close

Вход

Забыли?

вход по аккаунту

?

Estimating the length of incomplete long bones Forensic standards from Guatemala.

код для вставкиСкачать
AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 120:233–251 (2003)
Estimating the Length of Incomplete Long Bones:
Forensic Standards From Guatemala
Lori E. Wright1* and Mario A. Vásquez2
1
2
Department of Anthropology, Texas A&M University, College Station, Texas 77843-4352
Escuela de Historia, Universidad de San Carlos de Guatemala, Guatemala City, Guatemala
KEY WORDS
forensic anthropology; stature; long bone fragments; regression; Maya
ABSTRACT
We report on new standards for estimating long bone length from incomplete bones for use in
forensic and archaeological contexts in Central America.
The measurements we use closely follow those defined by
Steele ([1970] Personal Identification in Mass Disasters;
Washington, DC: Smithsonian Institution), but we add
several new landmarks. We measured the femur, humerus, tibia, and fibula of 100 Maya skeletons (68 males,
32 females) recovered from forensic exhumations. We derived the equations by regressing bone segment length on
bone length, and solved for bone length to maximize the
utility of the equations for taller populations. We generated equations for all segments that were significantly
correlated with bone length for males, for females, and for
both sexes combined, but accepted only regressions with
The estimation of standing stature during life is a
key goal in the forensic analysis of human skeletal
material, because height is a straightforward biological characteristic that may aid the investigator in
deducing the identity of a skeleton. Likewise, for
archaeological materials, stature provides an important means to address health and adaptation in the
past, as it is a sensitive measure of the growth
status of a population. Hence, the development of
techniques for estimating stature from skeletal remains has been a core focus of both forensic anthropology and bioarchaeology since their inception. In
both fields, stature estimation is often problematic
because of deterioration of the long bones during
burial. Methods to circumvent this problem by estimating stature from fragmentary bones have been
devised by several researchers. Prominent among
these are the equations developed by Steele (1970);
(also Steele and McKern, 1969) to estimate bone
length for the fragmentary humerus, femur, and
tibia. Criticisms of the method have focused on difficulty in identifying landmarks used in the equations, and on the possibility that the regressions
may be population-specific.
In this paper, we revisit Steele’s approach (1970)
to long bone length estimation. We explore the issue
of population specificity of bone segment proportions
in greater detail. As with variation in limb bone
proportions, interpopulation variation in the propor©
2003 WILEY-LISS, INC.
r2 ⬎ 0.85 as reliable. Landmarks defined by muscle attachment sites were more variable in location than landmarks on articular architecture; thus we retained few
equations that use these landmarks. We tested the male
and combined sex equations on 36 males of unknown
ethnicity exhumed from a military base in Guatemala,
and found that the equations performed satisfactorily. We
also evaluated the performance of equations by Steele
([1970] Personal Identification in Mass Disasters; Washington, DC: Smithsonian Institution) and Jacobs ([1992]
Am J Phys Anthropol 89:333–345) on the Maya bones, and
conclude that significant population variation in long bone
proportions hinders their application in Central America.
Am J Phys Anthropol 120:233–251, 2003.
©
2003 Wiley-Liss, Inc.
tions of long bone segments (or conversely, in the
relative locations of bony landmarks on the bone)
may be due to a diversity of factors, including aspects of genetic, climatic, and nutritional environments. However, the position of long bone landmarks may also be determined by functional
stresses on the limb (Jacobs, 1992). Do landmark
positions scale allometrically with bone length? Or
are functional environments and activity patterns
more significant? Here, we develop regression equations to estimate bone length for forensic Maya skeletons from Guatemala. Because of the extremely
small stature of Maya populations, we reasoned that
the proportions of long bone segments might vary
substantially from published values, as a function of
size alone. In addition to providing standards appropriate to this population, we use the Maya data to
Grant sponsor: Office of the Vice President for Research and Graduate Studies, Texas A&M University.
*Correspondence to: Lori E. Wright, Department of Anthropology,
Texas A&M University, College Station, TX 77843-4352.
E-mail: lwright@tamu.edu
Received 26 June 2001; accepted 18 February 2002.
DOI 10.1002/ajpa.10119
Published online in Wiley InterScience (www.interscience.wiley.
com).
234
L.E. WRIGHT AND M.A. VÁSQUEZ
examine the nature of interpopulation variation in
bone segment proportions.
STATURE ESTIMATION FROM FRAGMENTARY
LONG BONES
The estimation of bone length from incomplete
long bones was pioneered by Müller (1935), who
generated equations for the humerus, radius, and
tibia from measurements of the skeletal collections
of the Österreiches Beinhaus in Zellerndorf. Müller
(1935) defined 5 segments for the humerus, 4 for the
radius, and 7 for the tibia, using the margins of
articular surfaces and key points of muscle attachment to define the segments. She calculated the
percentage of total length represented by each section, and used this value to estimate the length of
fragmentary material.
Working with Mississippian archaeological material from northeast Arkansas (Steele and McKern,
1969; Steele and Bramblett, 1988) and with skeletons of American Blacks and whites from the Smithsonian’s Terry Collection (Steele, 1970), Steele generated a series of sex- and population-specific
equations for the humerus, femur, and tibia. He
defined landmarks to delimit 4 segments on the
humerus, 4 on the femur, and 5 on the tibia, in part
following the landmarks used by Müller (1935). For
each segment, he generated a regression equation to
estimate bone length. He also calculated multiple
regression formulae to estimate bone length using a
combination of segments, and provided equations
that relate segment length directly to stature, to
reduce the large standard error that would pertain
after applying a stature regression formula to estimated bone length. Standard errors of the formulae
for estimated bone length on the reference population are smaller for the multiple regressions than for
individual segment equations, and span 0.20 –2.93
cm. Stature estimates using Steele’s regressions
have standard errors of 3.71– 6.17 cm.
Critiques of the method of Steele (1970) have primarily focused on the difficulty that some osteologists have had in locating several of the landmarks
that define the bone segments (Brooks et al., 1990;
Holland, 1992; Simmons et al., 1990). In a survey of
members of the American Academy of Forensic Sciences, Brooks et al. (1990) found that 55% (6 of 11) of
respondents who had applied the formulae to remains for which they had an independent estimate
of stature found that Steele’s formulae (1970) did
indeed estimate stature accurately. They also underscored the problematic nature of stature data
obtained from documentary and cadaveral sources,
to which skeletal estimates are routinely compared.
Errors in these “known” data undoubtedly contribute to perceptions that skeletal stature estimates
are inaccurate.
Two studies proposed stature estimation standards that utilize transverse measurements taken
on long bones. Simmons et al. (1990) used standard
osteometric measurements of the femoral condyles,
neck, and head to estimate stature. Using skeletons
from the Terry Collection, they found reasonably
strong correlations between these measures and
long bone length (r ⫽ 0.22– 0.68). Similarly, Holland
(1992) used the biarticular breadth of the proximal
tibia to generate a stature regression equation for
skeletons from the Hamann-Todd Collection at the
Cleveland Museum of Natural History. Although
both of these approaches obtained statistically significant correlations between the transverse measurements and maximum bone length on the reference populations from which they were developed,
they may find less application than the longitudinal
measurement approach of Steele (1970). The transverse measurement methods emphasize parts of
bones (epiphyses and metaphyses) that are least
often preserved in forensic and archaeological contexts; their utility will be greatest for recent forensic
cases. Moreover, transverse measures vary substantially among populations, together with the degree
of sexual dimorphism. Such transverse measurement approaches are in no real sense a “revision” of
Steele’s method (1970) (contra Simmons et al.,
1990), but should be seen as complementary approaches to bone length estimation.
Steele (1970) had generated regression equations
independently for several populations because he
reasoned that bone segment proportions might differ among populations, much as total bone proportions do. In applying the equations to complete femora and tibiae of Mesolithic and Neolithic European
skeletons, Jacobs (1992) demonstrated interpopulation variation in the proportions of long bone segments. He observed that some of the equations of
Steele (1970) tended to overestimate bone length,
while others underestimated length significantly,
and he concluded that bone length could not be
accurately estimated for these skeletons using these
equations. However, he demonstrated that segment
lengths did show significant correlations with bone
length in this population, and he generated population-specific equations, thus confirming the utility of
Steele’s approach. Jacobs (1992) showed that the
poor performance of the femur equations of Steele
(1970) on the European sample was primarily due to
differences in the proportions of segments 2 and 3,
which are separated by a landmark defined by the
divergence of the medial and lateral supracondylar
lines from the linea aspera. Similarly, he observed a
different proportion of tibial segments 1 and 2,
which are divided by the landmark defined by the
proximal margin of the tibial tuberosity. He suggested that population differences in muscular activity would explain these differences in proportion,
and recommended that researchers search out samples with diverse behavioral characteristics and
adaptive strategies in order to generate regression
equations that might be more appropriate analogues
for both forensic and bioarchaeological applications
(Jacobs, 1992).
