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Classification and misclassification in sexing the Black femur by discriminant function analysis.

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AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 58:145-151(1982)
Classification and Misclassification in Sexing
the Black Femur by Discriminant
Function Analysis
ROBERT DIBENNARDO A N D JAMES V . TAYLOR
Metropolitan Forensic Anthropology Team, Department of Anthropology,
Lehman College, City University of New York, Bronx, New York 10468
KEY WORDS
Sexing, Black femur, Discriminant analysis
ABSTRACT
Stepwise discriminant function analysis for sex assessment was
applied to 130 North American Black femora. The measurements included femoral
length and three midshaft dimensions likely to be preserved in archaeologicallyderived and forensic remains. The method correctly assigned sex for 76.4%of the
sample (range 70.8-81.5%).This compares favorably with results achieved with
other skeletal parts; it also compares favorably with results using the femur in
sexing other racial groups. Among our other conclusions are: (1) a “general size
factor” is one of major significance in correct classification and in misclassification
of sex, and most misclassified individuals are anomalous for this factor: (2)the inconsistency in the relation between circumference and femoral length, which
characterizes the remaining misclassified individuals, suggests that anomalous
functional demands of body weightlmusculature are at fault, and affect circumference more than length; and (3) discriminant function analysis of the same variables in Whites produced similar results, suggesting that sex overrides race in sex
assessment; this was confirmed by cross-validating the predictive accuracy of
Black discriminant function coefficients on White data, and vice versa.
Black (1978) suggested and first applied a
method for sexing archeologically-derived
Amerindian materials using circumference of
the femoral shaft, a dimension likely to be preserved in fragmentary skeletal remains. In a
recent paper (1979) we tested this method on
White dissecting room femora of verified age,
race, and sex, using femoral circumference
alone and in combination with other more commonly employed femoral mesurements. The
overall accuracy of prediction ( 8 2 % )
suggested, first, that femoral circumference
might prove equally effective in sexing other
groups; and second, that such effectiveness
would be especially useful in forensic
casework. We are now able to verify these
assumptions on the basis of data recently
collected on North American Blacks.
MATERIALS A N D METHODS
Our sample of 130 Black femora was chosen
from the Terry Collection of dissecting room
skeletons of known age, sex, and race at the
Smithsonian Institution. The 65 male and 65
female femora were measured for maximum
0002-948318’215802-0145$02.50r j 1982 ALAN R LISS, INC
length and three midshaft dimensions: anteroposterior and transverse diameters, and
circumference.
Stepwise discriminant function analysis employing these measurements was used to
determine the optimal combination of variables for assessing sex of the femur. A number
of statistical packages were used to supplement each other, check for accuracy, and
derive the maximum amount of information
from the data. These were: BMDP, SAS, and
SPSS (Dixon and Brown, 1979; SAS Institute,
1979; and Nie et al., 1975).
Discriminant function analysis has two
broad objectives: (1)analysis - to delineate the
dimensions along which populations are maximally differentiated; and ( 2 )classification - to
assign individuals to groups on the basis of
shared similarities.
In analysis, by indicating which variables
are highly weighted, the discriminant function
coefficients highlight the dimensions along
which populations differ most. The stepwise
Received June 12. 1981; accepted October 9, 1981
146
R. DIBENNARDO AND J.V. TAYLOR
procedure additionally incorporates economy
into this search by eliminating variables that
contribute only minimally to discrimination.
Classification, on the other hand, is based on
comparison of an individual's profile with the
average profiles of the two or more groups, into
one of which he must be assigned. These comparisons are made by computing classification
functions for each group, and assigning the
individual to the group on whose function he
scores highest.
We have pursued both of these objectives of
discriminant function analysis in the present
paper with the following results.
remaining variable contributes significantly to
group separation.
Table 2 presents a summary of the stepwise
procedure. There are four steps: the first indicates that circumference alone is the single
best discriminator of sex; step two indicates
that circumference and length are the best pair
of discriminators; step three adds transverse
diameter, but this affects the discriminatory
power of circumference. The discriminatory
power of variables already entered can be altered by their relationships to entering variables; therefore, in step four, circumference is
dropped from the discriminant function,
because it evidently provides no information
not provided by transverse diameter in conjunction with length. The result is an optimal
discriminant function for Blacks based on
length and transverse diameter.
