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Determination of adult stature from metatarsal length.

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AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 79:275-279 (1989)
Determination of Adult Stature From Metatarsal Length
STEVE BYERS, KAORU AKOSHIMA, AND BRYAN CURRAN
Department of Anthropology, University of New Mexico,
Albuquerque, New Mexico 87131
KEY WORDS
Stature, Metatarsals, Regression
ABSTRACT
The results of a study to determine the value of foot bones in
reconstructing stature are presented. The data consist of length measurements
taken on all ten metatarsals as well as on cadaver length from a sample of 130
adults of documented race, sex, stature, and, in most cases, age. Significant
correlation coefficients (.58-.89) are shown between known stature and foot
bone lengths. Simple and multiple regression equations computed from the
length of each of these bones result in standard errors of estimated stature
ranging from 40-76 mm. These errors are larger than those for stature calculated from complete long bones, but are approximately the same magnitude for
stature calculated from metacarpals and fragmentary long bones. Given that
metatarsals are more likely to be preserved unbroken than are long bones and
given the ease with which they are accurately measured, the formulae presented here should prove useful in the study of historic and even prehistoric
populations.
The determination of adult living height is
an important part of the evaluation of skeletal remains, including those of early hominids, recent prehistoric populations, and modern forensic cases. The calculation of stature
usually involves measurements of complete
long bones, a process well known through the
work of Manouvrier (1893), Pearson (1899),
Stevenson (1929), Dupertius and Hadden
(1951), Trotter and Gleser (1952, 1958), Fully
and Pineau (1960),and others. However, various studies also have indicated that dimensions of vertebrae (Dwight, 1894), metacarpals (Musgrave and Harneja, 1978),clavicles
(Jit and Singh, 1956), scapulae (Olivier and
Pineau, 1957), incomplete long bones (Steele
and McKern, 1969; Steele, 1970), and more
recently, even footprints (Robbins, 1985;Giles
and Vallandigham, 1987), provide stature
estimations with varying degrees of accuracy. However, the use of foot bones to predict
living height has not been examined. Therefore, it is the purpose of this study to determine if metatarsals give useful estimates of
adult stature.
MATERIALS AND METHODS
The sample for this study consists of 130
macerated and dried skeletons; 66 from the
Terry Collection at the Smithsonian Institu-
@ 1989 ALAN R. LISS, INC.
tion and 64 from skeletons housed a t the
University of New Mexico’s Maxwell Museum
of Anthropology. Demographic information
(age, sex, and race) is documented on the
majority of these skeletons; however, the
ages of 11 individuals from the Maxwell
Museum collection are not known and had to
be determined by the authors using standard
techniques. Stature is recorded on hanging
cadavers of the Terry Collection (Trotter and
Gleser, 1952),while supine stature is recorded
for cadavers of the Maxwell Museum collection. There are 108Euro-Americans (57 males,
51 females) and 22 Afro-Americans (13males
and nine females) in all.
Grossly normal metatarsals were measured
from both sides of the skeleton. Length was
taken to the nearest 0.1 mm from the apex of
the capitulum to the midpoint of the articular
surface of the base parallel to the longitudinal axis of the bone. This measurement corresponds to Mt 1-4 of Martin and Saller
(1957) for the first four metatarsals. In some
instances, the shaft curved markedly in a
dorsal-plantar direction, in which case the
base and proximal shaft were taken to be the
longitudinal axis. For metatarsal V, measurements included both functional and
Rereived March 16, 1988: revision accepted J u l y 20, 1988.
276
S. BYERS ET AL.
morphological lengths, with the medial surface of the bone determining the long axis.
For the “functional” length, the proximal
point was the dorsoplantar midpoint of the
intersection between the fourth metatarsal
and cuboid facets. This corresponds to Mt 5
of Martin and Saller (1957). The morphological length was measured to the tip of the
tuberosity.