235
ESTIMATING LENGTH OF INCOMPLETE LONG BONES
TABLE 1. Mean stature for males and females in the Guatemalan forensic remains, and in comparative series
used for estimation of long bone length and stature
Male stature
Female stature
Skeletal series or
reference sample
Source
Mean (cm)
SD (cm)
N
Mean (cm)
SD (cm)
N
Forensic, Mayan1
Forensic, El Chal1
Mexican cadavers
Terry Collection, White
Terry Collection, Black
Mississippian1
This study
This study
Genovés, 1967
Steele, 1970
Steele, 1970
Steele and McKern, 1969
158.25
160.78
163.99
168.44
172.02
165.35
4.48
4.05
5.11
8.11
7.84
—
66
33
22
61
42
72
147.29
5.45
32
152.30
157.62
159.88
154.75
6.71
7.96
6.22
—
15
52
57
29
1
2
Stature is calculated from the measured maximum length of the femur, using the femur equation of Genovés (1967).
Unreported.
Although he confirmed the success of Steele’s
methodological approach, Jacobs (1992) demonstrated that the standards of (Steele, 1970) may not
accurately estimate bone length for all skeletal populations. This is likely to be especially true for populations that diverge significantly in completed
adult stature or body proportions from reference
populations of Steele’s. In both our forensic and bioarchaeological research in Guatemala, we are seldom able to estimate stature from intact bones due
to the rapid deterioration of bone in this tropical
environment, and due to other perimortem and postdepositional factors. We began our investigation
with the suspicion that the existing standards would
not be appropriate for Maya skeletal remains because of the extremely diminutive stature of Maya
populations. Twentieth century Maya populations
in Guatemala and Mexico experience marked stunting of stature due to nutritional insufficiency during
the period of childhood growth (Bogin and MacVean,
1984; Danforth, 1994; Furbee et al., 1988; Martorell,
1995; Martorell et al., 1994; McCullough, 1982). Table 1 illustrates that the forensic Maya skeletons
from Guatemala used in this study fall about 10 cm
short of the average stature of the skeletal series
from which Steele (1970) generated his regression
equations. Maya skeletal remains are also very
slight; established standards for sex estimation from
bone dimensions typically misclassify many males
as females. Therefore, most bioarchaeologists working on Maya remains have generated series-specific
discriminant functions for metric sex estimation
(Whittington, 1989; Wright, 1994). Both the stature
and robusticity of Maya skeletons raise the question
of whether Steele’s formulae would work on Maya
remains.
We report on new regression equations derived
from measurements of forensic skeletons from Guatemala. The skeletons were exhumed as part of the
ongoing process of reconciliation following Guatemala’s long civil war, which spanned the 1954 CIAsponsored coup d’etat to a final peace agreement
signed in 1996. Many of the remains that have been
the subject of forensic investigation derive from a
period of brutal “scorched earth campaigns” carried
out by the military between 1982–1984 (Arzobispado de Guatemala, 1998; Carmack, 1988; Equipo
de Antropologı́a Forense de Guatemala, 1997). Al-
though interments have also been recovered from
military bases and other contexts, most of the civilian victims of the conflict were rural subsistence
farmers of Maya descent and had been hastily interred in small “clandestine” cemeteries in remote
areas of the Guatemalan highlands. To investigate
the applicability of Steele’s approach to estimating
bone length from long bone segments, we generate
regression equations from measurements of these
forensic Maya remains. We test the regressions on
an independent forensic sample, and also evaluate
the accuracy of the regression equations of Steele
(1970; also Steele and Bramblett, 1988) and Jacobs
(1992) on forensic Maya remains.
MATERIALS AND METHODS
The skeletal remains used for this study are
treated as two separate samples. The largest sample, hereafter referred to as the “forensic Maya sample,” consists of some 100 human skeletons of rural
highland Maya villagers. We use this skeletal sample to generate regression equations to estimate long
bone length. The forensic Maya sample comprises 76
skeletons recovered by exhumations carried out by
the Area of Exhumations of the Office of Human
Rights of the Archbishop of Guatemala (ODHAG),
together with 24 skeletons recovered by the Foundation for Forensic Anthropology of Guatemala
(FAFG). Although the specific identity of many individual skeletons is not known, all of the remains
derive from clandestine cemeteries near remote rural communities. The circumstances of the massacres and subsequent interment are now well-documented, and permit identification of the remains as
to village and/or ethnicity. Positive identities were
achieved for a sizable proportion of the remains (Arzobispado de Guatemala, 1998; Equipo de Antropologı́a Forense de Guatemala, 1997; unpublished
data). We considered only adult skeletons, which
showed complete fusion of all long bone epiphyses.
Males outnumbered females almost 2:1 in the sample because females were less often the targets of
military action than males. We measured all complete adult remains that were available for study
during the period of data collection. The remains
include skeletons from five major highland Maya
ethnic groups (Table 2); there is no ethnic difference
in skeletal stature (as estimated from femur
236
L.E. WRIGHT AND M.A. VÁSQUEZ
TABLE 2. Maya forensic sample by ethnic group and sex
Ethnic group
Achi
Ixil
Kakchiquel
Keqchi
Quiche
Total
Male
Female
Total
1
3
17
14
33
68
5
5
3
16
3
32
6
8
20
30
36
100
lengths) among males of Kakchiquel, Keqchi, and
Quiche descent in the sample (ANOVA, P ⫽ 0.64).
Unfortunately, cell sizes are too small to test statural differences among ethnic groups for the females.
The second forensic sample consists of 36 male
skeletons exhumed by the FAFG from the grounds of
the military base at El Chal, Petén. No females were
recovered from this site. These remains are of “disappeared” individuals, so their ethnic identity is less
well-constrained than in the Maya sample. The
mean stature of the El Chal remains is approximately 2.5 cm taller than the mean stature of males
in the Maya sample (Table 1); thus it is likely that
the sample includes a greater proportion of Ladino
individuals (of mixed Spanish and indigenous Maya
ancestry). We use this sample to test the applicability of regression equations developed from the forensic Maya sample to forensic remains of unknown
ethnicity in Guatemala and Central America at
large.
A standard set of measurements was taken on
four major long bones for each skeleton. All of the
bones were measured by M.V., using the same osteometric board, between June–December 1998. He
measured the left bone for each skeleton, but substituted the right side for skeletons in which the
right bone was better preserved than the left. All
measurements were recorded in millimeters. The
landmarks we measured are described in Table 3
and illustrated in Figure 1. For the most part, the
landmarks measured follow those defined by Steele
(1970). However, we eliminated one landmark on
the tibia (no. 3) that we could not locate confidently,
and we added several new landmarks. In addition to
the humerus, femur, and tibia, we also measured
the locations of several landmarks on the fibula.
Rather than numbering the bone segments (Steele
and McKern, 1969), we refer to the segment lengths
by a code that incorporates a letter representing the
bone and the landmark numbers. For instance,
“F2–5” represents the segment between landmarks
F2 and F5 on the femur. Likewise, “H0 –2” represents the humerus segment from landmarks H0 to
H2, and “T3–5” represents the tibia segment from
landmarks T3 to T5. To avoid confusion between the
femur and fibula, we designate fibular landmarks
with “P,” from the Spanish, peroné.
The equations we derived relate the distances between these landmarks to the maximum length of
each long bone, measured following the standard
definitions (Bass, 1987). To measure the locations of
landmarks, we place each bone on the osteometric
board, with the long axis of the diaphysis parallel to
the length of the osteometric board. We use clear
plastic triangles to extrapolate the location of landmarks relative to the metric scale on the board. For
the humerus, femur, and fibula, we align the bone on
the osteometric board with the most proximal portion of the bone that is present at the zero stop; thus,
the landmarks are numbered from proximal to distal. For the tibia, the points are numbered from
distal to proximal because the maximum length
(landmark T7) must be measured with the block of
the board on the lateral malleolus in order to exclude the cruciate eminence. For the femur, all measurements are taken with the bone in a prone position on the osteometric board (dorsal surface up).
The fibula is placed on its dorsolateral surface, such
that the distal articulation is facing to one side and
slightly upwards. Because some of the landmarks on
the humerus and tibia are located on the ventral
aspect of the bone, while others are dorsal, the bone
must be turned over to measure several landmarks.
After turning the bone, we verify the total length of
the bone (or portion present) in order to ensure
accurate alignment.
Rather than the multiple regression approach
used by Steele (1970; also Steele and McKern, 1969;
Jacobs, 1992), we follow a univariate approach to the
regression analyses, calculating regression equations against bone length for the distance between
pairs of landmarks on each bone. Therefore, it is
possible to estimate length for bones that suffer from
erosion of intermediate landmarks, which would not
be possible using the multiple regression approach.
