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Discriminant function analysis of the central portion of the innominate.

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AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 315-320 (1984)
Discriminant Function Analysis of the Central Portion of the
Innominate
JAMES V. TAYLOR AND ROBERT DIBENNARDO
Metropolitan Forensic Anthropology Team, Department of Anthropology,
Lehman College of GUNK Bronx, New York 10468
KEY WORDS
Innominate
Discriminant analysis, Sex and race assessment,
ABSTRACT
Terry Collection innominates of 260 American whites and
blacks (65 males and 65 females of each race) were analyzed by discriminant
function analysis for sex assessment, race known, and for simultaneous race
and sex assessment. Measurements from the preservationally favored central
portion of the innominate were chosen for their potential usefulness in forensic
casework and to objectify long-recognized “formal” differences between the
sexes in the greater sciatic notch. These included acetabular diameter, greater
sciatic notch height, and position of greatest notch depth. Accuracy of sex
prediction when race is known is roughly 90% in both the base sample of 260
and a test sample of 200 (50 additional individuals for each group). For simultaneous race and sex assessment, accuracy of prediction is roughtly 60% for
each group in both samples. This represents about a 45% reduction in error
over random assignment by race and sex.
The highest accuracy of sex prediction
achieved on several populations by inspectional, osteometric, and discriminant function analyses of the innominate is based
largely upon use of the pubic area (American
whites and blacks; Washburn, 1948; Bantus
and Bushmen; Washburn, 1949; Eskimoes;
Hanna and Washburn, 1953; American
blacks; Thieme, 1957; Thieme and Schull,
1957; French whites; Howells, 1964; Japanese; Hanihara et al., 1964;American blacks
and whites; Phenice, 1969; DiBennardo and
Taylor, 1983). When this area is poorly preserved, its measurement and use in the ischium-pubis index, or the equally effective
inspectional method of Phenice, are precluded. In these cases, some investigators
have turned to the central portion of the innominate bone, especially the greater sciatic
notch.
The compelling reason for using the central portion of the innominate for sex assessment is its higher resistance to postmortem
damage. Although several successful techniques have been developed for sex assessment on this basis (Hooton, 1930; Angel,
1946; Genoves, 1959; Kelly, 19791, no similar
@ 1984 ALAN
R. LISS, INC
method has been used for race assessment. A
method for simultaneously sexing and racing
the preservationally favored central portion
of the innominate would, therefore, provide
a useful tool for the assessment of human
remains in forensic and archaeological
studies.
We present such a method here for application to skeletal materials that can be
assumed to be either American blacks or
whites, on a priori grounds. It derives from
the above considerations and combines the
dimensions in Kelly’s (1979) sciatic notch/
acetabular diameter index and Genoves’
(1959)greater sciatic notch index. By combining them in a multiple discriminant function
analysis, however, we hoped to capitalize on
the population differences in notch dimensions demonstrated by Letterman (1941) and
produce functions that optimally separate the
sexes and races simultaneously. As we demonstrate below, this four group separation
permits individual identification at a n acceptable level of accuracy, considering the
Received January 30, 1984; revised March 19, 1984; accepted
March 20, 1984.
3 16
J.V. TAYLOR AND R. DIBENNARDO
limited evidence provided by the body of the
innominate.
MATERIALS AND METHODS
Our base sample consists of the innominates of 260 North American whites and
blacks: 65 males and 65 females of each race.
They were obtained from the Terry Collection a t the Smithsonian Institution and are
of known age a t death, sex, and race. In addition, a further sample was measured to test
the reliability of statistics generated by the
base sample. It was also drawn from the
Terry Collection (50 individuals for each
group).
In keeping with our stated objective, the
three measurements chosen are 1) notch
height-the height of the greater sciatic notch
measured with sliding calipers between the
points of Lazorthes: the tubercle of Bouisson
(attachment of the piriformis muscle) and the
tip of the ischial spine (Fig. lA,B); 2) notch
position-the distance from the tip of the ischial spine to the intersection of the line of
notch height and the perpendicular dropped
from it to the deepest point in the notch (Fig.
1 B,C), measured with coordinate calipers; 3)
acetabular diameter-diameter of the acetabular rim measured with sliding caliper parallel to the long axis of the ischiai body (Fig.
1E,F).
Like Kelly (1979) and Genoves (19591, we
recognize the difficulties in using the fragile
ischial spine as a n osteometric point. However, the alternative use of the poorly defined
base of the spine consistently posed a greater
operational problem than did extrapolating
the position of the tip of the spine, where this
was necessary.