Table 3 presents the discriminant function
coefficients for each step. From the standardized coefficients it is apparent that length and
transverse diameter are of coequal importance
in the discriminant function. Finally, Table 4
presents the prediction matrices for accuracies
of prediction at each step in the procedure and
Figure 1 presents the histograms for the discriminant function scores of males and
females.
RESULTS
Table 1 presents the descriptive statistics
and univariate F's for a one-way ANOVA for
each variable. There is a statistically significant sexual dimorphism for all four
measurements.
In the stepwise procedure, variables are sequentially entered into the discriminant function on the basis of an entrance criterion. The
single variable that maximally separates the
groups is entered first. The variable with the
greatest residual discriminatory power is entered next, and the process is repeated until no
TABLE 1. Simple descriptive statistics and uniuariate F-ratios for the differences between Black males and females
Variable
X
Length'
6 475 (450)
Q 443 (423)
F'
S
-
31.4 (20.4)
23.6 (22.1)
44.72*
Circumference
5.6 15.9)
5.3 (3.9)
Anteropos terior
diameter
2.4 (2.4)
2.3 (1.7)
Transverse
diameter
2.1 (2.2)
2.0 (1.7)
45.30*
21.86*
40.71*
Data are from the 65 males and 65 females whose values were used in the stepwise discriminant function procedure summarized in Table 2 .
Values in parentheses are for U'hitrdatal50 males and 35 temalesl dcscrihed in IXHennardo and'l'aylorl19791 and Taylor and DiHennardoll9821.
'With 1 and 128 degrees of freedom.
'Measurements in millimeters.
'Significant a t a=0.05.
TABLE 2. Sumary of the stepwise discriminant function analysis o f male and female Black femora
Variable
Entered
Removed
~
Step
1
2
3
4
.
Circum
Length
Trans. Dia.
Circum
F t o enter
or-remove
No. of variables
in function
F for group differences
on function
Degrees of
freedom
45.30
11.18
6.11
0.42
1
2
3
2
45.30
30.04
22.87
34.25
1,128
2,127
3,126
2.127
147
S E X I N G T HE BLACK FEMUR
DISCUSSION
Accuracy
Although the innominate bone permits the
highest accuracy in discriminating sex (above
90%: Washburn, 1948; Hanna and Washburn,
1953; Thieme and Schull, 1957; Genqvese,
1959; Davivongs, 1963; Howells, 1964; Igcan,
1980,1981),the greater resistanceof the femur
to insult and decomposition often makes it of
greater value in the classification of archeological and forensic remains. This is especially
true of the femoral shaft, because it is composed almost entirely of cortical bone.
In this regard, it is apparent from Table 3
that sexing the Black femur by discriminant
function analysis provides a tolerably high degree of predictive acuracy (76.4%overall, with
a range from 70.8-81.5%). This is less than,
but comparable to, predictions made with the
White femur (80.7% overall, range 72-86%:
DiBennardo and Taylor, 1979; Taylor and DiBennardo, 1982, and is virtually as great a predictive accuracy as some investigators have
found with the inspectional approach to sexing
the skull (7770,Stewart, 1948). Moreover, its
range of predictive accuracy substantially
overlaps those reported in the literature for
sexing the skull and postcranial bones, singly
and in combination, by discriminant function
analysis (Henke, 1977).