We calculate the regression equation for a given pair
of points for each sex separately, and for both sexes
combined. In addition, we regress fibula segment
length against the maximum length of the tibia,
since fibula and tibia length are highly correlated
(r ⫽ 0.982, n ⫽ 76 for Maya males and females,
combined), and standards for stature estimation
from the fibula are scarce.
Instead of regressing bone length (y) on segment
length (x), as is commonly done in forensic stature
estimation, we regress segment length (y) on bone
length (x) and then solve for bone length. This
method, known as classical calibration, has been
applied to age estimation (Konigsberg et al., 1997),
and is the approach favored in the allometry literature. The former “inverse calibration” method approaches the problem from the perspective that bone
length is a product of segment length, an essentially
Bayesian approach. Classical calibration takes a
maximum likelihood approach, and sees segment
length as constrained by bone length. For reconstructing the length of fragmentary bones the latter
approach makes logical sense, especially for landmarks defined by muscle attachment sites, since
these features are determined by muscle size and
action in the context of a complete functioning limb.
Konigsberg et al. (1998); (also Hens et al., 2000)
have shown that inverse calibration is appropriate
ESTIMATING LENGTH OF INCOMPLETE LONG BONES
237
TABLE 3. Definitions of bone landmarks used in estimating bone length, with correspondence to landmarks of Steele (1970)
Bone
Humerus
Femur
Tibia
Landmark
(this study)
Landmark
(Steele, 1970)
H0
H1
H2
1
Prone
Supine
Supine
H3
H41
2
Prone
Supine
H5
H6
H7
3
4
5
Prone
Prone
Prone
F0
F1
F2
F32
1
Prone
Prone
Prone
Prone
F41
3
Prone
F5
4
Prone
2
F6
5
Prone
T7
1
Supine
T6
T51
2
Supine
Supine
T41
T31
Fibula
1
2
Position
of bone
Prone
Prone
T21
4
Supine
T1
5
Supine
T0
6
Supine
P0
P1
Supine
Supine
P22
P3
P4
Supine
Supine
Supine
Definition of landmark
Most proximal point on the head
Most proximal point of the greater tuberosity
Most projecting proximal point on the lesser
tuberosity, along its lateral border
Most distal point of circumference of the head
Most distal point of the deltoid tuberosity,
where the two deltoid lines join
Proximal margin of the olecranon fossa
Distal margin of the olecranon fossa
Most distal point of the trochlea
Most proximal point on the head
Most proximal point on the greater trochanter
Midpoint of the lesser trochanter
Distal limit of smooth bone between the union
of the pectineal line and linea aspera, at
which point the intersection of the lines is
filled with rough bone
Most proximal extension of the popliteal
surface at point where the medial and lateral
supracondylar lines become parallel below
the linea aspera
Most proximal point on margin of the
intercondylar fossa
Most distal point of the medial condyle
Most prominent point on the lateral half of the
lateral condyle
Most proximal point of the tibial tuberosity
Point at which the anterior crest crosses the
central axis of tibia, as drawn through the
tibial tuberosity
Nutrient foramen
Point on the popliteal line where it crosses over
the medial angle of the diaphysis
Point where the anterior crest crosses over to
the medial border of the shaft above the
medial malleolus
Proximal margin of the distal articular surface,
at a point opposite the tip of the medial
malleolus
Most distal point of the medial malleolus
Most proximal point of the head
Most laterally projecting point on the head,
opposite the proximal articulation
Nutrient foramen
Proximal border of the distal articular facet
Most distal point on the lateral malleolus
Landmark is not used in any of the equations listed in Table 5. However, it is used in equations listed in Appendix.
Landmark is not used in any of the equations generated and deemed acceptable in this study.
to contexts where the specimen is known to belong to
the same statistical distribution as that from which
the estimator was developed. But if the specimen is
not known to have come from a given distribution,
classical calibration is the preferred method. Equations generated by classical calibration will have
smaller standard errors than would those generated
by inverse calibration when applied to skeletons
with bone lengths that are substantially different
from the reference sample mean (Konigsberg et al.,
1998). Although inverse calibration might be more
appropriate for the narrow context of forensic Maya
skeletons in Guatemala, we hope that the equations
may find application in other closely related populations (e.g., forensic Ladinos in Central America, or
archaeological Maya remains) which are likely to be
taller than the forensic Maya sample. Thus, classical
calibration is the preferred method (Konigsberg et
al., 1998). We reject regression equations that show
r2 ⬍ 0.85, and retain only those equations with high
correlations and highly significant F values (P ⬍
0.0001).
RESULTS
Table 4 contains Pearson’s correlation coefficients,
together with sample sizes, for the correlation of
each possible segment with maximum bone length
in the forensic Maya sample, for males, for females,
and for the two sexes pooled. The correlations range
from essentially 0 – 0.99. Approximately half of the
238
L.E. WRIGHT AND M.A. VÁSQUEZ
Fig. 1. Landmarks used to estimate bone length from the humerus (a), femur (b), tibia (c), and fibula (d). Left bones are illustrated,
with ventral aspect at left, and dorsal aspect at right.
239
ESTIMATING LENGTH OF INCOMPLETE LONG BONES
TABLE 4. Pearson’s r for correlation of individual segment lengths with maximum bone length
Bone and
Segment
Humerus
H0–1
H0–2
H0–3
H0–4
H0–5
H0–6
H1–2
H1–3
H1–4
H1–5
H1–6
H1–7
H2–3
H2–4
H2–5
H2–6
H2–7
H3–4
H3–5
H3–6
H3–7
H4–5
H4–6
H4–7
H5–6
H5–7
H6–7
Femur
F0–1
F0–2
F0–3
F0–4
F0–5
F1–2
F1–3
F1–4
F1–5
F1–6
F2–3
F2–4
F2–5
F2–6
F3–4
F3–5
F3–6
F4–5
F4–6
F5–6
Tibia
T0–1
T0–2
T0–3
T0–4
T0–5
T0–6
T1–2
T1–3
T1–4
T1–5
T1–6
T1–7
T2–3
T2–4
T2–5
T2–6
T2–7
T3–4
T3–5
T3–6
T3–7
T4–5
T4–6
Maya males
Maya females
Combined sex
r
N
r
N
r
N
0.256*
0.185*
0.355
0.827
0.981
0.991
0.048*
0.150*
0.841
0.975
0.985
0.993
0.159*
0.785
0.941
0.966
0.977
0.773
0.948
0.974
0.981
0.621
0.679
0.731
0.219*
0.390
0.284*
54
57
56
57
58
58
53
52
53
54
54
54
55
56
57
57
57
55
56
56
56
57
57
57
58
58
58
0.015*
⫺0.068*
0.140*
0.836
0.976
0.984
⫺0.080*
0.112*
0.845
0.970
0.976
0.992
0.159*
0.873
0.959
0.965
0.976
0.806
0.952
0.953
0.974
0.012*
0.177*
0.265*
0.613
0.569
0.132*
23
23
24
23
24
24
23
23
23
23
23
23
23
23
23
23
23
23
24
24
24
23
23
23
24
24
24
0.179*
0.368
0.578
0.868
0.989
0.994
0.308
0.448
0.875
0.986
0.991
0.996
0.258*
0.830
0.969
0.980
0.986
0.789
0.967
0.979
0.986
0.694
0.748
0.789
0.371
0.513
0.294
77
80
80
80
82
82
76
75
76
80
80
77
78
79
80
80
80
78
80
77
80
76
82
80
80
82
77
0.198*
0.378
0.255*
0.798
0.984
0.358
0.213*
0.792
0.963
0.981
0.113
0.743
0.926
0.953
0.529
0.703
0.727
0.241*
0.305*
0.216*
64
64
59
64
65
62
57
62
63
64
58
62
63
64
58
58
59
63
64
65
0.491
0.679
0.544
0.839
0.986
0.559
0.370*
0.779
0.970
0.984
0.244
0.761
0.956
0.975
0.556
0.803
0.842
0.472
0.530
0.270*
32
31
32
32
32
31
32
32
32
32
31
31
31
31
32
32
32
32
32
32
0.268
0.628
0.513
0.862
0.988
0.637
0.459
0.852
0.976
0.988
0.292
0.789
0.944
0.970
0.524
0.717
0.772
0.314
0.445
0.450
96
95
91
96
97
93
89
94
95
96
89
93
94
95
90
90
91
95
96
97
0.167*
0.505
0.815
0.761
0.853
0.981
0.494
0.792
0.749
0.846
0.973
0.992
0.499
0.390
0.596
0.734
0.774
⫺0.179*
0.048*
0.302*
0.424
0.223*
0.419
65
63
64
65
63
60
63
64
65
63
60
65
63
63
63
60
60
64
63
60
64
63
60
0.115*
0.112*
0.731
0.832
0.808
0.981
0.095
0.722
0.801
0.816
0.975
0.996
0.580
0.652
0.841
0.849
0.879
⫺0.226*
0.009*
0.105*
0.298*
0.255*
0.614
30
30
29
30
30
29
30
29
30
30
29
30
29
30
30
29
27
29
29
28
29
30
29
0.294
0.525
0.814
0.845
0.883
0.988
0.497
0.792
0.828
0.877
0.982
0.996
0.510
0.539
0.711
0.822
0.859
⫺0.080*
0.124*
0.457
0.559
0.224*
0.536
95
93
93
95
93
89
93
93
95
93
89
95
92
93
93
89
87
93
92
88
93
93
89
(continued)
240
L.E. WRIGHT AND M.A. VÁSQUEZ
TABLE 4. (Continued)
Bone and
Segment
T4–7
T5–6
T5–7
T6–7
Fibula
P0–1
P0–2
P0–3
P1–2
P1–3
P1–4
P2–3
P2–4
P3–4
Tibia from fibula
P0–1
P0–2
P0–3
P1–2
P1–3
P1–4
P2–3
P2–4
P3–4
Maya males
Maya females
Combined sex
r
N
r
N
r
N
0.580
0.257*
0.407
0.434
65
60
63
60
0.728
0.302*
0.364*
0.356*
30
29
30
29
0.692
0.361
0.517
0.561
95
89
93
89
0.079*
0.335*
0.989
0.345*
0.964
0.981
0.444
0.460
0.322*
45
46
51
40
45
45
46
46
51
0.046*
0.110*
0.993
0.165*
0.984
0.990
0.449*
0.453*
0.162*
23
24
25
23
23
23
24
24
25
0.073*
0.353
0.992
0.398
0.979
0.990
0.459
0.501
0.538
68
70
76
63
68
68
70
70
76
0.081*
0.376
0.972
0.401
0.947
0.947
0.392
0.396
0.228*
45
46
51
40
45
45
46
46
51
0.061*
0.090*
0.984
0.150*
0.972
0.966
0.462*
0.459*
0.052*
23
24
25
23
23
23
24
24
25
0.076*
0.364
0.982
0.416
0.969
0.970
0.441
0.475
0.474
68
70
76
63
68
68
70
70
76
* P ⱖ 0.01.