The statistical analysis was carried out in
two parts. First, we elaborated on Kelly’s
protocol by adding notch position to his two
variables and using the discriminant function technique, instead of a n index, to discriminate sex when race is known. This adds
a “formal” component to Kelly’s simple linear approach and permits the calculation of
posterior probabilities of group membership
for individual cases (e.g., in forensic case
work). Second, we used the same three variables in a multiple discriminant function
analysis for simultaneously discriminating
race and sex.
The DISCRIMINANT procedure of SPSS,
METHOD=DLRECT, was used in both analyses (Nie et al., 1975). The coefficients generated by both analyses were then used to
classify the test samples.
RESULTS
Table I provides the simple descriptive statistics for our data. Tables 2 and 3 give the
results for our analysis of sexing when race
is known, and Tables 4 and 5 give results for
the simultaneous discrimination of sex and
race.
Fig. 1. Illustration of the innominate showing the
measurements used in the study. See text for details.
Sex, race known
The structure coefficients in both whites
(Table 2) and blacks (Table 3) indicate that
males tend to have larger acetabular diameters, smaller notch heights, and the position
of maximum depth situated more superiorly
than females.
On the original samples, accuracy of prediction averages 94.6% for whites (Table 2)
and 90.8% for blacks (Table 3). On the test
samples, accuracy declines to a n average of
89% for whites, but remains about 91% for
blacks (Tables 2 and 3). Overall (i.e., weighted
across samples), whites average 92.1% and
blacks 90.9%. In short, both races can be
correctly classified about 91% of the time.
317
DISCRIMINANT FUNCTION ANALYSIS OF THE INNOMINATE
TABLE 1. Simple descriptive statistics for the base sample analyzed in the text. N
each erouu and all dimensions are i n millimeters
Variables
=
65 i n
White males
White females
Black males
Black females
SD
56.5
3.2
50.3
2.6
55.1
2.8
50.0
2.6
Notch
height
Mean
SD
48.6
4.6
51.7
5.7
44.7
5.2
49.3
5.3
Notch
position
Mean
39.5
4.4
33.7
4.9
37.0
5.2
33.5
4.7
Acetabular
diameter
Mean
SD
TABLE 2. Discriminant function for sex assessment when race is known to be white
Variable
Raw
coefficients
Acetabular
diameter
0.24674
Notch
height
-
Notch
position
Constant
Group
White males
White females
Standardized
coefficients
0.15865
1.15406
~
-
Structure
coefficients
0.71313
0.89
0.81941
--0.35
0.71512
0.64
10.85599
Group
means
-
1.46
1.46
96 Accuracy
base sample
95.4
93.8
% Accuracy
test sample
88.0
90.0
All coefficients are for the base sample: raw coefficients are for computing discriminant scores
from raw measurements, standardized coefficients are for computing scores from standardized
data, and structure coefficients are correlations between discriminant scores and original
variables, over the total sample. Discriminant scores are standardized within groups so that the
pooled within-groups dispersion matrix is a n identity matrix.
TABLE 3. Discriminant function for sex assessment when race is known to be black
Variable
Raw
coefficients
Acetabular
diameter
Notch
height
0.21627
-
Notch
position
Constant
Group
Black males
Black females
Standardized
coefficients
0.19787
0.18268
-
0.58603
-
1.04304
0.90882
Structure
coefficients
0.86
-0.50
0.42
8.50729
Group
means
1.34
- 1.34
% Accuracy
base sample
90.8
90.8
% Accuracy
test sample
92.0
90.0
All coefiicients are for the base sample: raw coefficients are for computing discriminant scores
from raw measurements, standardized Coefficients are for computing scores from standardized
data, and structure coefficients are correlations between discriminant scores and original
variables, over the total sample. Discriminant scores are standardized within groups so that the
pooled within-groups dispersion matrix is a n identity matrix.
318
J.V. TAYLOR AND R. DIBENNARDO
TABLE 4. Discriminant functions for simultaneous race and sex assessment o f whites
and blacks
Variable
Function 1
Function 2
Function 3
Raw coefficients
Acetabular diameter
Notch height
Notch position
Constant
0.23417
0.17650
0.16645
- 9.81200
0.18120
0.18891
- 0.06092
- 16.57900
-
0.22282
0.04641
0.23183
5.72817
0.65602
0.50763
0.98578
- 0.29310
-
0.62423
0.24217
1.11543
-
0.25
0.38
0.70
Standardized coefficient
Acetabular diameter
Notch weight
Notch position
- 0.92102
Structure coefficient
Acetabular diameter
Notch height
Notch position
- 0.42
Group means on functions
White male group
White female group
Black male group
Black female group
-
0.80085
0.87
-
0.53
0.43
0.82
0.48
1.41
1.55
1.37
1.24
0.43
0.24
- 0.41
- 0.26
0.04
0.06
- 0.04
0.07
-
All coefficients are for the base sample described in the text. Structure coefficients are correlations
between discriminant scores and original variables, over the total sample. Discriminant scores are
standardized within group so that the pooled within-groups dispersion matrix is a n identity matrix.
