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Estimation of adult stature from the calcaneus and talus.

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AMERICAN JOURNAL
OF PHYSICAL ANTHROPOLOGY 96:315-320 (1995)
Brief Communication: Estimation of Adult Stature From the
Calcaneus and Talus
THOMAS DEAN HOLLAND
United States Army Central IdentifKation Laboratory, Hawaii, Hickam
AFB, Hawaii 96853-5530
KEY WORDS
Hamann-Todd Collection, Tarsals
ABSTRACT
Calcanei and tali of 100 skeletons in the Hamann-Todd Collection at the Cleveland Museum of Natural History were measured. The
skeletons represented 50 males and 50 females distributed equally by race,
i.e., whites and blacks. Linear-regression equations, with standard errors
ranging from 4.09 to 6.11 cm, were derived from these measurements for the
purpose of estimating stature. Two independent control samples, including
one comprised of remains of American servicemen lost in World War I1 and
the Korea and Vietnam wars, were tested with relatively accurate results.
0 1995Wiley-Liss, Inc.
A variety of mathematical techniques for several reasons. First, Steele (1976) has
have been developed to estimate living stat- already demonstrated the value of the calcaure from skeletal remains. Probably the neus and talus in assessing sex, thus premost widely used technique in the United senting the potential to determine both sex
States is that devised by Trotter and Gleser and stature from the same elements. Secin a series of articles in the 1950s (1951, ond, the calcaneus and talus preserve rela1952, 1958; also Trotter, 1970). A similar tively well (e.g., Pickering, 1986). Finally,
technique developed by Genoves (1967) is the required measurements taken from the
not uncommonly applied to Native North calcaneus and talus are relatively easy to
obtain and replicate.
American archaeological samples.
As effective as these technique are, howMATERIALS AND METHODS
ever, they suffer from a limited applicability
A total of 119 calcaneuskalus pairs and
to fragmented remains since they require
intact long bones. Unfortunately, both ar- one unpaired calcaneus from the Hamannchaeological specimens as well as those of Todd Collection at the Cleveland Museum of
forensic interest commonly are recovered Natural History were measured. The elewithout intact or even reparable long bones. ments represented 60 males and 60 females
In response, several authors have presented distributed equally by race (American
techniques for use in cases where intact limb whites and blacks). The individuals reprebones are not available. Some (e.g., Holland, sented ranged in age a t death from 16 to 81
1992; Steele, 1970; Steele and McKern, years. No element with obvious or suspected
1969; Simmons et al., 1990) have focused on pathology that might have adversely affragmented long limb bones, while others fected the results was used.
The Hamann-Todd specimens were di(e.g., Byers et al.,1989; Meadows and Jantz,
1992; Musgrave and Harneja, 1978) have vided into two samples. Sample 1 consisted
opted for methods employing alternative el- of 100 calcaneudtalus pairs representing 50
ements such as metacarpals and metatar- males and 50 females distributed equally by
race. This sample was used to formulate the
sals.
The technique presented in this paper
was devised for use with the calcaneus
Received April 8,1994; accepted September 20,1994.
and/or talus. These elements were selected
0 1995 WILEY-LISS, INC.
316
T. D. HOLLAND
TABLE 1. Sample-1 statistics
Measurement
Race
Sex
Number
Mean
Standard
deviation
White
White
Black
Black
White
White
Black
Black
White
White
Black
Black
Male
Female
Male
Female
Male
Female
Male
Female
Male
Female
Male
Female
25
25
25
25
25
25
25
25
25
25
25
25
81.66
75.38
82.84
75.86
58.64
53.50
60.46
53.09
61.44
56.02
61.96
53.67
4.87
4.15
4.95
4.48
3.58
3.07
2.81
3.56
2.63
2.91
3.59
3.09
~
MCAL
PCAL
MTAL
regression equations used to estimate stature. The second sample (Sample 2) represented 20 individuals distributed equally by
race and sex and consisted of 19 calcaneusl
talus pairs and one unpaired calcaneus. The
purpose of Sample 2 was to serve as a control group to better gauge the accuracy of the
equations derived from Sample 1.
