method using a large sample (223 skeletons: 114 males
and 109 females) from two skeletal assemblages of European origin, the documented Spitalfields Coffin-Plate Collection (N 5 171) and the archaeological Raunds Furnells
Collection (N 5 52). The three measurements from the
original study (Grant and Jantz, 2003), defined as the
notch length (NL), the width of the olecranon process
(OW), and the height of the coronoid process (CH) were
tested, with the addition of a new variable radial notch
height (RNH). Significant differences (P < 0.001) were
found between male and female ulna measurements. Discriminant analysis found the original discriminant equation classified individuals with accuracies of only 40% for
males but 99% for females. New discriminant functions
were developed using direct and stepwise analyses of the
Spitalfields sample. A direct multivariate function based
on four dimensions (NL, OW, CH, RNH) produced an
overall classification accuracy of 85.4% (males 82.4%;
females 88.4%). A second function based on the original
three measurements (NL, OW, CH) yielded nearly identical classification accuracies (males 81%; females 88.5%).
Crossvalidation of the Spitalfields data using the threevariable function yielded an overall classification rate of
84.2%. This study indicates that the ulna is sexually
dimorphic but its development is population-specific. Am J
Phys Anthropol 135:469–478, 2008. V 2008 Wiley-Liss, Inc.
Assessment of sex is one of the fundamental priorities
of skeletal analysis, especially in forensic cases where
the determination of sex can substantially narrow the biological profile for unidentified remains. While morphological analysis of complete ossa coxae and crania have
suggested accuracies of up to 100%, they are often damaged, making it necessary to find methods of assessing
sex from other skeletal elements. Many such studies
have been developed, a large proportion of which are
devoted to metrical analysis of the major weight-bearing
bones, such as the femur and tibia (e.g., Singh et al.,
1975; Black, 1978; Dibennardo and Taylor, 1979, 1982;
Ruff and Hayes, 1983; Iscan and Miller-Shaivitz, 1984a,b;
Holland, 1991; Kieser et al., 1992; France, 1998; Stojanowski and Seidemann, 1999). However, the propensity
for missing or fragmentary elements in archaeological
assemblages and degraded forensic cases has resulted in
the compilation of metrical data for a large number of
skeletal elements (e.g., Singh and Singh, 1972; Stewart,
1979; Dibennardo and Taylor, 1983; Berrizbeitia, 1988;
Holman and Bennet, 1991; Scheuer and Elkington, 1993;
Falsetti, 1995; Introna et al., 1997; Steyn and Iscan,
1997, 1999; Iscan et al., 1998; Stojanowski, 1999; Bidmos
and Dayal, 2004). A number of studies have focused on
the ulna (Godycki, 1957; Maia Neto, 1959; Steel, 1972;
Singh et al., 1974; MacLaughlin and Bruce, 1985;
Purkait, 2001), of which many have either proven largely
inaccurate or required the complete bone for analysis.
An early morphological study of the ulna (Godycki,
1957) proposed that the lunar notch of the proximal portion is divided vertically, through the medial portion, in
male individuals. Initial findings indicated that the
method had an accuracy of 95% for males and 85% for
females. However, a corroborative study by Maia Neto
(1959) showed the original findings to be largely inaccurate. For example, of 204 ulnae without the lunar
division and therefore theoretically female, 25% were
misclassified as male.
Steel (1972) was one of the first researchers to devise
a metrical method of assessing sex from the complete
ulna. Using a documented shelf collection, discriminant
function equations were used to analyze data from three
osteometric dimensions taken from complete ulnae. The
dimensions included the total length of the bone, the
coronoid height, and the width of the distal epiphysis.
Although reasonable classification accuracies were
reported, the study relied upon a relatively small sample. Again, the requirement of a complete bone for this
method renders it unusable with fragments. Another
study (Singh et al., 1974) developed demarking points
relating to the total length, midshaft circumference, and
the distal end breadth of the ulna. Nearly 100% accuracy
C 2008
V
WILEY-LISS, INC.
C
*Correspondence to: Robert F. Pastor, Department of Anthropology, University of Oregon, Eugene, Oregon 97403-1205.
E-mail: rfpastor@uoregon.edu
Received 19 December 2006; accepted 31 October 2007
DOI 10.1002/ajpa.20771
Published online 10 January 2008 in Wiley InterScience
(www.interscience.wiley.com).
470
L.S. COWAL AND R.F. PASTOR
was achieved through this method and the technique
was found to be applicable to 99.75% of the Indian population used to create it. However, the method has never
been validated for accuracy or to determine its applicability to other populations. A recent study by Purkait
(2001) focussed on three dimensions of the proximal ulna
measured on whole elements from a contemporary documented Indian sample. Accuracies of 80–96% were found
from discriminant function analysis of various combinations of variables.
It is surprising that little effort has been made to develop a metrical method from the more robust proximal
end of the ulna, with the exception of Purkait (2001),
since a recent study by Grant and Jantz (2003) indicated
high accuracies using a small set of metric variables.