TABLE 5. Accuracy ofsimultaneous race and sex
assessment for the discriminant function analysis
giuen in Table 4
Group
White males
White females
Black males
Black females
% Accuracy
base samule
% Accuracy
63.1
58.5
64.6
58.5
62.0
58.0
56.0
52.0
test samule
Race and sex, simultaneously
Only the first two canonical discriminant
functions are statistically significant at the
0.05 level (although the third is retained for
classificatory purposes). From the group
means (Table 4) it is clear that function 1
separates the sexes (males have positive
scores, females negative ones). Function 2,
on the other hand, separates the races (positive for whites, negative for blacks). The
structure coeficients (Table 4). suggest that
the bases for these separations differ. For the
sex function, males have larger acetabular
diameters, smaller notch heights, and more
superiorly situated positions of maximum
depth. This is consistent with our analysis of
sex with race known. The race function, however, shows all positive coefficients, suggesting that racial separation is based primarily
on size, with whites generally larger than
blacks.
For the original sample, accuracy of prediction over all four groups averages 61.2%. On
the test sample, this declines to 57%. Random assignment of race and sex would produce a n expected accuracy of only 25%. To
express the improvement achieved by these
discriminant functions, we used a proportional reduction in error statistic, tau, given
in Klecka (1980, pp. 50-51). For our original
sample, tau = 48.2%, and for the test sample,
42.7%. The functions, therefore, represent a
48.2% and 42.7% reduction in error over
chance, for these two samples, respectively.
DISCUSSION
In the inspectional approach to sex assesment, the form of the greater sciatic notch is
described as usually wide and shallower in
the female (Hooton, 1930; Angel, 1946; Washburn, 1948). But though HrdliEka considered
notch form as the single most effective sexing
criterion of the pelvis (in Stewart, 1952),only
Hooton and Angel have employed it in a
purely inspectional approach to sexing the
innominate bone (see Genovks, 1959, p. 49).
Both of these investigators use notch form
with either the subpubic angle (Hooton, 1930)
or subpubic angle and the degree of excavation of the preauricular sulcus (Angel, 1946).
As noted above, use of the subpubic angle
may be compromised by the circumstances of
preservation. However, when the notch form
DISCRIMINANT FUNCTION ANALYSIS OF THE INNOMINATE
has been used alone, the stated accwacy of
sex prediction ranges from 79 to 81% (Hooton, 1930; Genoves, 1959). These are tolerably good results, roughly comparable to those
achieved with the skull (70 to 80% according
to Stewart, cited in Kelly, 1979).
Admittedly, it is difficult to assess the validity of such estimates because of the subjective component in inspectional assessments.
Stewart (1954) has summarized the strength
of the inspectional method in his remark that
it may be rather a waste of effort to measure
simply to verify what can be so quickly seen
and integrated into a total morphological
pattern by the trained eye. Nonetheless, some
objective criteria of sex assessment are
clearly desirable for court testimony in forensic cases, as Stewart himself acknowledges
(1979).
Such objective quantitative assessments of
predictive accuracy have been customarily
given in metric approaches to sexing and
racing the greater sciatic notch. The use of a
metric approach does not, of course, always
insure success. Letterman (19411, for example, could not race and sex American whites
and blacks using three measurements of the
notch. He found that the degree of overlap,
especially in notch height (cf. Washburn,
1949; and Genoves, 19591, made classification of race and sex uncertain in a high percentage of cases. This is not surprising,
however, since his simple measure by measure approach to morphology does not, in fact,
provide a n analysis of “form.” What are
needed are indices or other compound-derived measures. For example, Genoves’ (1959)
greater sciatic notch index uses two of Letterman’s measurements to demonstrate the formal fact that the perpendicular from the
maximum height line to the deepest point in
the notch divides the height into roughly
equal chords in females; in males the upper
chord is typically smaller. His accuracy of
sex prediction with this index is 79.9% (Bruxelles and Saint Bride series combined). Kelly
improved on this accuracy of prediction by
adding the acetabular diameter to the sciatic
notch height-ie, his sciatic notchlacetabular
index; however, this index omits any formal
description of the sciatic notch.