Two corrections to living stature have been
applied. First, as discussed by Trotter and
Gleser (1951),maximum stature is attained in
humans at around 21 years of age and
decreases after age 30 years a t a n average
rate of .06 cm per year, irrespective of race
or sex. Given this situation, we added .6 (age
- 30) mm to the stature of individuals over 30
years of age so that all analyses are based on
estimated maximum height attained during
life. The second correction accounts for the
differences between hanging cadaver stature
and living height. Trotter and Gleser (1952)
and Trotter (1970) indicate that for the Terry
Collection, the average stature of hanging
cadavers is 2.5 cm greater than is living
height. Dupertius and Hadden (1951) conclude that any difference between living
stature and supine cadaver length is insufficient to warrant special consideration. Therefore, we substracted 25 mm from the stature of
the individuals from the Terry Collection,
whereas those from the Maxwell Museum
whose stature was actually supine length
remained unchanged.
After applying the stature corrections, the
following calculations were performed. First,
descriptive statistics were calculated for the
measurements as a way of noticing deviations from the normal distribution since
nonnormality can affect the validity of further computations. Second, Pearson’s Product Moment Correlation Coefficient (r) was
calculated between each metatarsal and stature. Third, plots of metatarsal measurements
against stature were examined using the
technique of Draper and Smith (1966) to
determine if the relationship between the
measures is linear. Fourth, simple linear
regression equations were calculated so that
stature could be predicted from metatarsal
measurements. Last, multiple regression
analysis was performed to determine if better
estimates of stature could be generated by
using two or more metatarsal lengths. (Model
I regression was used in these latter computations because it provides smaller errors of
estimate than does Model 11.) For the above
calculations, all data first were combined and
then broken down into six biological groups:
all males, all females, Euro-American males,
Euro-American females, Afro-American
males, and Afro-American females. Division
into the groups is justified because previous
work (Trotter and Glesser, 1952,1958; Dupertius and Hadden, 1951; Genoves, 1967; Stevenson, 1929) indicate that the relationship
between long bone lengths and stature differ
by sex and race.
Since the data of this study are composed
of measurements from both sides of the same
individuals, this factor had to be taken into
account during analysis. I n this same situation, Trotter and Gleser (1952) use a n average
of the right and left long bones in their
regression formulae, Musgrave and Harneja
(1978) calculate separate formulae for each
side in their study of metacarpals, and Dupertius and Hadden (1951) use only right-side
long bones in their analyses. Since a consensus on how to handle sides does not exist in
the literature, we use a n average of right and
left bones.
RESULTS
Euro-Americans constitute 82.7% of the
sample, while Afro-Americans represent
17.3%;both groups are evenly divided between
the sexes. The results of the calculation of
descriptive statistics indicate that there are
significant deviations (at the .05 level) from
the normal distribution for one of the female
measurements. Since there is a 92% probability of performing a type I error given the
number of tests for skewness and kurtosis,
these deviations are considered chance anomalies and their effect on further analyses have
been disregarded.
All metatarsal lengths are significantly
correlated with stature in each biological
group. Fairly strong relationships between
the metatarsal measurements and stature
are indicated by coefficients generally exceeding .60 (see Table 1). Simple linear
regression formulae are presented in Table 1
for combined data and the six biological
groups. Notice that the standard error of the
second and third metatarsals in the formulae for all males and Euro-American males
is larger t h a n the errors for the combined
data. This is due t o a chance aberration in
our sample, which, in all probability, would