There is, however, a notable difference in the
relative accuracy of classifying males versus
females with the femur, both within and between racial groups. Specifically, in Blacks
there is consistently greater accuracy in
predicting males (as Black, 1978 also found for
Amerindians),while in Whites the opposite obtains. Additionally, in Blacks of both sexes,
circumference alone is roughly as accurate a
TABLE 3.Discriminant function coefficients for the three steps in the stepwise procedure summarized in Table 2
Variable(s)
in
function
Standardized canonical
discriminant function
coefficients
Circumference
Uns tandardized
coefficients
0.184
1.000
Canonical correlation =
Chi-square =
Degrees of freedom =
0.51
38.63
1
(constant) -15.823
Group mean for males =
Group mean for females =
Circumference
Length
0.107
0.021
(constant) -18.744
0.590
0.570
Length
Transverse diameter
0.660
0.610
0.024
0.300
(constant) -18.744
0.59
-0.59
Canonical correlation =
Chi-square =
0.57
49.20
Degrees of freedom =
Group mean for males =
Group mean for females =
2
0.68
-0.68
Canonical correlation =
Chi-square =
0.59
54.78
Degrees of freedom =
Group mean for males =
Group mean for females =
2
0.73
-0.73
TABLE 4 . Classification results (Yo correctly predicted) of each discriminant function generated zn the stepwise analyszs
of sex differences in the Black femur
~
~
Variables
~
_ in function
_
~
_
~
_
_
Males (N
~
_ = 65) _
~~
~
Females
( N~
= 65)
~
Circumference
Circumference and length
Length and transverse
diameter
(Circumference,length
and anteroposterior diameter)
75.4 (72)
81.5 (78)
70.8 (86)
75.4 (80)
73.1 (79)
78.4 (79)
78.5
76.9
77.7
Average Across Functions
78.5 (77.3)
(82)
Values in parenlheses are t o r White data ITayIor a n d DiRennardo. 19821
(86)
74.4 (84)
_
Average across sexes
(84)
76.4 (80.7)
~
148
R. DIBENNARDO AND J.V. TAYLOR
4
8
12
16
B-Function
Females
'
I
2: Circumference, Length
16
12
8
4
4
8
12
16
C-Function
Females
3 : Length, Transverse Diameter
16
12
8
Males
12
16
Females
Fig. 1. Histograms for the discriminant function scores of males and females for the discriminant functions summarized
in Table 2. Hatched areas represent misclassified individuals.
predictor of sex as it is in White males, but
White females are exceptional in the high
degree of predictive accuracy (86%)provided
by circumference alone.
Overall, therefore, we conclude that the level
of sex prediction permitted with the femur indicates a high degree of usefulness in the identification of archeological and forensic
materials.
Misclassification
Our stepwise procedure permits classification of any particular case by three different
functions. I t occurred to us that there might be
discernible morphological patterns in the misclassified cases, and that such patterns might
be revealed by the constancies and inconstancies of misclassifications across discriminant
SEXING THE BLACK FEMUR
functions. We have designated as constants
those cases misclassified by all three functions, and as inconstants, those misclassified
by some function(s) but not by all.
The constants appear to comprise males
with small dimensions for all traits investigated, and, conversely, females with large
dimensions overall. This suggests that a
"general size factor" is of major significance in
correct classification and in misclassification
of sex by discrimination function analysis of
the femur. It also suggests, that in so far as
size is the major component of sexual dimorphism, the constants represent a hard core of
cases that will be consistently misclassified by
any set of variables chosen for analysis. These
constants comprise the larger group of
misclassified cases ( 11 of 17 males or 65%, and
12 of 23 females or 52%).
The inconstants comprise two subgroups.
Most fall into a subgroup (a)anomalous for circumference relative to femoral length (males of
normal stature but exceptionally gracile, and
females of normal stature but exceptionally robust). As a subgroup, they account for the improved accuracy of classification when length
is added to circumference in the second discriminant function. The other subgroup (b)
comprises individuals anomalous for length
relative to femoral circumference (normal male
circumference but exceptionally short, and.
normal female circumference but exceptionally
tall). These individuals would tend to be misclassified by the second discriminant function,
but since their number is small relative to
subgroup "a," there is net gain in the second
discriminant function over the first.
The above analysis is explicable on the premise that stature (and hence long bone length) is
largely determined by intrinsic factors
(Osborne and DeGeorge, 1959; Tanner, 1977).
On the other hand, as we have argued elsewhere, variation in femoral circumference appears to be largely dependent on the functional
demands of weightbearing and/or muscular
activity (DiBennardo and Taylor, 1979; see
also Schultz, 1953).It follows, then, that (1)the
primary basis of sexual dimorphism of the
femur appears to be the intrinsic factor of
length in combination with commensurable
body weight. Anomalous variation in the latter
may account for the variations observed in
both subgroups of inconstants; in contrast,
anomalies in length, accompanied by commensurable variation in weight (and presumably
circumference), account for the misclassification of constants. (2) Both Black and White
males, and Black and White females, have sim-
149
ilar average circumferences, respectively
(Table 1); on the other hand, the four groups
differ widely in average lengths. This suggests
that the functional demands on long bone circumference (weight bearinglmuscular activity)
permit less variability across race in circumference than in length dimensions.