Advantages of this method include its applicability to
poorly preserved skeletal material, such as in degraded
archaeological assemblages or from aircraft crash sites
and other mass disasters, and its reputed high accuracy
of classification (Grant and Jantz, 2003). According to
these authors, the proximal ulna is superior to the cranium and other postcranial elements for sex attribution.
The original study by Grant and Jantz (2003) used
three different documented skeletal samples of known age
and sex. The study’s primary aim was to determine if it
was possible to determine sex from measurements taken
from the proximal ulna. The sample comprised 217 individuals of European–American and African–American
descent from three different collections. The initial study
was carried out on the William M. Bass Donated Collection, comprising modern individuals of known sex, age,
and race, the latter being primarily Americans of European or African ancestry. Skeletal material from two
documented collections was used to test the original findings and develop the method: Terry Collection (NMNH,
Smithsonian); and the Joint POW/MIA Accounting Command’s Central Identification Laboratory (JPAC/CIL, formerly CILHI). The Terry Collection consists of individuals
born in the late 19th and early 20th centuries of known
sex and age while the JPAC/CIL test skeletons are all
American military casualties from previous conflicts.
A mixture of left and right-sided bones with no evidence of pathology was used for the Grant and Jantz
(2003) study, although left bones were preferred. Three
measurements were then taken from the proximal ulna
and the findings were examined by means of discriminant
analysis. The results produced an accuracy of 100% for
African–American
males
and
European–American
females. However, there were four misclassifications in
the sample of European–American males, which resulted
in an accuracy of 94.4%. One set of remains in the sample
of African–American females was misclassified, resulting
in an accuracy of 97.1%. This discrepancy was attributed
to the width of the olecranon process, which was the most
strongly weighted variable (Grant and Jantz, 2003).
Indeed, the misclassification of the males was the result
of narrow olecranon widths and the misclassification of
the single female was due to a wide olecranon width.
In the present study, the original discriminant function (equation) devised by Grant and Jantz (2003) is
tested on a documented historic European sample of
known age and sex. It also tests the method further
using a European archaeological sample, where sex has
been assessed using morphological analysis of the ossa
coxae and crania. The objective is to evaluate whether
the proximal ulna is indeed sexually dimorphic and if so,
to determine the accuracies of models from the original
American Journal of Physical Anthropology
TABLE 1. Documented and archaeological samples
with sex distribution
Skeletal collection
Females, N
Males, N
Total
Spitalfields Coffin-Plate
Raunds Furnell
Total
86
23
109
85
29
114
171
52
223
study and its reliable application to other historical populations.
The rationale for this study focused on two principal
hypotheses. The null hypothesis states that no significant sexual dimorphism is exhibited for dimensions of
the proximal ulna. Alternative hypotheses propose that
the proximal ulna exhibits systematic and significant
sexual dimorphism for dimensions of the proximal ulna
in European samples, and for which reasonably accurate
discriminant equations can be produced.
MATERIALS AND METHODS
The sample used in the present study comprised two
separate osteological collections: the documented Spitalfields Coffin-Plate Sample and the Raunds Furnells
archaeological collection. Sample sizes and sex distributions are shown in Table 1.
The Spitalfields Coffin-Plate sample, housed at the
Natural History Museum in London was the primary
focal point of this study. Excavation of the Spitalfields
Christ Church Crypt began in November 1984 and
resulted in the recovery of 387 sets of postmedieval
remains with coffin-plates, documenting the deceased’s
names, date of birth and date of death, the latter of
which spanned from 1729 to 1852 (Cox, 1996). Subsequently, it was discovered that the majority of the population was of French Huguenot ancestry with only 33%
of British origin (Cox, 1996). Because of varied levels of
preservation only 171 sets of remains from the coffinplate sample were suitable for analysis with regards to
this study. The Raunds Furnells Collection, housed at
the University of Bradford’s Biological Anthropology
Research Centre (BARC), comprises an Anglo-Saxon population from East Northamptonshire. Excavations starting in 1977 led to the discovery of 376 sets of remains
buried between the 10th and 12th centuries. Of the 191
adults excavated only 182 could be assessed for sex
(Powell, 1996) however, the explosion of a petroleum gas
station in 1983 led to the damage and loss of several
sets of remains. Subsequently, 52 individuals were available for this study. Because of the absence of documented sex and age information for the Raunds Furnells
collection, sex assessment was carried out on this sample
by the first author using standard morphological indicators of the ossa coxae. In all cases, sex assessment of the
skeletons in the sample matched the original assessment
reported by Powell (1996).