Statures for the individuals represented
by the Sample 1 and Sample 2 foot bones
were taken from the Hamann-Todd files
(see Todd and Lindala, 1928, for information
on how statures were recorded for this collection) and represent stature a t the time of
death. Previously, Dupertuis and Hadden
(1951) observed that the statures obtained
from the Hamann-Todd cadavers were
equivalent to living statures. Given the age
range of the specimens used, however, corrections for age-related stature changes
were made using the protocol outlined by
Giles (1991). Corrected statures range from
56.5-74.4 in. for Sample 1 and 59.2-73.2 in.
for Sample 2.
A second control sample (Sample 3) consists of 9 calcanei and 10 tali representing
10 American servicemen (mostly aircraft
crews) lost during World War I1 (n = 2), the
Vietnam War ( n = 6), and the Korean War
(n = 5) and subsequently identified at the
United States Army Central Identification
Laboratory, Hawaii (CILHI). Statures for
these individuals were taken from antemortem medical records on file at CILHI and
range from 66.0 to 73.5 in. (in cases where
two or more statures were recorded for the
same individual, either the mean or the
modal value was used). The ages at death for
this sample range from 20.0 to 41.0 years.
The purpose of Sample 3 was to further
gauge the accuracy of the formulas developed and t o provide some insight, albeit limited, into possible problems associated with
secular trends in stature.
Two measurements for each calcaneus
and one for each talus were taken t o the
nearest 0.10 mm using a vernier sliding caliper (Sample-l statistics are shown in Table
1). The Sample 2 specimens were measured
twice, over a 2-day period, to assess intraobserver error. The low intraobserver rates
(0.37-0.50%) attest to the simplicity of the
requisite measurements. The measurements are described below (see Fig. 1).
1. Maximum length of the calcaneus
(MCAL): maximum length of the calcaneus
as taken parallel to the long axis.
2. Posterior length of the calcaneus
(PCAL):maximum length between the most
anterior point of the posterior talar articular
surface and the most posterior point of the
calcaneus (on the tuberosity ignoring any
extensive exostoses).
3. Maximum length of the talus (MTAL):
maximum length between the most anterior
point of the head and the posterior tubercle.
Note that this measurement differs from the
more common measure of talar length in
that the posterior landmark is the posterior
tubercle rather than the sulcus for the flexor
hallucis longus muscle.
Simple and multiple linear-regression
equations were formulated using the SYSTAT statistical package [version 5.2.1 (Wilk-
STATURE FROM THE CALCANEUS AND TALUS
317
Fig. 1. Measurements of the calcaneus and talus utilized in this study. For discussionsee text.
erson et al., 1992)l on a Macintosh Classic I1
computer. (Curvilinear equations also were
formulated but failed to significantly improve predictive power.) Selected equations
and their corresponding standard errors are
listed in Table 2. Race- and sex-specific
equations that failed to estimate stature as
accurately as more general formulas using
the same measurement(s) are not presented
(eg., the formula derived for white male tali,
and not listed on Table 2, has a standard
error of 6.23 cm as compared to the standard
error of 6.07 cm for the comparable formula
derived for use on either white or black
males). To use the equations, the selected
measurement (in mm) is multiplied by the
appropriate coefficient and the product is
added to the corresponding constant. The resulting value is the estimated stature (in
cm). The equation with the lowest standard
error is always preferred.
RESULTS
As Table 2 shows, race- and sex-specific
formulas do not always provide the most accurate results nor the lowest standard errors. This may in fact suggest that the
lengths of the calcaneus and talus are linearly related to stature as opposed to the
allometric, racially and sexually proportional relations that seemingly characterize
long-bone length and body stature. In other
words, short bodies generally have short foot
bones and tall bodies generally have long
foot bones in somewhat disregard for the
mitigating influence of sex and race. Certainly the correlations between calcaneal
and talar length and stature seem to bear
this relation out (correlation coefficients for
MCAL,, PCAL, MTAL,, and stature are r =
.723, r = .817, and r = .731, respectively). In
fact, the efficacy of, and rationale behind,
population-generic stature-estimation formulas has been presented elsewhere (e.g.,
Sj~vold,1990) and is not a novel concept.