segments show correlations greater than 0.9. In general, longer segments are better correlated with
bone length than are shorter segments, as might be
expected. Many shorter segments show nonsignificant correlations with bone length. Segments defined by landmarks that lie on articular architecture
or secondary centers of ossification also show higher
correlations than segments defined by muscle markings or nutrient foramina. For instance, segments
defined in part by H4 (the most distal point on the
deltoid tuberosity) show a lower correlation than
several other humeral segments. Likewise, correlations are low for segments defined by femoral landmarks F3 and F4, as well as tibial segments T5, T3,
and T2. Indeed, segment T3– 4 is negatively (but not
significantly) correlated with tibia length. This is
largely due to the variable location of landmark T4,
the nutrient foramen; other tibial segments delimited by the nutrient foramen also show poor correlations with bone length. The nutrient foramen on
the fibula, P2, is also fairly variable in location, as
indicated by the low correlations of segments that it
defines. Correlations between fibular segment
lengths and tibial length are comparable to those for
fibular length.
We generated regression equations for segment
length vs. total bone length for each of the segments
that showed a statistically significant correlation at
P ⱕ 0.01 (Table 4). In total, we generated some 215
regression equations: 73 for males, 57 for females,
and 85 for sexes combined. Of these, 75 equations
have r2 ⬎ 0.85, and highly significant F values (P ⬍
0.0001); they are listed in Table 5. Because the articular architecture of the humerus lends itself to
the definition of several landmarks, the humerus
presents the largest number of successful equations,
providing 11 equations each for males, females, and
sexes combined. For the femur, we accepted five
equations for each sex. The tibia and fibula each
resulted in three equations per sex, as was also the
case for the estimation of tibial length from fibular
measurements. Table 5 also includes the standard
errors of the estimated bone lengths. For most equations, the error is quite small, ranging between
2.86 –18.43 mm. Standard errors are smaller for the
combined sex equations, because of the larger sample size on which the regressions were based. The
Appendix contains 19 additional equations that
have r2 between 0.6 – 0.85. Although these have significant F values (P ⬍ 0.0001), they predict bone
length with less success than the equations in Table
5, as indicated by the lower r2 and larger standard
errors. Because these equations are defined by muscle attachment sites, they should be applied only
with extreme caution. We rejected 121 equations
with r2 ⬍ 0.6, and those with standard errors ⬎20
mm.
To evaluate the applicability of the regression
equations in Table 5 on Guatemalan remains of
unknown ethnicity, we apply the equations to complete bones from 36 male skeletons from the military
base at El Chal, Petén. Figure 2 illustrates the relationship between measured bone length and bone
length estimated using a selection of the Maya male
regression equations. Estimates derived with all
three equations are represented for the tibia and
fibula. The slopes of regression lines drawn through
these data range from 0.9 –1.1 for all of the equations, including those not illustrated in Figure 2.
Following Feldesman and Fountain (1996), we use
241
ESTIMATING LENGTH OF INCOMPLETE LONG BONES
TABLE 5. Regression lines for estimation of total bone length for forensic Maya skeletons1
Regression line
A. Humerus
Sexes combined
(H0–5) ⫽ ⫺7.561 ⫹ 0.918 * Humerus length
(H0–6) ⫽ ⫺4.805 ⫹ 0.968 * Humerus length
(H1–5) ⫽ ⫺8.145 ⫹ 0.903 * Humerus length
(H1–6) ⫽ ⫺4.803 ⫹ 0.951 * Humerus length
(H1–7) ⫽ ⫺0.361 ⫹ 0.984 * Humerus length
(H2–5) ⫽ ⫺4.255 ⫹ 0.848 * Humerus length
(H2–6) ⫽ ⫺3.072 ⫹ 0.904 * Humerus length
(H2–7) ⫽ 1.328 ⫹ 0.937 * Humerus length
(H3–5) ⫽ ⫺7.229 ⫹ 0.808 * Humerus length
(H3–6) ⫽ ⫺4.192 ⫹ 0.857 * Humerus length
(H3–7) ⫽ ⫺0.191 ⫹ 0.892 * Humerus length
Males
(H0–5) ⫽ ⫺8.976 ⫹ 0.923 * Humerus length
(H0–6) ⫽ ⫺3.008 ⫹ 0.962 * Humerus length
(H1–5) ⫽ ⫺7.817 ⫹ 0.902 * Humerus length
(H1–6) ⫽ 1.191 ⫹ 0.931 * Humerus length
(H1–7) ⫽ 4.032 ⫹ 0.97 * Humerus length
(H2–5) ⫽ ⫺10.958 ⫹ 0.87 * Humerus length
(H2–6) ⫽ ⫺7.981 ⫹ 0.92 * Humerus length
(H2–7) ⫽ ⫺5.936 ⫹ 0.961 * Humerus length
(H3–5) ⫽ ⫺20.641 ⫹ 0.851 * Humerus length
(H3–6) ⫽ ⫺14.351 ⫹ 0.89 * Humerus length
(H3–7) ⫽ ⫺12.205 ⫹ 0.931 * Humerus length
Females
(H0–5) ⫽ 6.396 ⫹ 0.866 * Humerus length
(H0–6) ⫽ ⫺7.124 ⫹ 0.977 * Humerus length
(H1–5) ⫽ 5.387 ⫹ 0.852 * Humerus length
(H1–6) ⫽ ⫺4.765 ⫹ 0.95 * Humerus length
(H1–7) ⫽ ⫺4.223 ⫹ 0.998 * Humerus length
(H2–5) ⫽ ⫺9.534 ⫹ 0.869 * Humerus length
(H2–6) ⫽ ⫺19.686 ⫹ 0.967 * Humerus length
(H2–7) ⫽ ⫺19.144 ⫹ 1.016 * Humerus length
(H3–5) ⫽ ⫺13.503 ⫹ 0.834 * Humerus length
(H3–6) ⫽ ⫺27.023 ⫹ 0.945 * Humerus length
(H3–7) ⫽ ⫺19.899 ⫹ 0.968 * Humerus length
B. Femur
Sexes combined
(F0–5) ⫽ ⫺4.716 ⫹ 0.932 * Femur max. length
(F1–5) ⫽ ⫺2.152 ⫹ 0.890 * Femur max. length
(F1–6) ⫽ 0.138 ⫹ 0.960 * Femur max. length
(F2–5) ⫽ ⫺4.139 ⫹ 0.757 * Femur max. length
(F2–6) ⫽ ⫺3.780 ⫹ 0.832 * Femur max. length
Males
(F0–5) ⫽ ⫺18.842 ⫹ 0.964 * Femur max. length
(F1–5) ⫽ ⫺17.956 ⫹ 0.928 * Femur max. length
(F1–6) ⫽ ⫺1.231 ⫹ 0.965 * Femur max. length
(F2–5) ⫽ ⫺42.396 ⫹ 0.846 * Femur max. length
(F2–6) ⫽ ⫺27.202 ⫹ 0.887 * Femur max. length
Females
(F0–5) ⫽ ⫺13.195 ⫹ 0.957 * Femur max. length
(F1–5) ⫽ 9.809 ⫹ 0.861 * Femur max. length
(F1–6) ⫽ 22.378 ⫹ 0.901 * Femur max. length
(F2–5) ⫽ ⫺6.179 ⫹ 0.769 * Femur max. length
(F2–6) ⫽ 2.260 ⫹ 0.820 * Femur max. length