All remains missing the left proximal ulna were
excluded from the study as were ulnae showing signs of
pathological alteration or erosion to the proximal end. In
cases where the left and right ulnae were present, both
were measured. However, remains where only the right
ulna was present were excluded from the study. All
measurements pertaining to the Spitalfields sample were
performed ‘‘blind’’ to prevent biasing the results. The
resulting sample consisted of 171 (86 females and 85
males) individuals from the Spitalfields Collection and
SEXUAL DIMORPHISM IN THE PROXIMAL ULNA
Fig. 1. Ulnar notch length (NL) measurement, lateral view.
471
Fig. 2. Ulnar olecranon width (OW) measurement, anterior
view.
52 (23 females and 29 males) individuals from the
Raunds Furnells Collection.
Five measurements were taken from the proximal
ulna. The first three, classified as the notch length (NL),
olecranon width (OW), and the coronoid height (CH), are
those defined and analyzed in the original study by
Grant and Jantz (2003) (Figs. 1–3). The fourth and fifth
(Figs. 4 and 5) are new measurements chosen for additional analysis during this study: the radial notch height
(RNH) and the radial notch width (RNW). All measurements were taken using a set of digital sliding calipers,
to the nearest tenth of a millimeter.
Notch length
The maximum distance between the most proximal
point on the lateral articular rim of the olecranon process to the most distal point on the articular rim of the
radial notch (see Fig. 1). With the ulna held so that the
radial notch faces the individual taking the measurement, the sliding calipers are then positioned parallel to
the longitudinal axis of the diaphysis, with the fixed arm
of the calipers resting along the proximal surface of the
articular rim of the semilunar notch. The calipers are
adjusted to meet the most distal point on the articular
rim of the radial notch. It should be noted that the shape
and position of the radial notch are variable, so the calipers will not always lie neatly across the length of the
articular rim.
Fig. 3. Ulnar coronoid height (CH) measurement, lateral
view.
articular rims of the semilunar notch could alter the outcome of the measurement.
Olecranon width
Coronoid height
The maximum distance between the proximal medial
articular rim and the proximal lateral articular rim on
the semilunar notch of the olecranon process (see Fig. 2).
This measurement is taken by holding the ulna so that
the semilunar notch faces towards the individual taking
it. The fixed arm of the sliding calipers are held parallel
to the lateral articular rim of the semilunar notch and
the calipers adjusted to meet the most distal point on
the medial articular rim. While enthesophytic lipping is
common on the most proximal and dorsal surfaces of the
olecranon process this should not affect the measurement. However, erosion along the medial and lateral
This measurement is the maximum distance between
the most ventral aspect on the articular rim of the coronoid process and the point on the dorsal surface of the
proximal ulna, perpendicular to the length of the diaphysis (see Fig. 3) (McHenry et al., 1976; Bräuer, 1988). To
take this measurement, the ulna is held horizontally
with the semilunar notch facing upwards. The sliding
calipers are positioned perpendicular to the longitudinal
axis of the diaphysis with the fixed arm on the most ventral aspect of the articular rim of the coronoid process.
The calipers are then adjusted to meet the dorsal surface
of the proximal ulna. It should be noted that osteophytic
American Journal of Physical Anthropology
472
L.S. COWAL AND R.F. PASTOR
Fig. 4. Ulnar radial notch height (RNH) measurement, lateral view.
lipping is common on the ventral aspect of the coronoid
process and could alter the measurement.
Radial notch height
This measurement is the maximum distance between
the most proximal aspect on the articular rim of the radial notch and the most distal aspect on the articular
rim of the radial notch (see Fig. 4) (similar to ulna measurement 9a in Bräuer, 1988). To take this measurement, the ulna is held so that the radial notch faces toward the individual taking it. With the fixed arm of the
sliding calipers on the proximal articular rim of the radial notch the calipers are adjusted to meet the distal
articular rim of the radial notch.
Radial notch width
The maximum distance between the most dorsal point
on the articular rim of the radial notch and the most
ventral point on the articular rim of the radial notch
(see Fig. 5) (similar to ulna measurement 9b in Bräuer,
1988). This measurement should be taken while holding
the ulna so that the radial notch faces the individual
taking it. The sliding calipers are held perpendicular to
the longitudinal axis of the diaphysis with the fixed arm
of the calipers positioned parallel to the diaphysis along
the dorsal articular rim of the radial notch. The calipers
are then adjusted to meet the most ventral point on the
articular rim of the radial notch.
A paired-sample Student’s t test was carried out to
test the intraobserver error for all measurements. The
first 20 individuals with both the left and right ulnae,
from the Spitalfields sample, were utilized for this purpose. Each of the five metric variables (NL, OW, CH,
RNH, and RNW) was measured on the left and the right
ulnae of each individual during the first day of data collection. The same measurements were then repeated
5 days later without reference to the original metrical
values.