Our own results, whether by the functions
for sex alone or for race and sex together,
confirm and objectify the observations of
HrdliEka concerning notch form and ratify
the metrical conclusions of Genoves. Namely,
in males the notch has a n inverted “J” shape,
319
and in females, a n open “C” shape. Addition
of the acetabular diameter sharpens the contrast between the sexes by emphasizing the
greater acetabular size in males in conjunction with their smaller notch heights. This
corroborates Kelly’s findings with regard to
his index.
As compared with Kelly (1979), our accuracy of prediction for the sexing functions is
slightly higher, a t least as regards our base
sample (92.7 vs. 90.0%). This might be accounted for by the additional variable in our
study (notch position) andor the discriminant function method. However, the difference in accuracy of prediction between our
base sample and test series (for whites, a 5%
difference) indicates that such percentages
must be accepted with caution. Rather than
a rigid figure, they suggest a domain of accuracy, which in this case is quite high.
Finally, it would appear from the structure
coefficients for the racing function (Table 4,
function 2), that “size,” especially with regard to notch height, is the primary discriminator between the races. Thus, whites are
generally larger in this central portion of the
innominate, as they also are in measurements of the entire innominate (see Di Bennardo and Taylor, 1983).
In conclusion, our discriminant functions
using notch height, notch depth position, and
acetabular diameter express long, recognized
formal distinctions between the sexes and
allow high accuracy of sex prediction. Additionally, they express the size differences between blacks and whites we have reported
elsewhere and provide a substantial improvement in race prediction over chance assignment-especially considering the limited
evidence given by the central portion of the
innominate.
ACKNOWLEDGMENTS
We thank Dr. J.L. Angel and the support
staff of the NMNH at the Smithsonian Institution for their valuable assistance. We also
thank Dean F.C. Shaw for his continuing
support of the Metropolitan Forensic Anthropology Team at Lehman College. This study
was made possible by PSC-CUNY grants
#13456 and #6-62088.
LITERATURE CITED
Angel, JL (1946) Skeletal change in ancient Greece. Am.
J. Phys. Anthropol. I3:489.
DiBennardo, R, and Taylor, JV (1983)Multiple discriminant function analysis of sex and race in the postcranial skeleton. Am. J. Phys. Anthropol. 61.305-314.
320
J.V. TAYLOR AND R. DIBENNARDO
Genoves, S (1959) L’estimation des differences sexuelles
dans 1’0s coxal: Differences metriques et differences
morphologiques. Bull. Mem. Soc. Anthropol. (Paris)
IO(X):3-95.
Hanihara, K, Kimura, K, and Miaamidate, T (19641 The
sexing of Japanese skeletons by means of discriminant
functions. Nihon Hogaku Zassi (Japanese Journal of
Legal Medicine) 18t107-114.
Hanna, RE, and Washburn, SL (1953) The determination
of sex of skeletons, as illustrated by a study of the
Eskimo pelvis. Hum. Biol. 2 5 2 - 2 7 .
Hooton, EA (1930) The Indians of Pecos Pueblo. A study
of Their Skeletal Remains. New Haven: Yale University Press.
Howells, WW (1964) Determination du sex du basin par
fonction discriminante: Etude de materiel du Docteur
Gaillard. Bull. Mem. Soc. Anthropol. Paris 7(11):95105.
Kelly, MA (1979) Parturition and pelvic changes. Am. J.
Phys. Anthropol. 51:541-545.
Klecka, WR (1980) Discriminant Analysis. Beverly Hills:
Sage Publications.
Letterman, G (1941) The greater sciatic notch in Ameri-
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28:99-116.
Nie, NN, Hull, CH, Jenkins, JG, Steinbrenner, K, and
Bent, DH (1975). Statistical Package for the Social
Sciences. New York McGraw-Hill.
Phenice, TW (1969) A newly developed method of sexing
the 0s pubis. Am. J . Phys. Anthropol. 30:297-301.
Stewart, TD (ed.) (1952) HrdliEka’s Practical Anthropometry. Fourth Edition. Philadelphia: Wistar.
Stewart, TD (1954) Sex determination of the skeleton by
guess and by measurement. Am. J. Phys Anthropol.
12t385-392.
Stewart, TD (1979) Essentials of Forensic Anthropology.
Springfield C.C. Thomas.
Thieme, F P (1957) Sex in Negro skeletons. J. Forenslc
Med. 432-81.
Thieme, FP, and &hull, WJ (1957) Sex determination of
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Washburn, SL (1946) Sex differences in the pelvic bone.
Am. J. Phys. Anthropol. 6:199-208.
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