The standard errors for the formulas presented in Table 2 range from 4.13 to 6.25 cm
and are somewhat greater than the standard errors for formulas using intact long
bones. The widely used Trotter and Gleser
formulas for long bones of whites and blacks,
for example, range from 2.99 t o 5.05 cmabout 1.14 cm smaller on average than those
presented here. Certainly, the calcaneus or
talus should never be used when an intact
long bone is available. However, the formulas presented in Table 2 do compare favorably with some of the techniques commonly
318
T. D. HOLLAND
TABLE 2. Eauations for estimatinp stature (in em) from the calcaneus and talus
Rniiation
Standard
error ( k 1
Sample-2l
Accuracy %
1SE
2SE
White Male (mean age 48 years, SD 13 years)
80
100
5.55
80
100
5.75
Black Male (mean age 36 years, SD 17 years)
80
80
4.88
0.710(MCAL) + 118.30
4.81
60
100
1.283(PCAL) + 99.54
80
80
4.69
1.046(MTAL)+ 112.26
0.373(MCAL) + 0.790(PCAL) + 98.38
4.75
80
100
0.362(MCAL) + 0.707(MTAL) + 103.27
4.59
80
80
0.792(PCAL)+ 0.709(MTAL) + 85.28
4.38
80
80
White or Black Male (mean age 42 years, SD 17 years)
5.44
70
100
01.271(PCAL) + 98.47
80
100
6.07
1.045(MTAL)+ 109.66
5.33
90
100
1.039(PCAL) + 0.489(MTAL) + 82.14
White Female (mean age 48 years, SD 17 years)
5.46
100
100
1.159(MCAL)+ 74.59
4.15
40
60
1.932(PCAL) + 58.64
4.22
40
60
O.l41(MCAL)+ 1.785(PCAL)+ 55.87
0.974(MCAL) + O.GOO(MTAL) + 54.94
5.34
80
100
1.780(PCAL)+ 0.347(MTAL) + 47.29
4.13
60
60
Black Female (mean age 37 years, SD 16 years)
100
100
5.52
1.046(MTAL)+ 97.55
4.83
100
100
-0.519(MCAL) + 1.294(PCAL) +
0.556(MTAL) + 103.14
White or Black Female (mean age 42 years, SD 18 years)
0.854(MCAL) + 97.55
5.52
100
100
1.405(PCAL) + 87.27
4.72
70
100
0.951(MTAL) + 109.99
5.89
70
100
5.35
100
100
0.669(MCAL) + 0.543(MTAL) + 81.76
1.275(PCAL)+ 0.252(MTAL) + 80.37
4.72
70
100
White (Sex Unknown) (mean age 48 years, SD 16 years)
1.078(MCAL)+ 82.00
5.81
70
100
1.552(PCAL) + 79.57
5.11
70
90
0.309(MCAL) + 1.220(PCAL) + 73.94
5.06
70
90
0.781(MCAL)+ 0.597(MTAL) + 70.82
5.63
70
100
Black (Sex Unknown) (mean age 37 years, SD 17 years)
90
5.23
70
1.500(MTAL)+ 82.97
0.292(MCAL) + 1.248(MTAL)+ 74.35
5.17
80
90
o.agi(Pcm) + 0 . 8 2 5 ~ +~71.44
~ ~ ~ )
4.66
90
90
White or Black (Sex Unknown) (mean age 42 years, SD 17 years)
1.150(MCAL) + 77.37
6.25
80
100
70
95
1.617(PCAL) + 76.91
5.22
1.411(MTAL) + 85.95
75
100
6.18
O.lGO(MCAL) + 1.448(PCAL)+ 73.84
5.22
70
95
90
100
0.644(MCAL) + 0.836(MTAL) + 68.56
5.69
70
100
1.230(PCAL) + 0.495(MTAL) + 69.89
5.02
1.003(PCAL) + 112.42
0.674(MCAL) + 116.24
Sample-3'
Accuracy %
1SE
2SE
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
86
80
86
100
100
100
83
67
83
80
100
100
100
100
100
100
100
100
100
100
100
75
91
63
86
71
100
100
100
100
100
100
'Percentage of applicable Sample-2 individuals whose estimated stature falls within one standard error USE) and two standard errors (2SE).