Cross-validation
The variables utilized in the present study of
sexual dimorphism in the Black femur were
similarly used in sexing the White femur
(DiBennardo and Taylor, 1979; Taylor and
DiBennardo, 1982. Some of the similarities
and differences in results are worth noting.
(1)For both races, circumference is the single
best discriminator of sex, and circumference
and length, the best pair of discriminators.
(2) The best triplet of discriminators,
however, is circumference, length, and anteroposterior diameter for Whites, but, circumference, length, and transverse diameter for
Blacks. Moreover, in Whites the addition of
anteroposterior diameter in the stepwise
procedure produces an optimal function with
three variables, while in Blacks, the addition of
transverse diameter causes circumference to
drop out of the function, leaving an optimal
function with only two variables.
The similarities in results suggests that in
sex assessment, sex differences override race
differences, a conclusion in accord with those
of Giles and Elliot (1963), Giles (1964), and
Richman, et al. (1978),for sexing the skeletons
of Blacks and Whites by discriminant function
analysis. To test this conclusion, we have run a
cross validation analysis of our Black classification functions on our White data, and of our
White classification functions on our Black
data. The accuracies of prediction are given in
Table 5.
I t is clear from Table 5 that circumference retains a high consistency of predictive accuracy
across race (70.8-85.770).Classification functions that include length, on the other hand,
are much more variable in predictive success
(66-94.170).
The latter variability is apparently
due to the marked differences in femoral
length between Blacks and Whites. Almost all
White females have femoral lengths below the
average of Black females. Therefore, the Black
female classification functions employing
femoral length virtually assure a female classification for all White females (94.1 and 91.4%).
Conversely, because most White males have
femoral lengths below the Black male average,
Black discriminant functions using length
150
R. DIBENNARDO AND J.V. TAYLOR
TABLE 5. Classification results (% correctly predicted) o f (a)Black discriminant functions on White data and Ib) White
discriminant functions on Black data
Males
Whites
~~
WGes
Blacks
~~~
A Cross validation of Black discriminant
functions on White data
~ _ _ _ _ _ _ _ ~ ~
~~~
~~
Circumference
Circumference
Length
Length
Transverse Dia
(75 4)*
(81 5)
72 0
66 0
68 0
~
~~
~ _ _ _ _ _ _ _ ~
Females
Blacks
~~
~~~
85 7
94 1
91 4
178 5)
~
~~~
176 9)
-~
~~~
~
B Cross validation of White discriminant functions on Black data
Circumference
Circumference
Length
Circumference
Length
Anteroposterior
Diameter
170 7)
(75 4)
_______
~__________
75 4
84 6
172 0)
178 0)
70 8
67 7
(85 7 )
180 0)
84 6
182 0 )
69 2
(85 71
*Cdlues in pdrenthezez indicdte accuracies for the datd Iron1 a h i c h thc f u n c t i o n i %eregenerated
tend to classify White males as females. This
ratifies our earlier conclusion that femoral
length is probably a better criterion for racial
differentiation than circumference, because it
is less responsive to functional demands. At
the same time, the contrasting significance of
circumference in the optimal functions for
Blacks and Whites, suggests a second major
component of femoral variation between
Blacks and Whites: the independence of anteroposterior diameter from circumference in
Whites may reflect an element of pilastry that
is absent in Blacks. This racial difference in
pilastry has been attributed to differences in
musculature andlor anterior bowing of the
shaft (Hooton, 1946; Stewart, 1962; Walensky,
1965 ; Gilbert, 1976).
In summary, the functional implications in
the present study point the direction to further
research emphasizing the analytical rather
than classificatory aspect of discriminant
function analysis. We are presently expanding
our data base to include variables such as
femoral bowing, p i l a s t r y , and other
dimensions which should throw light on the
bases of sexual and racial variation in femoral
morphology.