C. Tibia
Sexes combined
(T0–6) ⫽ 10.807 ⫹ 0.904 * Tibia length
(T1–6) ⫽ 8.847 ⫹ 0.873 * Tibia length
(T1–7) ⫽ ⫺2.770 ⫹ 0.972 * Tibia length
Males
(T0–6) ⫽ 7.407 ⫹ 0.914 * Tibia length
(T1–6) ⫽ 2.803 ⫹ 0.890 * Tibia length
(T1–7) ⫽ ⫺5.478 ⫹ 0.979 * Tibia length
Females
(T0–6) ⫽ 3.281 ⫹ 0.930 * Tibia length
(T1–6) ⫽ ⫺5.925 ⫹ 0.923 * Tibia length
(T1–7) ⫽ ⫺8.034 ⫹ 0.990 * Tibia length
D. Fibula
Sexes combined
(P0–3) ⫽ 2.877 ⫹ 0.924 * Fibula length
(P1–3) ⫽ ⫺5.000 ⫹ 0.909 * Fibula length
(P1–4) ⫽ ⫺9.305 ⫹ 0.990 * Fibula length
r2
N
F
SE
0.978
0.989
0.973
0.982
0.993
0.939
0.961
0.972
0.935
0.958
0.971
82
82
77
77
77
80
80
80
80
80
80
3,567.4
7,036.4
2,709.7
4,180.6
9,972.8
1,191.7
1,916.2
2,714.7
1,126.1
1,760.9
2,653.0
4.46
3.35
5.03
4.27
2.86
7.12
5.98
5.21
6.98
5.92
5.02
0.963
0.983
0.951
0.970
0.986
0.886
0.933
0.955
0.899
0.949
0.963
58
58
54
54
54
57
57
57
56
56
56
1,441.2
3,200.8
1,000.6
1,668.2
3,783.4
426.2
765.8
1,162.1
481.2
999.3
1,401.0
7.24
5.06
8.49
6.79
4.70
12.51
9.87
8.37
11.55
8.37
7.40
0.952
0.969
0.941
0.953
0.983
0.919
0.932
0.952
0.905
0.907
0.949
24
24
23
23
23
23
23
23
24
24
24
437.1
682.7
333.7
426.4
1,222.4
238.2
286.0
414.3
210.7
215.4
407.4
11.24
10.14
12.61
12.44
7.72
15.24
15.47
13.50
15.59
17.48
13.02
0.977
0.952
0.976
0.890
0.941
97
95
96
94
95
3,999.0
1,852.7
3,893.0
751.8
1,484.7
6.01
8.44
6.28
11.25
8.81
0.968
0.928
0.963
0.858
0.909
65
63
64
63
64
1,899.8
789.7
1,624.7
367.6
617.9
9.24
13.80
10.01
18.43
14.91
0.973
0.941
0.968
0.915
0.948
32
32
32
31
31
1,076.5
478.7
911.9
311.5
557.2
11.28
15.22
11.55
16.78
13.39
0.976
0.965
0.991
89
89
95
3,551.3
2,402.1
10,473.2
5.04
5.92
3.16
0.963
0.948
0.985
60
60
65
1,504.2
1,047.4
4,042.0
8.04
9.39
5.26
0.962
0.951
0.992
29
29
30
684.6
521.1
3,488.0
11.09
12.62
5.24
0.984
0.958
0.980
76
68
68
4,463.6
1,504.4
3,173.4
4.55
7.73
5.79
(continued)
242
L.E. WRIGHT AND M.A. VÁSQUEZ
TABLE 5. (Continued)
Regression line
Males
(P0–3) ⫽ ⫺6.583 ⫹ 0.951 * Fibula length
(P1–3) ⫽ ⫺13.376 ⫹ 0.933 * Fibula length
(P1–4) ⫽ ⫺7.512 ⫹ 0.984 * Fibula length
Females
(P0–3) ⫽ ⫺13.445 ⫹ 0.981 * Fibula length
(P1–3) ⫽ ⫺23.848 ⫹ 0.974 * Fibula length
(P1–4) ⫽ ⫺10.529 ⫹ 0.993 * Fibula length
E. Tibia from fibula
Sexes combined
(P0–3) ⫽ ⫺6.216 ⫹ 0.941 * Tibia length
(P1–3) ⫽ ⫺11.450 ⫹ 0.918 * Tibia length
(P1–4) ⫽ ⫺13.239 ⫹ 0.990 * Tibia length
Males
(P0–3) ⫽ ⫺20.435 ⫹ 0.981 * Tibia length
(P1–3) ⫽ ⫺24.067 ⫹ 0.954 * Tibia length
(P1–4) ⫽ ⫺13.214 ⫹ 0.990 * Tibia length
Females
(P0–3) ⫽ ⫺9.256 ⫹ 0.953 * Tibia length
(P1–3) ⫽ ⫺15.667 ⫹ 0.934 * Tibia length
(P1–4) ⫽ 1.646 ⫹ 0.941 * Tibia length
1
r2
N
F
SE
0.977
0.930
0.962
51
45
45
2,097.4
573.4
1,089.5
7.01
13.21
10.11
0.986
0.968
0.979
25
23
23
1,569.9
626.6
998.0
7.66
12.09
9.77
0.965
0.938
0.942
76
68
68
2,033.5
1,003.4
1,067.6
6.94
9.67
10.11
0.944
0.896
0.897
51
45
45
826.5
370.3
373.7
11.65
16.99
17.56
0.967
0.945
0.932
25
23
23
684.1
362.2
290.0
11.45
15.47
17.42
All measurements, estimated bone lengths, and standard errors are in mm. max., maximum.
the mean absolute deviation (MAD)1 and the mean
squared error (MSE)2 for the difference between
measured and estimated bone length to evaluate the
accuracy of the Maya male and combined sex equations on the El Chal remains. Smaller MAD and
MSE values indicate better accuracy of the equations. Table 6 contains the r2, sample size, MAD,
and MSE, as well as the mean differences and probability for a paired t-test between estimated and
measured lengths for each equation. Positive mean
differences indicate a tendency to underestimate
bone length using a given equation, while a negative
mean difference indicates that the regression equation overestimates bone length. Given the large
number of equations for which we calculated t-tests,
we consider these differences to be significant only
when P ⬍ 0.001, to minimize the likelihood of type I
errors.
For all bones, estimated length is highly correlated with measured length in the El Chal remains,
with values of r2 above 0.84 for all of the equations in
Table 5. For the humerus, mean absolute deviations
are less than 3 mm and are well within the standard
error of the estimating equations, and estimated
humeral lengths do not differ significantly from
measured length for any equation. However, all
mean differences are positive, indicating slight underestimation of humerus length. Although a few of
1
Mean absolute deviation is calculated as follows (after Feldesman
and Fountain, 1996):
MAD ⫽
冘
兩共estimated ⫺ measured兲兩
n
2
Mean squared error is calculated as follows (after Feldesman and
Fountain, 1996):
MSE ⫽
冘
共estimated ⫺ measured兲2
n
the femoral equations show statistically significant
mean differences, and larger values of MAD and
MSE than the humeral equations, the MAD are
substantially smaller than the standard error of the
estimating equations. The Maya equations perform
less well on El Chal tibiae, and tend to overestimate
tibia length. Tibial length estimates using the T1– 6
equations differ significantly from measured tibial
lengths. For the fibula, none of the equations produced estimates that differed significantly from
measured fibular length; MAD and MSE are very
small. Estimates of tibial length from fibular measurements at El Chal appear to work better than
estimates based on tibial measurements. Overall,
the absolute differences between measured and estimated lengths of the El Chal long bones are quite
small, the largest MAD being only 6.4 mm. Despite
the significance of some mean differences, we believe
that the forensic Maya equations estimate bone
length with sufficient accuracy for the El Chal sample, and can be applied in diverse forensic contexts
in Guatemala with confidence.