Two-sample Student’s t tests were conducted for all
measurements from each individual to compare the left
American Journal of Physical Anthropology
Fig. 5. Ulnar radial notch width (RNW) measurement, lateral view.
measurement to the right. This process was repeated on
the first twenty individuals with both the left and right
ulnae from the Raunds Furnells sample to determine
whether different metric variables were affected between
the two populations. Finally, where present, the measurements from the right NL, OW, and CH of each individual from the Spitalfields and Raunds Furnells
samples were used to assign sex assessments using the
original Grant and Jantz (2003) equation. The results
were then compared with the sex assessments from the
left bone to determine whether asymmetrical variation
was great enough to alter the results of the equation.
Paired-sample Student’s t tests were done to determine whether there were significant size differences
between males and females. The left ulnae of the Spitalfields males and females were compared for this purpose,
resulting in the comparison of 85 males with 86 females
(total sample of 171, see Table 1).
The original three measurements (NL, OW, and CH)
from both samples were used to test the discriminant
function equation devised by Grant and Jantz (2003). All
data compilation and statistical analyses were conducted
using various subroutines of SPSS version 12.0 (SPSS
Science, Inc., 2004).
New discriminant function equations were generated
for the Spitalfields documented sample using stepwise,
univariate, and direct analyses. Unstandardized coefficients were used to create the new discriminant functions using left elements. Functions were developed
using the original three measurements (NL, OW, CH) as
well as the new variables. In addition, formulae were
generated using direct discriminant function analysis of
selected combinations of variables for use with fragmentary skeletal remains. New equations were then used to
ascribe sex assessments to the left bones from the
Raunds Furnells sample.
Finally, crossvalidation discriminant analysis of the
Spitalfields sample was done in SPSS using a ‘‘leaveone-out’’ classification protocol on functions derived from
combinations of variables. This type of discriminant
473
SEXUAL DIMORPHISM IN THE PROXIMAL ULNA
function subroutine holds one specimen out of the sample in a sequence and then calculates the group variance
based on the data from all other specimens. As such,
this discriminant analysis approximates a ‘‘jackknife’’
analysis (Afifi et al., 2004; Jerwood, personal communication) to derive a truer picture of the error rate for classifications based on the reference sample.
To explore the contribution of shape characteristics,
compared with size, for the proximal ulna to any dimorphism present, additional discriminant analyses were
conducted using log transformed raw measurements
(Darroch and Mosimann, 1985). The log transformations
were calculated as the ratio of each individual measurement (e.g., from NL) to the geometric mean for that variable. These ‘‘log shape’’ variables were then used as
scale-free indices where shape characteristics of individual variables are given greater statistical weight in the
analyses compared with the size characteristics (Holliday, 1997; Powell and Neeves, 1999). Using these variables, separate additional discriminant functions (univariate and multivariate) were generated to test whether
there were significant shape differences in the proximal
ulna between the sexes.
RESULTS
Results from the intraobserver error analysis indicated
that one of the two new measurements (RNW) was unreliable, so this variable was subsequently excluded from
the rest of the analyses. All other measurements were
found to have negligible intraobserver error (P \ 0.05).
Statistical comparison of the left and right ulnae from
the two samples indicated significant asymmetry (P \
0.01) for the NL measurement and nearly so (P \ 0.06)
for RNH in the Spitalfields sample and OW in the
Raunds Furnells sample. From the 129 Spitalfields individuals with both ulnae present, a comparison of sex
classifications from the right ulnae with the left showed
that 10 cases were classified differently, while 92.3% proTABLE 2. Means, standard deviations, univariate F-ratios, and
P values for Spitalfields left proximal ulna measurements
Males
(N 5 85)
duced the same sex assessment from both left and right
elements. Of these 10 differential side comparisons, the
majority (7) of correct sex classifications were from the
right side. Only one individual from the Raunds Furnells
sample, where both ulnae were present, resulted in an
alternate classification.
The descriptive statistics for each of the four variables
for Spitalfields males and females are provided in Table
2. F-test results showed that there were significant differences (P \ 0.001) between the metrical values of the
male and female ulnae. For all dimensions, male proximal ulnae were significantly larger than those of
females, indicating that the proximal ulna is sexually
dimorphic in this European population.
Table 3 presents the results obtained from testing the
Grant and Jantz (2003) equation on the complete European sample. All 86 females from the Spitalfields sample
were classified correctly, while a single female from the
Raunds Furnells sample was misclassified. In contrast,
50 males from the Spitalfields sample and nine males
from the Raunds Furnells sample were misclassified as
females. Consequently, only 41.2% of males in the Spitalfields sample were correctly classified and 69% of
males in the Raunds Furnells sample using the original
equation.
The results of the stepwise procedure carried out on
the four variables (NL, OW, CH, and RNH) from the Spitalfields sample are listed in Table 4 (Function 1). Of the
four measurements entered in the analysis, only NL and
width of the olecranon process (OW) were selected as
optimal discriminating variables, producing an overall
classification accuracy of 85.4%. A stepwise analysis
of the original three variables, excluding RNH, produced
identical results. The canonical discriminant coefficients
and other data produced by the stepwise analysis
for Function 1, for univariate analyses, and for direct
analyses of other combinations of variables are shown in
Table 4.