ACKNOWLEDGMENTS
The authors gratefully acknowledge the help
received from Drs. L. Angel and L. St. Hoyme,
and the support staff of the NMNH a t the
Smithsonian Institution. This research was
supported by CUNY-PSC grant 13456.
LITERATURE CITED
Black TK 111 (1978) A new method for assessing the
sex of fragmentary skeletal remains: femoral
shaft circumference. Am. J. Phys. Anthrop., 48:227-231.
Davivongs, V (1963) The pelvic girdle of the Australian
aborigine; sex differences and sex determinations. Am. J.
Phys. Anthrop., 21:443-455.
DiBennardo, R and Taylor, JV (1979)Sex assessment of the
femur: a test of a new method. Am. J. Phys. Anthrop.,
503535-638.
Dixon, WJ. and Brown, MB (1979)BMDP-79. University of
California Press, Berkeley.
Genovese. S (1959) L'estimation des differences sexuelles
dans l'os coxal; differences metriques et differences morphologiques. Bull. Mem. SOC.Anthrop. (Paris), 10 (X
serie):3-95.
Gilbert, BM (1976) Anterior femoral curvature: its p r o b
able basis and utility as a criterion of race assessment.
Am. J. Phys. Anthrop.. 4.2601-604.
Giles, E (1964) Sex determination by discriminant function
analysis of the mandible. Am. J. Phys. Anthrop.,
22129-135.
Giles, E, and Elliot, 0 (1963)Sex determination by discriminant function analysis of crania. Am. J. Phys. Anthrop.,
21:53-68.
Hanna, RE, and Washburn, SL (1953)The determination of
the sex of skeletons, as illustrated by a study of the
Eskimo pelvis. Hum. Biol.. 2521-27.
Henke, K (1977) On the method of discriminant function
analysis for sex determination of the skull. J. Hum. Evol.,
695-100.
Hooton. EA (1946) Up From the Ape. Second ed. MacMillan, New York.
Howells, WW (1964) Determination du sex du basin par
fonetion discriminante: Btude de material du Docteur
Gaillard. Bull Mem. Soc. Anthrop. Paris (11 series),
295-105.
Igcan, MY (1980) Differences in pelvic dimension between
American Blacks and Whites. Am J. Phys. Anthrop.,
52239-240.
Igcan, MY (1981) Metrical analysis of pelves of American
Indians, Whites and Blacks. AM. J. Phys. Anthrop.,
54936.
.
.
S E X I N G THE BLACK FEMUR
Nie, NN. Hull, CH, Jenkins, JG, Steinbrenner, K, and
Bent, DH (1975) Statistical Package for the Social
Sciences. McGraw-Hill, New York.
Osborn, DH, DeGeorge, RH, and DeGeorge, FV (1959)
The Genetic Basis of Morphological Variation. Harvard
University Press, Cambridge.
Richman, MS, Michel, ME, Schulter-Ellis, F P and
Corruccini, RS 11978) Determination of sex by discriminant function analysis of postcranial skeletal measure
ments. J. For. Sci., 23:159-167.
SAS Institute Inc. (1979) SAS User's Guide. SAS Institute
Inc., Raleigh.
Schultz. AH (1953) The relative thickness of the long bones
and the vertebrae in primates. Am. J. Phys. Anthrop.,
11:277-312.
Stewart, TD (1948) Medico-legal aspects of the skeleton. 1.
151
sex, age, race and stature. Am. J. Phys, Anthrop..
6315-322.
Stewart, TD (1962) Anterior femoral curvature: its utility
for race identification. Hum. Biol., M49-62.
Tanner, J M (1977) In, GA, JS Weiner, J M Tanner, and
NA Barnicot (eds):Human Biology (2nd ed.), Harrison,
Oxford Oxford University Press.
Taylor, J V , and Dibennardo. R (1982) Determination of sex
of White femora by discriminant function analysis; forensic implications. J. For. Sci., (in press).
Thieme, FP. and Schull. WJ (1957) Sex determination from
the skeleton. Hum. Biol., 29242-273.
Walensky. NG (1965) A study of anterior femoral curvature
in man. Anat. Rec., 151:559-570.
Washburn, SL (1948) Sex differences in the pubic bone.
Amer. J. Phys. Anthropol. 6199-207.
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