We used the equations of Steele (1970), Steele and
McKern (1969), also Steele and Bramblett (1988),
and Jacobs (1992) to examine the applicability of
other standards for long bone length estimation on
Maya remains. We limit our comparison to Steele’s
equations based on segment combinations that were
shown to be highly correlated (r ⱖ 0.9) with bone
length in the original studies, in order to assess
equations of similar accuracy to those generated
here. Because we did not measure Steele’s tibia
landmark 3, direct comparison with many of the
tibia equations of Steele (1970) and of Jacobs (1992)
is not possible. Single segment regressions for the
tibia have P ⬍ 0.9, so we compare only equations for
humerus length and femur length. Although it may
seem obvious that these equations should be less
ESTIMATING LENGTH OF INCOMPLETE LONG BONES
243
Fig. 2. Comparison of measured and estimated bone length for El Chal male skeletons, with lengths estimated using male forensic
Maya regression equations.
accurate on Maya remains than the Maya equations
are, this exercise is a useful demonstration of the
magnitude of population differences.
For the forensic Maya males and females, Figure
3 illustrates the relationship of measured humerus
length to humerus length estimated using the “best”
(segment 1 ⫹ 2 ⫹ 3) and “worst” (segment 2) of the
humerus equations of Steele (1970) as judged by
MAD and MSE. Table 7 lists the r2, sample sizes,
MAD, MSE, mean differences, and paired t-test
probabilities for all the regression lines that we compared. Figure 4 and Table 8 provide comparable
data for the femur. On the Maya skeletons, the
equations of Steele’s give high MAD and MSE, and
almost all of the lengths estimated using published
equations are significantly different from measured
lengths. Yet several equations give estimated
lengths that are strongly correlated with measured
length, for which the regression lines pass through
zero and have slopes close to one.
For the humerus, the white male segment 1 ⫹ 2 ⫹
3 equation appears to give a fairly good estimate of
Mayan male humerus length (Fig. 3a), but the Black
male 1 ⫹ 2 ⫹ 3 equation consistently overestimates
humerus length, while the Mississippian male 1 ⫹
2 ⫹ 3 equation grossly underestimates humerus
length. White and Black male equations for segments 1 ⫹ 2, 2 ⫹ 3, and 2 ⫹ 3 ⫹ 4 overestimate
humerus length consistently, while the Mississippian equations substantially underestimate humerus length (Table 7). These population differences
are less evident for Maya females, for whom many of
244
L.E. WRIGHT AND M.A. VÁSQUEZ
TABLE 6. Comparison of measured bone length to estimated bone length for male skeletons from El Chal
Equation
Humerus
Maya male H0–5
Maya male H0–6
Maya male H1–5
Maya male H1–6
Maya male H1–7
Maya male H2–5
Maya male H2–6
Maya male H2–7
Maya male H3–5
Maya male H3–6
Maya male H3–7
Maya combined sex H0–5
Maya combined sex H0–6
Maya combined sex H1–5
Maya combined sex H1–6
Maya combined sex H1–7
Maya combined sex H2–5
Maya combined sex H2–6
Maya combined sex H2–7
Maya combined sex H3–5
Maya combined sex H3–6
Maya combined sex H3–7
Femur
Maya male F0–5
Maya male F1–5
Maya male F1–6
Maya male F2–5
Maya male F2–6
Maya combined sex F0–5
Maya combined sex F1–5
Maya combined sex F1–6
Maya combined sex F2–5
Maya combined sex F2–6
Tibia
Maya male T0–6
Maya male T1–6
Maya male T1–7
Maya combined sex T0–6
Maya combined sex T1–6
Maya combined sex T1–7
Fibula
Maya male P0–3
Maya male P1–3
Maya male P1–4
Maya combined sex P0–3
Maya combined sex P1–3
Maya combined sex P1–4
Tibia from fibula
Maya male P0–3 tibia
Maya male P1–3 tibia
Maya male P1–4 tibia
Maya combined sex P0–3 tibia
Maya combined sex P1–3 tibia
Maya combined sex P1–4 tibia
r2
N
0.97
0.98
0.94
0.95
0.98
0.93
0.95
0.96
0.93
0.96
0.96
0.97
0.98
0.94
0.95
0.98
0.93
0.95
0.96
0.93
0.96
0.96
32
32
30
30
30
30
30
30
31
31
31
32
32
30
30
30
30
30
30
31
31
31
0.9
0.1
1.5
0.6
0.6
1.8
1.3
1.0
0.9
0.4
0.3
0.8
0.1
1.4
0.6
0.5
1.9
1.4
1.1
1.5
0.7
0.6
0.99
0.95
0.97
0.84
0.88
0.99
0.95
0.97
0.84
0.88
34
32
32
34
34
34
32
32
34
34
0.95
0.93
0.98
0.95
0.93
0.98
MAD
MSE
0.0270
0.6571
0.0172
0.2769
0.0724
0.0076
0.0232
0.0321
0.1367
0.3401
0.4527
0.0486
0.6146
0.0194
0.2475
0.1897
0.0062
0.0155
0.0296
0.0300
0.1623
0.2011
1.8
1.1
2.7
2.1
1.4
2.5
2.1
2.0
1.9
2.9
2.6
1.7
1.1
2.7
2.1
1.4
3.0
2.5
2.2
2.8
2.1
2.2
5.5
2.1
11.4
7.3
3.6
9.2
6.8
6.4
5.6
14.5
12.0
5.3
2.2
11.3
7.4
3.6
15.6
9.5
7.0
15.4
7.3
6.8
1.3
0.1
⫺1.3
⫺1.4
⫺2.5
1.8
⫺0.4
⫺2.1
⫺1.3
⫺2.8
0.0006
0.9253
0.0332
0.2774
0.0238
⬍0.0001
0.5610
0.0011
0.3275
0.0148
1.9
3.2
5.4
5.9
5.2
2.1
3.2
3.1
6.4
5.5
5.6
16.0
38.0
52.7
42.0
7.0
16.6
14.6
60.8
46.4
29
29
29
29
29
29
⫺2.4
⫺4.0
⫺1.2
⫺2.4
⫺4.0
⫺1.1
0.0017
⬍0.0001
0.0067
0.0021
0.0001
0.0128
3.7
5.0
2.0
3.7
5.1
1.9
18.8
36.4
6.1
19.1
37.3
6.0
0.99
0.95
0.96
0.99
0.95
0.96
15
12
12
15
12
12
⫺1.8
⫺1.3
0.5
⫺1.7
⫺1.2
0.8
0.0025
0.2112
0.5565
0.0066
0.2480
0.3756
1.8
3.2
2.6
1.9
2.6
2.7
6.3
12.5
8.4
6.8
10.2
8.8
0.94
0.91
0.93
0.94
0.91
0.93
13
10
10
13
10
10
⫺3.6
⫺2.9
⫺1.3
⫺3.4
⫺2.8
⫺1.4
0.0067
0.0830
0.3220
0.0136
0.1021
0.3134
4.8
5.0
3.4
4.8
4.8
3.4
27.9
29.3
16.5
27.0
27.7
16.5
the equations give comparably good results, but tend
toward slightly overestimating humerus length (Fig.
3b, Table 7). All of the equations for segment 2
overestimate humerus length substantially for both
Maya males and females, especially for individuals
with shorter humeri (Fig. 3c,d). The segment 2 equations stand out as the least successful predictors of
humerus length on the Mayan remains.
Figure 4 illustrates the comparison of measured
maximum femur length with maximum femur
length, estimated using the 1 ⫹ 2 and 1 ⫹ 2 ⫹ 3
equations of Steele (1970), Steele and Bramblett
(1988), and Jacobs (1992) on the forensic Maya sample. Table 8 lists the r2, MAD, MSE, mean differ-
Mean difference
P
ences, and paired t-test probabilities for all of the
femoral regression lines that we compared. The
equations for segments 1 ⫹ 2 perform very poorly on
Maya femora. They show very low correlations, low
slopes, large MAD, and large MSE. The white and
Black 1 ⫹ 2 equations dramatically underestimate
maximum length for most femora, while the Mississippian and European equations overestimate maximum length. The nonsignificant mean difference
and small MAD and MSE shown for males using the
Mississippian 1 ⫹ 2 equation is misleading; it is an
artifact of the low slope and sample mean. The equations based on femoral segments 1 ⫹ 2 ⫹ 3 perform
much better. Although they too show statistically
ESTIMATING LENGTH OF INCOMPLETE LONG BONES
245
Fig. 3. Comparison of measured and estimated humerus length for forensic Maya skeletons, with lengths estimated using
regression equations of Steele (1970) and Steele and Bramblett (1988, p. 166).
significant mean differences from measured femur
length, these are smaller than for most other equations. For both Maya males and females, the white,
Black, and European equations are coincident, and
slightly overestimate femoral length, while the Mississippian 1 ⫹ 2 ⫹ 3 equations underestimate femoral length consistently. Femoral length estimates
based on equations using segments 2 ⫹ 3 and 2 ⫹
3 ⫹ 4 also show high correlations with measured
femur length and small MAD. Yet the equations
based on segments 2 ⫹ 3 tend to overestimate femur
length slightly, while the equations based on segments 2 ⫹ 3 ⫹ 4 tend to underestimate femur
length. The Mississippian male 2 ⫹ 3 and Mississippian female 1 ⫹ 2 ⫹ 3 equations perform well, but in
general, the Mississippian equations show larger
deviations than the white, Black, or European equations.