disappear if more metatarsal data were collected. Also using the techniques of Neter
and Waserman (1974), the slopes of the for-
277
STATURE AN11 METATARSAL LENGTH
TABLE 1. Simple linear regression of stature calculated from metatarsal measurements (all measurements in mm)
Metatarsal/group
First
Combined data
All males
All females
Euro-American males
Euro-American females
Afro-American males
Afro-American females
Second
Combined da ta
All males
All females
Euro-American males
Euro-American females
Afro-American males
Afro-American females
Third
Combined d a t a
All males
All females
Euro-American males
Euro-American females
Afro-American males
Afro-American females
Fourth
Combined data
All males
All females
Euro-American males
Euro-American females
Afro-American males
Afro-American females
Fifth (functional)
Combined da ta
All males
All females
Euro-American males
Euro-American females
Afro-American males
Afro-American females
Fifth (total)
Combined da ta
All males
All females
Euro-American males
Euro-American females
Afro-American males
Afro-American females
Formula
St = 634 + 16.8 (Metl)
S t = 815 14.3 (Metl)
S t = 783 13.9 (Metl)
S t = 768 15.2 (Metl)
St = 656 16.3 (Metl)
S t = 556 17.6 (Metl)
S t = 796 12.8 (Metl)
+
+
+
+
+
+
S t = 675 + 13.4 (Met2)
S t = 873 + 11.1 (Met2)
St = 791 + 11.5 (Met2)
S t = 868 + 11.3 (Met2)
St = 712
St = 605
St = 783
+ 12.8 (Met2)
+ 14.0 (Met2)
+ 10.9 (Met2)
St = 720 + 13.6 (Met3)
S t = 909 + 11.2 (Met3)
St = 836 + 11.6 (Met3)
S t = 862 + 12.0 (Met3)
St = 732 + 13.3(Met3)
S t = 706 + 13.3 (Met3)
St = 904 + 9.9 (Met3)
S t = 715 + 14.0 (Met4)
S t = 910 + 11.6 (Met4)
S t = 835 + 11.9 (Met4)
S t = 863 + 12.3 (Met4)
St = 719 + 13.8 (Met4)
S t = 759 + 13.0 (Met4)
St = 961 + 9.3 (Met4)
St = 782 + 14.7 (Met5m
St = 989 + 11.8 (Met5F)
S t = 953 + 11.3 (Met5m
St = 938 + 12.8 (Met5F)
S t = 900 + 12.3 (Met5F)
St = 761 + 14.7 (Met5F)
St = 979 + 10.2 (Met5F)
St = 768 + 12.8 (Met5)
S t = 952 + 10.6 (Met5)
S t = 922 + 10.2 (Met5)
St = 912 + 11.2 (Met5)
S t = 905 + 10.6 (Met5)
S t = 846 + 11.5 (Met5)
St = 891 + 10.2 (Met5)
mulae for all males, all females, EuroAmerican males, Euro-American females,
Afro-American males, and Afro-American
females are different (at the .05 level and
beyond) whereas intercepts are not. Therefore, it should be assumed that the lines
representing the relationship between stature and metatarsal lengths differ for the
sexes and races.
Table 2 presents multiple regression formulae for stature against all five metatarsal
measurements. The level for inclusion of a n
independent variable is a calculated F-value
Standard
error
No.
r
130
70
.79
.72
.71
.72
.79
.87
.70
65.4
64.2
56.1
63.2
49.6
I
.78
.66
.73
.63
.77
.86
.83
65.4
69.8
54.8
70.1
52.0
56.8
39.9
128
69
57
57
48
10
7
.76
.66
67
.65
.71
.89
.78
67.6
68.1
59.7
68.9
57.5
42.2
44.9
126
68
56
57
47
9
7
.76
.67
.67
.65
.72
.88
.76
68.5
68.0
59.9
68.5
57.5
46.5
46.5
128
68
58
57
49
9
7
.69
.59
.61
.60
.72
.75
76.0
73.8
63.3
72.2
63.3
68.0
47.4
.73
.63
.61
.63
60
.76
.78
71.2
70.9
63.6
70.3
64.9
64.2
45.2
58
57
49
11
7
129
69
58
57
49
10
128
68
58
57
49
9
7
63
51.0
50.8
with a probability less than or equal to .05;
the residual plots indicate t h a t the relationship between independent a n d dependent
variables is linear. Only metatarsals 2 and 4
provide a significant contribution to the
accuracy of calculated stature when included
with metatarsal 1. Finally, there are no formulae for all females, Euro-American males,
Afro-American males, and Afro-American
females. This is because the inclusion of
other metatarsal measurements in the formulae for stature predicted by second metatarsal in all females, and stature predicted
278
S. BYERS ET AL.
TABLE 2. Multiple regression formulae for stature from metatarsal measurements (all measurements in mm)
Group
Standard
error
Formulae
Combined da ta
All males
Euro-American females
St = 573
S t = 737
S t = 558
+ 10.9 (Metl) + 6.3 (Met4)
+ 10.4 (Metl) + 4.6 (Metl)
+ 9.1 (Metl) + 7.4 (Met2)
by first metatarsal in Euro-American males,
does not reduce the predictor error significantly. Multiple regression formulae are not
computed for the Afro-Americans because
the number of independent variables too
closely approximates the number of data
points.