Percentage of applicable Sample-3 individuals whose estimated stature falls within one standard error (1SE)and two standard errors (2SE).
employed in cases where no intact long
bones are present; the Simmons et al. (1990)
and Steele (1970) formulas for incomplete
long bones range from 5.47 to 7.16 cm and
3.99 t o 7.06 cm, respectively, while the Byers et al. (1989) equations for metatarsals
range from 3.99 to 7.60 cm, and the Meadows and Jantz (1992) metacarpal equations
range from 5.10 to 5.67 cm.
Analysis of residuals reveals an overall
random pattern of values. There is a slight
tendency to underestimate taller statures
(>180 cm) and overestimate shorter statures (<160 cm), though both trends are
rather weak. Furthermore, the results obtained for the two control samples suggest
that the formulas presented in Table 2 provide reasonably accurate results when
STATURE FROM THE CALCANEUS AND TALUS
applied to bones not directly involved in the
creation of the regression models, i.e., they
can be used on independent samples. For
the most part, Sample 2 was accurately estimated (defined as an estimate within one
standard error of the known stature) approximately 70-100% of the time. Some of
the equations applicable to white females
had the lowest accuracy rates due to the inclusion of what appear to be two statistical
outliers (one female with unusually large
and one female with unusually small foot
bones for their statures) within the randomly selected sample of five individuals.
The results obtained for Sample 3 are particularly encouraging, however, since the biological and socioeconomic profiles of this
group no doubt differ markedly from that of
the Hamann-Todd dissection-room population. In addition, the accuracy (generally
70-100%) with which the Sample-3 statures
were estimated suggests that the calcaneus
and talus may not be as affected as the long
bones by recent secular increases in stature.
CONCLUSIONS
The calcaneus and talus are solid, relatively compact elements that commonly are
recovered in contexts where intact long
bones may not be, and the measurements of
these elements needed to estimate stature
are simply and reliably obtained. While any
set of formulas derived from an early twentieth-century dissection-room population will
suffer from some degree of population specificity, the equations presented in Table 2
would appear to have some utility in providing stature estimates in cases where other
methods are not applicable. Unfortunately,
the technique presently is restricted to use
on whites and blacks, as its applicability to
mongoloid remains is undocumented. Certainly, common sense should be exercised in
determining when, where, and under what
circumstances to employ these equations.
ACKNOWLEDGMENTS
The measurements used in this study
were obtained by William Mayhew, who declined to be listed as a coauthor, but whose
contribution was no less essential. I thank
the Cleveland Museum of Natural History,
319
in particular Bruce Latimer and his staff, for
allowing us access to the Hamann-Todd
Collection. I also thank Bruce Anderson,
William Grant, Kim Schneider Kimminau,
Robert Mann, William Maples, and Ted
Rathbun for reading and commenting on
early drafts of the manuscript. The assertions contained in this work are those of the
author and should not be construed to represent those of the United States Army or the
Department of Defense.
LITERATURE CITED
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Phys. Anthropol. 79:27%279.
Dupertuis CW, and Hadden JA, J r (1951) On the reconstruction of stature from long bones. Am. J. Phys.
Anthropol. 9:15-53.
Genoves S (1967)Proportionality of long bones and their
relation to stature among Mesoamericans. Am. J .
Phys. Anthropol. 26:67-78.
Giles E (1991) Corrections for age in estimating older
adults’ stature from long bones. J . Forensic Sci. 36:
898-901.
Holland TD (1992) Estimation of adult stature from
fragmentary tibias. J. Forensic Sci. 37:1223-1229.
Meadows L, and Jantz RL (1992) Estimation of stature
from metacarpal lengths. J. Forensic Sci. 37:147-154.
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Pickering RB (1986) Population differences in the calcan e w as determined by discriminant function analysis. In KJ Reichs (ed.): Forensic Osteology. Springfield, IL: CC Thomas, pp. 160-170.
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320
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Trotter M, and Gleser GC (1951)The effect of aging on
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