The inaccuracies in estimating bone length using
the published equations must be due to different
proportions of the bone in the reference populations
from which the published equations were derived.
Table 9 contains the mean proportions of each of
Steele’s segments in the Maya forensic sample, together with the mean proportions of the segments in
both the reference samples of Steele (1970), Steele
and McKern (1969), and in the prehistoric European
sample of Jacobs (1992). For the humerus, segment
proportions are quite similar among the Terry
whites, Blacks, and the Maya. The Mississippians
have a slightly longer humerus segment 3. However,
the generally similar proportions imply that the in-
246
L.E. WRIGHT AND M.A. VÁSQUEZ
TABLE 7. Comparison of measured humerus length to estimated humerus length of Maya skeletons,
using equations of Steele (1970) and Steele and Bramblett (1988, p. 166)
Equation
Males
White male 2
White male 1 ⫹ 2
White male 2 ⫹ 3
White male 1 ⫹ 2 ⫹ 3
White male 2 ⫹ 3 ⫹ 4
Black male 2
Black male 1 ⫹ 2
Black male 2 ⫹ 3
Black male 1 ⫹ 2 ⫹ 3
Black male 2 ⫹ 3 ⫹ 4
Mississippian male 2
Mississippian male 1 ⫹ 2
Mississippian male 2 ⫹ 3
Mississippian male 1 ⫹ 2 ⫹ 3
Mississippian male 2 ⫹ 3 ⫹ 4
Females
White female 2
White female 1 ⫹ 2
White female 2 ⫹ 3
White female 1 ⫹ 2 ⫹ 3
White female 2 ⫹ 3 ⫹ 4
Black female 2
Black female 1 ⫹ 2
Black female 2 ⫹ 3
Black female 1 ⫹ 2 ⫹ 3
Black female 2 ⫹ 3 ⫹ 4
Mississippian female 2
Mississippian female 1 ⫹ 2
Mississippian female 2 ⫹ 3
Mississippian female 1 ⫹ 2 ⫹ 3
Mississippian female 2 ⫹ 3 ⫹ 4
r2
N
Mean difference
P
MAD
MSE
0.899
0.962
0.943
0.984
0.956
0.899
0.962
0.941
0.984
0.955
0.899
0.964
0.949
0.984
0.968
56
56
56
56
56
56
56
56
56
56
56
56
56
56
56
⫺10.6
⫺4.8
⫺5.5
⫺0.9
⫺2.9
⫺12.4
⫺6.0
⫺7.0
⫺4.4
⫺5.8
⫺10.8
10.0
16.4
7.2
7.4
⬍0.0001
⬍0.0001
⬍0.0001
0.0003
⬍0.0001
⬍0.0001
⬍0.0001
⬍0.0001
⬍0.0001
⬍0.0001
⬍0.0001
⬍0.0001
⬍0.0001
⬍0.0001
⬍0.0001
15.5
10.0
10.7
6.7
8.2
17.2
11.1
12.0
9.5
10.8
15.6
14.8
21.1
12.2
12.6
1,720.2
1,622.5
1,633.4
1,597.0
1,609.4
1,760.1
1,635.7
1,650.8
1,615.5
1,633.5
1,723.5
1,695.4
1,862.7
1,647.0
1,652.3
0.906
0.924
0.906
0.980
0.968
0.906
0.939
0.906
0.968
0.945
0.906
0.931
0.904
0.968
0.943
24
24
24
24
24
24
24
24
24
24
24
24
24
24
24
⫺10.8
0.7
⫺3.2
2.1
⫺3.6
⫺6.5
⫺1.1
⫺5.3
⫺2.4
⫺2.5
⫺11.8
⫺3.7
0.1
1.0
1.7
⬍0.0001
0.3160
0.0004
0.0003
0.0015
⬍0.0001
0.0820
⬍0.0001
⬍0.0001
0.0004
⬍0.0001
⬍0.0001
0.9066
0.0324
0.0125
10.3
2.4
4.1
2.2
2.6
6.4
2.3
5.8
2.7
2.9
11.3
4.1
2.5
1.8
2.3
125.2
10.5
23.1
9.5
13.3
53.9
9.1
41.5
9.8
13.9
149.4
22.9
13.2
5.0
10.9
accuracies of the humerus equations on Maya remains are due more to the absolute difference in
bone size than in the relative length of the segments.
For humerus segment 2 in both sexes, this is suggested by the lower slope of the regression (Fig.
3c,d), which illustrates that the equation overestimates the length of shorter humeri more than it
does for longer humeri. This may simply be due to
the fact that the mean length of Maya humeri is
substantially less than the mean length of humeri in
any of the reference series.
Table 9 illustrates that Maya femora have a proportionately shorter segment 2 and longer segment
3 than the white, Black, and Mississippian series,
but the prehistoric European series have a still
shorter segment 2 and longer segment 3 than the
Maya. These differences undoubtedly account for
the poor performance of the segment 1 ⫹ 2 equations
on Maya remains. Equations that incorporate both
segments 2 and 3 perform better because these differences of proportion are minimized by including
both in the calculation.
Although it was not possible to estimate Maya
tibia length using the equations of Steele (1970) or
Jacobs (1992) because we did not measure landmark
3, the proportions of the segments can be compared
by adding segments 2 and 3 together. For both males
and females, Maya tibia have shorter segments 1
and 2 ⫹ 3, but a longer segment 4 than in other
reference series. This suggests that the tibia equa-
tions would also provide unreliable estimates of
Maya tibia length.
DISCUSSION
The results of this study indicate that long bone
length can be estimated from incomplete bones with
considerable accuracy using longitudinal measurements, and provides strong support for Steele and
McKern’s (1969) methodological approach. Standard
errors for the forensic Maya regression equations
defined here are slightly larger than those of the
better-performing equations of Steele (1970), in part
due to our use of classical calibration rather than
inverse regression. The broader standard errors for
the Maya female equations are due to the smaller
sample size of Maya females that we were able to
measure.
Like Steele (1970), also Steele and McKern (1969),
we found that landmarks defined by joint architecture and secondary centers of ossification were easier to identify than those identified by muscle markings. Moreover, segments defined by articular
landmarks are more highly correlated with bone
length than are segments defined by muscle attachment sites. Intrapopulation variation in muscle
mass and activity presumably accounts for this
lower correlation. Therefore, we believe that many
of the regression equations that use these landmarks cannot be used with confidence. Where possible, we recommend that bone length estimates be
ESTIMATING LENGTH OF INCOMPLETE LONG BONES
247
Fig. 4. Comparison of measured and estimated femur length for forensic Maya skeletons, with lengths estimated using regression
equations of Steele (1970), Steele and Bramblett (1988, p. 230), and Jacobs (1992).
limited to those equations presented in Table 5. The
regression equations given in the Appendix should
be used only with extreme caution; investigators
who wish to apply them should first evaluate the
accuracy of the equations on more complete skeletons from the same skeletal series.
Critiques of Steele’s method have focused on the
difficulty that some investigators have had in identifying landmarks, and on inaccuracy in bone length
estimates (Bass, 1987; Brooks et al., 1990; Simmons
et al., 1990). We discarded only one of Steele’s points
that we could not identify with confidence (tibia
landmark 3). We suspect that the difficulties other
investigators may have encountered with the
method center on locating those points that are defined by muscle attachment sites, some of which we
also found difficult to pinpoint. Because these points
also show greater intrapopulation variation than
articular points, uncertainty in identifying these
points probably contributes to perceptions of inaccuracy of the equations overall. Together these factors
might contribute to an exaggerated bias against the
method. For instance, Simmons et al. (1990; p 629)
cite comments by Steele (1970; p 87) regarding a
landmark that he discarded,3 to support their claim
3
This landmark, defined as the point of narrowest anterior-posterior diameter of the humerus proximal to the deltoid tuberosity, was
proposed by Steele and McKern (1969), but discarded by Steele (1970).
Modified versions of the 1969 regression equations for Mississippians
that do not use this landmark were published by Steele and Bramblett
(1988, p. 166).