DISCUSSION
The standard errors for the simple linear
regressions between various bones and stature are presented in Table 3. Notice that
those for metatarsals are not as small as
those for long bones; however, they are of the
same order of magnitude a s those for fragmentary long bones and metacarpals. Considering the small amount of error involved
in measuring and the greater probability of
being perserved unbroken, metatarsals along
with metacarpals should provide the most
easily attained and accurate estimates of
stature when long bones are absent or fragmentary.
The standard errors listed in Tables 1 and
2 indicate that the best estimates of stature
are obtainable from the multiple regression
equations, followed (generally) by the simple linear regression equations for metatarsals 1, 2, 3, 4, 5, and 5 (functional), respectively. If the first and fourth or first and
second metatarsals are available, the multiple regression equations provide the best
stature estimates. If any of these bones are
absent, the appropriate formula from Table
1 with the lowest standard error should be
used. It is not recommended that the results
for different formulae be averaged since this
treats all equations as though they are
equally accurate (the standard errors indicate that they are not). If sex is known, the
formulae for the identified sex should be
used since these will provide statures with
lower error estimates. Similarly, if it is
known or caq be inferred, the proper biological group formula should be used to produce
estimates w3h even lower errors.
Two modifications to calculated stature
deserve consideration. First, since the formulae of this study are based on greatest
61.8
61.3
48.4
TABLE 3. Standard errors (in em) of simple linear
regression equations for stature calculated from
various bones
Bone'
Complete
Humerus
Radius
IJlna
Femur
Tibia
Fibula
Fragmentary
Humerus
Femur
Tibia
Metatarsal
1
2
3
4
5 (functional)
5 (total)
Metacarpal
1
2
3
4
5
Euro-American
Afro-American
Male
Female
Male
Female
4.1
4.3
4.3
3.3
3.3
3.3
4.5
4.2
4.3
3.7
3.7
3.6
4.4
4.3
4.4
3.9
3.8
4.1
4.3
4.6
4.8
3.4
3.7
3.8
4.8-5.3
3.9-4.4
4.2-5.5
5.1-5.4
4.8-4.9
4.7-5.7
4.6-5.0
3.7-3.7
3.9-4.5
4.8-4.9
5.8-6.2
4.5-5.0
6.3
7.0
6.9
6.9
7.2
7.0
5.0
5.2
5.7
5.8
6.3
6.5
5.1
5.7
4.2
4.7
6.8
6.4
5.1
4.0
4.5
4.7
4.7
4.5
5.5-5.8
5.8-5.8
5.8-6.0
5.8-6.0
6.3-6.3
7.2-5.5
5.6-4.7
6.6-4.7
7.6-5.0
8.3-4.7
-
-
-
-
-
-
'Data for complete long bones from Trotter and Gleser (1952);
range of standard errors for incomplete long bones from Steele
(1970); right and left metacarpal standard errors from Musgrave
and Harneja (1978).
height attained in life, calculated stature
should be adjusted for age (if possible) by
subtracting the factor that we added [i.e.,
(age - 30) X 61. Second, Trotter and Gleser
(1952) discuss the differences between dry
and wet bone lengths. They conclude that
long bones may shrink a s much as 2 mm
during drying. This shrinkage causes a calculated stature difference of 4-8 mm. Since
long bones are known to shrink with drying,
it is logical to assume that metatarsals
would shrink in proportion to their size and
that this proportional shrinkage would affect
calculated stature to approximatelythe same
degree a s it does long bone shrinkage. This
should be considered when reconstructed
heights are reported. It is important to note
t h a t the bias introduced by age and shrink-
STATURE AND METATARSAL LENGTH
age is always smaller t h a n the standard
error of the formulae; however, by considering their effect, a beneficial increase in
accuracy might be obtained.
CONCLUSIONS
Regression formulae of stature on metatarsal lengths are calculated from the average of
the left and right metatarsals of 130 EuroAmericans and Afro-Americans of both sexes.