Sex assessment of a bone from an unknown skeleton
can be achieved by multiplying each measurement by its
corresponding coefficient and adding the products together with the constant. For example, for Function 1
the discriminant score (y) is calculated as follows:
y ¼ ðNL30:254Þ þ ðOW30:235Þ þ ð14:175Þ
Females
(N 5 86)
Variablea
(mm)
Mean
SD
Mean
SD
F-ratiob
P value
NL
OW
CH
RNH
36.05
25.08
36.50
11.29
2.97
2.04
2.68
1.34
32.01
21.93
32.43
9.90
1.98
2.22
2.44
1.14
108.79
93.28
107.21
52.99
0.000
0.000
0.000
0.000
a
NL, notch length; OW, olecranon process width; CH, coronoid
process height; RNH, radial notch height.
b
Degrees of Freedom 5 169. All significant at P \ 0.001.
using the dimensions for NL and OW of an ulna of undetermined sex. For a score that is greater than the sectioning point (0.005), the individual can be classified as
male, while for a lower score the individual would be
considered female.
The raw counts and classification frequencies from a
direct discriminant function analysis using the original
three dimensions (Function 2) are shown in Table 5. For
males, 70 ulnae were correctly classified while 15 were
TABLE 3. Classification matrix for sex attribution using the original discriminant equationa for proximal ulnae
Males
Females
Skeletal collection
Classified
correctly, N
Misclassified,
N
Total,
N
Accuracy
(%)
Classified
correctly, N
Misclassified,
N
Total,
N
Accuracy
(%)
Spitalfields
Raunds Furnell
Total
35
20
55
50
9
59
85
29
114
41.2
69.0
48.2
86
22
109
0
1
1
86
23
110
100
95.6
99.1
a
From Grant and Jantz (2003).
American Journal of Physical Anthropology
474
L.S. COWAL AND R.F. PASTOR
TABLE 4. Canonical discriminant function coefficients, Wilk’s Lambdas group centroids, structure and sectioning points,
and accuracies for Spitalfields males and females
Functions and
variables
Unstandardized
coefficient
Standardized
coefficient
Wilk’s
lambda
Structure
point
Group
centroid
Sectioning
pointa
Accuracy (%)
Stepwise analysis
1 NL
OW
Constant
0.254
0.235
214.175
0.642
0.503
0.608
0.559
0.903
0.836
M 5 0.888
F 5 20.878
0.005
85.4
Direct analysis
2 NL
OW
CH
Constant
3 NL
OW
CH
RNH
Constant
4 OW
CH
RNH
Constant
5 OW
CH
Constant
6 NL
CH
Constant
7 NL
RNH
Constant
8 OW
RNH
Constant
9 CH
RNH
Constant
0.174
0.184
0.130
214.718
0.145
0.182
0.121
0.127
214.719
0.212
0.200
0.210
214.102
0.228
0.247
213.874
0.218
0.206
214.523
0.341
0.182
213.513
0.360
0.358
212.249
0.320
0.251
213.680
0.440
0.394
0.333
0.547
0.881
0.816
0.875
M 5 0.910
F 5 20.900
0.005
85.4
0.366
0.389
0.311
0.159
0.542
0.873
0.809
0.867
0.610
M 5 0.919
F 5 20.908
0.006
0.453
0.514
0.262
0.557
0.832
0.892
0.627
M 5 0.892
F 5 20.882
0.005
84.8
0.487
0.635
0.571
0.856
0.918
M 5 0.867
F 5 20.857
0.005
84.2
0.552
0.529
0.572
0.928
0.922
M 5 0.864
F 5 20.854
0.005
81.3
0.861
0.227
0.599
0.981
0.685
M 5 0.817
F 5 20.808
0.005
81.3
0.768
0.446
0.598
0.905
0.682
M 5 0.821
F 520.811
0.005
80.7
0.822
0.313
0.592
0.960
0.675
M 5 0.830
F 5 20.820
0.005
78.4
M 5 0.743
F 5 20.734
0.005
85.4
M 5 0.802
F 5 20.793
0.005
81.3
M 5 0.796
F 5 20.787
0.005
77.2
M 5 0.560
F 520.553
0.004
70.8
Univariate analysis
10 OW
Constant
D.P.c
11 NL
Constant
D.P.c
12 CH
Constant
D.P.c
13 RNH
Constant
D.P.c
0.468
211.011
0.396
213.462
0.389
213.408
0.802
28.496
Females \ 23.51 \ Males
Females \ 34.03 \ Males
Females \ 34.47 \ Males
Females \ 10.60 \ Males
(84.2)b
85.4
(83)b
a
Discriminant scores less than the sectioning point indicate a female while values greater than the sectioning point would be
considered male.
b
Accuracy from cross-validation analysis using ‘leave-one-out’ classification.
c
D.P. 5 Demarking point (in mm).
classified as female, resulting in an accuracy of 82.4%.