The majority of Pearson’s Product Moment
Correlation Coefficients for the relationship
between the foot bones and height range
from .58 to .79. The errors of estimating
stature from metatarsals are greater than
those of estimates of stature from long bones;
however, they are approximately the same
size as those for fragmentary long bones and
metacarpals. Given this situation, the equations from this study should prove to be useful for calculating stature from fragmentary
human remains of historic or prehistoric
origin.
ACKNOWLEDGMENTS
The authors thank the Smithsonian Institution and the Maxwell Museum a t the University of New Mexico for allowing access to
their skeletal collections. Stan Rhine, Erik
Trinkaus, and Jeff Long also are thanked for
their review and comments of earlier versions
of this paper. The authors accept full responsibility for any errors or omissions in this
text.
LITERATURE CITED
Draper NR, and Smith H (1966) Applied Regression Analysis. New York: John Wiley & Sons, Inc.
Dupertius CW, and Hadden J A (1951) On the reconstruction of stature from long bones. Am. J. Phys. Anthropol.
9:15-54.
Dwight T (1894) Methods of estimating the height from
parts of the skeleton. Med. Res. Rev. 46.293-296.
Fully G, and Pineau H (1960) Determination de la stature
au moyen du squette. Ann. Med. Leg. 40:145-154.
279
Genoves S (1967) Proportionality of the long bones and
their relation to stature among Mesoamericans. Am. J .
Phys. Anthropol. 26:67-78.
Giles E, and Vallandigham P (1987) Error estimates in
calculating stature from foot and shoe lengths (abstract).
J. Can. SOC.Forensic Sci. 20(3):172.
Jit I, and Singh S (1956)Estimation of stature from clavicles. Indian J . Med. Res. 44:137-155.
Manouvrier L (1893) La determination de la taille d’apres
les grandes 0s des membres. Mem. Sac. Anthropol.
(Pans) 4:347-402.
Martin R, and Saller K (1957) Lehrbuch der Anthropolopie, 3rd Ed. Stuttgart: Gustav Fischer.
Musgrave JH, and Harneja NK (1978) The estimation of
adult stature from metacarpal bone length. Am. J . Phys.
Anthropol. 48:113-120.
Neter J, and Wasserman W (1974) Applied linear statistical models. Homewood, IL: Richard D. Irwin, Inc.
Olivier G, and Pineau H. (1957) Biometrie du scapulum;
Asymetrie, correlations et differences sexuelles. Arch.
Anat. (Pans) 3357-88.
Pearson K (1899) Mathematical contributions to the theory of evolution. V. On the reconstruction of stature of
prehistoric races. Philos. Trans. R. Sac. Land. 192:
169-244.
Robbins L (1985) Footprints: Collecton, Analysis and
Interpretation. Springfield, I L Charles C. Thomas.
Snedecor GW, and Cochran WG (1967) Statistical Methods.
Ames, IA: The Iowa State University Press.
Steele DG (1970) Estimates of stature from fragments of
long bones. In T Stewart (ed): Personal Identification in
Mass Disasters. Washington, DC: National Museum of
Natural History, pp. 85-97.
Steele DG, and McKern TW (1969) A method for assessment of maximum long bone length and living stature
from fragmentary long bones. Am. J . Phys. Anthropol.
31:215-227.
Stevenson PH (1929) On racial differences in stature long
bone regression formulae, with special reference to
stature reconstruction formulae for the Chinese. Biometrika 21:303-321.
Trotter M (1970) Estimation of stature from intact long
bones. In T Stewart (ed):Personal Identificationof Mass
Disasters. Washington, DC: National Museum of Natural History, pp. 71-83.
Trotter M, and Gleser G (1951) The effect of ageing on
stature. Am. J . Phys. Anthropol. 9:311-324.
Trotter M, and Gleser G (1952) Estimation of stature from
long bones of American whites and Negroes. Am. J.
Phys. Anthropol. 10:463-514.
Trotter M, and Gleser G (1958) A re-evaluation of estimation of stature based on measurements of stature taken
during life and of long bones after death. Am. J. Phys.
Anthropol. 16:79-123.
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