Ten females from the original sample of 86 ulnae were
incorrectly classified. As such, Function 2 produced an accuracy of 88.4% for females. Overall, 85.4% of the original
grouped cases were correctly classified (Tables 4 and 5).
Combined accuracies for both sexes using direct analysis of select combinations of two to four variables ranged
from 78.4 to 85.4% (Table 4). The best separations from
the multivariate analyses (85.4%) were produced by
Functions 2 and 3, followed closely by Functions 4 and 5
(84.8 and 84.2%, respectively). The structure points and
Wilk’s Lambda scores shown in Table 4 for these functions indicate that, as with the stepwise procedure
(Function 1), notch size (NL) and/or OW were responsible for the majority of the variance in these functions.
American Journal of Physical Anthropology
The univariate analyses produced a wider range of classification accuracies (70.8–85.4%) with the highest contribution from OW alone followed by notch size. The RNH provided the lowest separation (70.8%) for a single variable.
The high classification accuracies for Functions 2 to 5 where
OW is included, and as the sole variable in Function 10,
provide further evidence for the importance of this dimension for sex assignment compared with CH and RNH.
High accuracies were achieved when applying the new
functions to the Raunds Furnells archaeological sample.
Only two males were misclassified resulting in an accuracy of 93.1% and four females were misclassified resulting in an accuracy of 82.6%. The new functions correctly
classified six Raunds Furnells males that were originally
misclassified by the Grant and Jantz (2003) equation. It
475
SEXUAL DIMORPHISM IN THE PROXIMAL ULNA
TABLE 5. Classification results for discriminant Function 2
using three variables (NL, OW, CH) from Spitalfields sample
Predicted group
membership
Original analysisa
[Count (N)]
Percent (%)
Cross-validatedb
[Count (N)]
Percent (%)
a
b
Sex
Female
Male
Total
Female
Male
Female
Male
Female
Male
Female
Male
76
15
88.4
17.6
74
15
86.0
17.6
10
70
11.6
82.4
12
70
14.0
82.4
86
85
100
100
86
85
100
100
85.4% of original grouped cases correctly classified.
84.2% of crossvalidated grouped cases correctly classified.
is likely that the two males and one female that
remained misclassified when using the new equations
were the result of particularly gracile males and a robust
female.
For ease of classification when single variables are
used with fragmentary remains, demarking points are
also provided in Table 4 for comparison of the dimension
of a specimen in question. A bone measurement for one
of the four variables is simply compared with the
demarking point listed in Table 4 for that variable to
determine the sex of the element. For example, a proximal ulnar fragment where OW was available would be
considered male if the measurement was greater than
the demarking point of 23.51 mm but female if below
this threshold.
The crossvalidation discriminant analysis for Functions 2 and 3 yielded only slightly lower overall classification rates than the direct analyses (Table 4). The
‘‘leave-one-out’’ protocol using the combination of four
variables including RNH (Function 3) yielded a classification rate of 83%, whereas the accuracy for the standard direct analysis was 85.4%. A slightly higher overall
classification rate (84.2%) was obtained from crossvalidation of the original set of three variables (Function 2)
compared with the 85.4% accuracy from the standard
direct analysis. Table 5 lists the complete classification
results (counts and percentages) for the crossvalidated
analysis using these three variables. For females, 74 of
86 ulnae (86%) were classified correctly when subjected
to crossvalidation compared with the 88.4% accuracy
obtained with the original discriminant analysis. A
slightly lower classification rate was obtained from crossvalidation of male ulnae (70 of 85 specimens, 82.4%), an
accuracy identical to that for the original direct analysis.
Table 6 shows the descriptive statistics (means, standard deviations) for the log shape variables and the
results of univariate discriminant function analyses for
each of the four transformed variables. The very low
F-ratios and high probability values (P 5 0.882–0.994)
indicated that none of these univariate analyses, nor any
of the various combinations of variables from multivariate analyses (not shown), yielded significant differences
between Spitalfields males and females for shape characteristics of the proximal ulna.
DISCUSSION
A number of previous studies have developed discriminant function models for ulnar dimorphism, although
fewer have focussed on proximal dimensions. For exam-
TABLE 6. Descriptive statistics and univariate discriminant
function analysis of log shape variables for Spitalfields
left proximal ulna measurements
Males
(N 5 85)
Females
(N 5 86)
Variablea
Mean
SD
Mean
SD
F-ratio
P value
NL
OW
CH
RNH
1.003
1.003
1.002
1.006
0.082
0.081
0.073
0.119
1.001
1.004
1.002
1.006
0.062
0.101
0.075
0.115
0.022
0.006
0.000
0.000
0.882
0.936
0.994
0.991
a
Log shape variables (Darroch and Mosimann, 1985) calculated
as the ratio of each individual measurement (e.g., from NL) to
the geometric mean for that variable. All Wilk’s Lambdas equal
1. Degrees of Freedom 5 169.
ple, Mall et al. (2001) conducted discriminant analyses
on arm bones from a contemporary German autopsy
sample. Ulnar length alone provided 87% accuracy but
for their ‘‘proximal ulnar width,’’ the dimension closest
to OW in this study, a much lower classification accuracy
of 72.14% was obtained. Ulnar length combined with the
proximal and distal widths yielded a higher accuracy
(90.58%). France (1998) reported that two diameters of
the ulnar diaphysis provided 91% correct classification
on a European–American sample. For the humerus a
combination of three dimensions, including epicondylar
breadth, yielded 92% accuracy from the same sample.
Interestingly, use of a single distal humeral measurement alone (articular width) provided 93% correct classification. This articular dimension is probably most
closely associated with the two ulnar variables, OW and
NL, which provided 85 and 81% accuracy, respectively,
in the present study and which comprise much of the
ulnar portion of the ulna–humerus articulation. A recent
metric study of humeri from a Guatemalan forensic sample (Frutos, 2005) also noted classification accuracies
greater than 90% for the epicondylar breadth, and similar accuracies were found for this single humeral dimension in several documented Asian skeletal samples
(Iscan et al., 1998).
A recent study of long bone circumferences from a
Late Roman archaeological sample (Safont et al., 2000)
revealed that arm bone circumferences produced higher
sex classification accuracies than those of the leg. Univariate discriminant analyses of ulnar circumferences
yielded 91.1% accuracy compared with the slightly more
dimorphic humerus (92.6%). However, with this and
many of the other methods a complete element is preferable to obtain measurements in the desired locations.
For example, it is difficult to determine the exact point
of the midshaft in a fragmented bone (MacLaughlin and
Bruce, 1985), while the distal epiphysis is the least likely
section of the ulna to survive.
Purkait (2001) devised a method to assess sex specifically from the proximal ulna using discriminant functions. Three measurements were taken from bones in a
contemporary Indian collection: the olecranon–coronoid
angle, and the length and width of the inferior medial
trochlear notch. When all three variables were used, the
method reached an accuracy of 96% for males and 80%
for females. The single best discriminator was the olecranon coronoid angle with an accuracy of 85% and when
combined with the trochlear NL an accuracy of 90.6%
was obtained. Despite having seemingly good accuracies,
this study is not without its problems. Although the
method was designed to specifically use the proximal
American Journal of Physical Anthropology
476
L.S. COWAL AND R.F. PASTOR
ulna, determination of the olecranon-coronoid angle is
complicated and requires the ulna to be nearly intact
making the method difficult to use with fragmentary
elements.
Grant and Jantz (2003) determined that the OW was
weighted most heavily in determining sex, followed by
the CH and finally the NL. However, the European discriminant functions indicated that the NL was the greatest contributor followed by the OW, the CH and finally
the RNH. It is therefore evident that different variables
will have more of an impact in assessing sex within different populations. Similar population differences have
been reported in a variety of studies focused on the metric assessment of sex and as such this result is not
entirely surprising. (e.g., Stewart, 1948; MacLaughlin
and Bruce, 1985). The fact that Function 3 with RNH
present has a slightly lower crossvalidated classification
rate (83%) than for Function 2 where this dimension is
not included argues that the RNH contributes less to
the overall variance than the other variables (Table 4).
This is also confirmed by the comparatively low single
dimension classification accuracy for RNH (70.8%, Function 13).
The two dimensions (NL and OW) exhibiting side
asymmetry in the Spitalfields and Raunds Furnells samples, respectively, are both directly associated with the
size of the distal humerus. Many studies have indicated
that the humerus is prone to developmental changes
from physical activity, leading to increased cortical bone
thickness as a result of mechanical loadings on the bone.
This can be caused by a number of factors including
body mass, muscle attachments, and body proportion
(Ruff, 1992; Knüsel, 2000). Consequently, if an arm bone
is used repetitively over a long period of time, for example, from a work-related activity, the cortical bone thickness will increase (Claussen, 1982; Mays, 1998). It is
likely that the bilateral asymmetry in proximal ulna size
for the European samples is associated with functional
alterations of the distal humerus due to activity related
movement in the dominant arm (Claussen, 1982; Ruff,
1992; Mays, 1998). The fact that the sizes of male ulnae
were generally more variable than those of females
(Table 2), which were in general uniformly small, is consistent with the findings of Grant and Jantz (2003) and
may be further evidence for the effects of activity-related
movement.
It is evident from the analyses using the original equation (Grant and Jantz, 2003) that assessing sex from the
proximal ulna produced unsatisfactory results when
applied to the European groups. The results indicate
that Spitalfields and Raunds have smaller proximal ulna
dimensions than the American samples analyzed in the
original study. The less robust dimensions of the European samples result in all the females being correctly
classified because they are in the female range, but
many males are misclassified because of their smaller
size and resemblance to the American female ulnae.
Conversely, classifying the American groups on a Spitalfields function would result in getting males correct but
with the result of missing many of the females because
they fall in the size range of Spitalfields males.
Nevertheless, it is somewhat surprising that the
method presented here for the proximal ulna, although
providing reasonably good accuracies with the European
samples, did not yield the extremely high accuracies
reported by Grant and Jantz (2003) for their American
samples. Previous studies have documented secular
American Journal of Physical Anthropology
changes between the 19th and 20th centuries in the size
and proportion of long bones (e.g., Meadows and Jantz,
1995). The differences observed here may be due to secular changes (e.g., Boldsen, 1995; Meadows and Jantz,
1995) for the American samples whereby male elbows
are more robust than females due to nutritional or developmental differences, or from genetic differences
between the samples. It is possible the relatively lower
dimorphism in the Spitalfields population is a result of
similar occupations (i.e., artisans primarily in the weaving trade) shared by men and women in this London
group (Cox, 1996), which might limit the developmental
differences such as musculature. In addition, this population was likely under low but chronic nutritional and
environmental stress due to the cramped and polluted
living conditions in London during the post-Medieval
industrial era (Molleson and Cox, 1993; Lewis, 2002). It
is a well-known phenomenon that a population under
severe environmental stress will have diminished sexual
dimorphism (e.g., Stinson, 1985) but after amelioration
of the stressors that the males in the population often
then experience augmented growth and development
compared with females (Frisancho, 1993; Boldsen, 1995;
Bogin, 1999). This could explain some of the differences
seen between the populations examined in the present
study and the contemporary groups used in the Grant
and Jantz (2003) study.
However, it is apparent from this study that the
method can produce relatively high standards of accuracy when assessing sex, although it is evident that one
equation cannot be applied universally. Original data
obtained by Grant and Jantz (2003) were unavailable for
examination, making comparison of the two studies
purely based on their central tendencies. However,
results from this comparison have highlighted that
dimensions of the proximal ulna are not consistent
throughout different populations. The method appears to
be highly size sensitive and therefore it would be inadvisable to extend results from one sample to another
unless the ulna dimensions can be shown to be similar.
This point is echoed by the fact that the comparisons
between size information and shape information
revealed no significant shape differences in the proximal
ulna between the sexes.
CONCLUSIONS
This study tests the original work of Grant and Jantz
(2003) on two European populations, the documented
Spitalfields Coffin-Plate sample and a British archaeological sample (Raunds Furnells). The study confirms
that the proximal ulna is sexually dimorphic and that
the three metric traits devised in their study are easily
undertaken and repeated. Two new metric variables
were tested, one of which (RNH) provided reasonable
univariate classification accuracy but performed better
when combined with other variables. The Grant and
Jantz (2003) equation was found to be highly inaccurate
when applied to European males, with correct classifications dropping to 50%. Several new discriminant functions were developed using the documented Spitalfields
sample and produced good accuracies when applied to
both European populations.
Results from this study demonstrate that the size of
the proximal ulna is associated to its direct articulation
with the distal humerus and subsequent developmental
change due to mechanical loadings on the bone. This
SEXUAL DIMORPHISM IN THE PROXIMAL ULNA
method and the derived equations are inherently population-specific, as shown previously in numerous metric
analyses of other skeletal elements demonstrating sexual
dimorphism as well as associations with stature (e.g.,
Trotter and Gleser, 1952a,b; Stewart, 1979; Krogman
and Iscan, 1986; King et al., 1998; Bidmos and Asala,
2003, 2005). Consequently, the optimism expressed in
the original study (Grant and Jantz, 2003) for ranking
the proximal ulna ahead of the cranium and most other
postcranial elements for sex assignment is tempered by
the lower overall accuracy (85.4%) for formulas developed from the 18th and 19th century European sample.
Results from this study indicate that while the method
provides good accuracies and a quick and easy manner
of assessing sex, care should be taken when applying it
to populations of alternate origin. While the equations
presented here would be applicable to other European
historical and archaeological groups, tests of the method
on other populations especially modern samples would
be beneficial in the application to medico-legal investigations and for the classification of other archaeological
series.
ACKNOWLEDGMENTS
Appreciation is extended to Louise Humphrey and Rob
Kruzynski (The Natural History Museum, London) for
access to the Spitalfields Collection. Thanks are also
extended to Holger Schutkowski for assistance with German translations of anatomical definitions and to Richard Jantz for providing helpful comments on an earlier
draft of this article. The authors also acknowledge Clark
Larsen and two anonymous reviewers for their very useful thoughts and comments that greatly improved the
original manuscript. Finally, they thank Josh Snodgrass
and Steven Frost (University of Oregon Department of
Anthropology) for fruitful discussions on skeletal shape
analysis and JS for helpful comments on the revised
manuscript.
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