248
L.E. WRIGHT AND M.A. VÁSQUEZ
TABLE 8. Comparison of measured femur length to estimated femur length on Maya skeletons,
using equations of Steele (1970), Steele and Bramblett (1988, p. 230), and Jacobs (1992)
Equation
Males
White male 1 ⫹ 2
White male 2 ⫹ 3
White male 1 ⫹ 2 ⫹ 3
White male 2 ⫹ 3 ⫹ 4
Black male 1 ⫹ 2
Black male 2 ⫹ 3
Black male 1 ⫹ 2 ⫹ 3
Black male 2 ⫹ 3 ⫹ 4
Mississippian male 1 ⫹ 2
Mississippian male 2 ⫹ 3
Mississippian male 1 ⫹ 2 ⫹ 3
Mississippian male 2 ⫹ 3 ⫹ 4
European male 1 ⫹ 2
European male 2 ⫹ 3
European male 1 ⫹ 2 ⫹ 3
European male 2 ⫹ 3 ⫹ 4
Females
White female 1 ⫹ 2
White female 2 ⫹ 3
White female 1 ⫹ 2 ⫹ 3
White female 2 ⫹ 3 ⫹ 4
Black female 1 ⫹ 2
Black female 2 ⫹ 3
Black female 1 ⫹ 2 ⫹ 3
Black female 2 ⫹ 3 ⫹ 4
Mississippian female 1 ⫹ 2
Mississippian female 2 ⫹ 3
Mississippian female 1 ⫹ 2 ⫹ 3
Mississippian female 2 ⫹ 3 ⫹ 4
European female 1 ⫹ 2
European female 2 ⫹ 3
European female 1 ⫹ 2 ⫹ 3
European female 2 ⫹ 3 ⫹ 4
r2
N
Mean difference
P
MAD
MSE
0.640
0.852
0.966
0.899
0.640
0.856
0.968
0.899
0.623
0.861
0.968
0.908
0.554
0.861
0.968
0.909
62
61
61
61
62
61
61
61
62
61
61
61
62
61
61
61
25.2
⫺9.2
⫺5.5
0.5
39.7
⫺10.8
⫺4.1
3.7
⫺1.4
⫺4.0
13.1
14.7
⫺31.5
⫺4.5
⫺6.1
5.9
⬍0.0001
⬍0.0001
⬍0.0001
0.5420
⬍0.0001
⬍0.0001
⬍0.0001
⬍0.0001
0.3767
0.0003
⬍0.0001
⬍0.0001
⬍0.0001
0.0001
⬍0.0001
⬍0.0001
25.1
16.3
11.9
11.7
39.2
17.3
10.7
12.5
9.8
13.4
19.1
20.7
30.8
13.7
12.4
13.5
780.3
2,899.9
2,791.7
2,791.5
1,753.2
2,924.2
2,777.9
2,802.9
146.3
2,828.8
2,926.6
2,992.5
1,130.9
2,837.8
2,798.2
2,824.6
0.736
0.908
0.968
0.939
0.769
0.914
0.966
0.924
0.783
0.914
0.968
0.943
0.787
0.912
0.969
0.939
31
31
31
31
31
31
31
31
31
31
31
31
31
31
31
31
30.1
⫺0.7
⫺4.2
3.5
24.6
⫺10.9
⫺7.1
7.9
⫺13.8
⫺10.0
3.4
1.0
⫺31.8
⫺2.6
⫺3.1
4.6
⬍0.0001
0.5505
⬍0.0001
0.0006
⬍0.0001
⬍0.0001
⬍0.0001
⬍0.0001
⬍0.0001
⬍0.0001
⬍0.0001
0.3702
⬍0.0001
0.0237
0.0001
⬍0.0001
30.1
4.6
4.7
5.0
24.6
10.9
7.2
8.1
14.7
10.2
3.9
4.8
31.8
4.9
4.2
5.5
1,008.8
36.2
29.3
36.6
693.5
153.0
64.1
91.2
281.3
140.9
24.0
33.9
1,100.5
43.6
24.7
45.2
that the landmarks he retained were impossible to
locate. Although Simmons et al. (1990) suggested
that the method is “plagued” by difficulty and therefore is seldom used, recall that Brooks et al. (1990)
surveyed a small number of forensic investigators
who do use the method and who found it to have
considerable accuracy.
In contrast, we found the points defined by articular architecture and secondary centers of ossification to be extremely easy to identify. Greater reliance on these articular landmarks, coupled with the
linear regression approach used here (vs. Steele’s
multiple regression approach) may improve the ease
of use and accuracy of longitudinal measurements
for bone length estimation. By using the distance
between pairs of landmarks in linear regressions on
bone length, we eliminate error that would be introduced by imprecision in locating intermediate landmarks, as well as error due to inter- and intrapopulation variation in the location of intermediate
landmarks. That we found estimates of Maya bone
length using the equations of Steele (1970) to be
more accurate for equations based on longer segments than those based on shorter segments provides some support for this argument.
By discarding landmarks defined by muscle attachment sites, however, the length of bone required
to obtain an estimate becomes larger. Our equations
demand that the entire diaphysis as well as some
marginal articular bone be present in order to apply
the equations. Thus, they will not permit estimation
of extremely fragmentary remains. Nonetheless, the
equations can be used to estimate the length of
bones with broken or eroded articular surfaces, such
as femora that lack the head and neck or condyles.
Standard errors of the equations described in this
study are smaller than those obtained by Simmons
et al. (1990) for transverse measurements of small
fragments of the femur. Holland (1992) generated
equations that relate proximal tibial measures to
stature. Standard errors for his equations are comparable to the regressions of Simmons et al. (1990)
against stature for femora, which indicates that regression of proximal tibia measures on tibia length
would also be larger than the standard errors obtained here for longitudinal measurements. Thus, if
sufficient length of the diaphysis is available, estimates of bone length from longitudinal measurements should be superior to those from transverse
measurements. Of course, the longitudinal and
transverse measurement regressions should be seen
as complementary methods.
We observed that estimates of bone length using
the equations of Steele (1970), also Steele and Bramblett (1988), and Jacobs (1992) for the Maya remains
often differed significantly from measured bone
lengths. This finding confirms the observation by
Jacobs (1992) that significant interpopulation differ-
249
ESTIMATING LENGTH OF INCOMPLETE LONG BONES
TABLE 9. Proportions of long bone segments in forensic Maya sample, and in comparative series1
Bone
Males
Humerus
Femur
Tibia
Females
Humerus
Femur
Tibia
Forensic Maya
Proportion of total bone length
Segment
(Steele, 1970)
Segment
(this study)
Mean
SD
N
Maya
Terry White
Terry Black
Mississippian
European
Total length
1
2
3
4
Max length
1
2
3
4
Total length
1
2⫹3
4
5
Total length
H0–3
H3–5
H5–6
H6–7
Max length
F0–2
F2–4
F4–5
F5–6
Max length
T6–7
T2–6
T1–2
T0–1
297.4
32.8
232.4
17.7
14.2
417.6
72.7
207.8
102.2
32.3
340.9
22.1
202.2
104.7
12.5
14.0
2.7
12.0
2.4
1.8
20.0
6.2
19.0
13.0
3.6
18.0
3.5
14.0
11.0
2.2
58
56
56
58
58
66
64
62
63
65
65
60
60
63
65
1.00
0.11
0.78
0.06
0.05
1.00
0.17
0.50
0.24
0.08
1.00
0.06
0.59
0.31
0.04
1.00
0.11
0.77
0.06
0.05
1.00
0.17
0.59
0.15
0.08
1.00
0.09
0.62
0.27
0.04
1.00
0.11
0.78
0.06
0.05
1.00
0.17
0.59
0.16
0.08
1.00
0.08
0.62
0.28
0.04
1.00
0.10
0.77
0.08
0.04
1.00
0.16
0.56
0.19
0.08
1.00
0.07
0.65
0.25
0.04
1.00
0.16
0.47
0.28
0.09
1.00
0.07
0.62
0.26
0.04
Total length
1
2
3
4
Max length
1
2
3
4
Max length
1
2⫹3
4
5
Total length
H0–3
H3–5
H5–6
H6–7
Max length
F0–2
F2–4
F4–5
F5–6
Max length
T6–7
T2–6
T1–2
T0–1
271.2
28.5
212.6
16.5
13.5
386.3
65.3
191.3
99.4
28.2
312.3
18.6
185.1
97.2
11.2
12.0
2.7
10.0
2.2
2.1
21.0
5.2
15.0
11.0
3.2
16.0
3.2
17.0
8.6
1.5
24
24
24
24
24
32
31
31
32
32
30
29
29
30
30
1.00
0.11
0.78
0.06
0.05
1.00
0.17
0.50
0.26
0.07
1.00
0.06
0.59
0.31
0.04
1.00
0.11
0.78
0.06
0.05
1.00
0.17
0.60
0.15
0.08
1.00
0.08
0.64
0.25
0.04
1.00
0.11
0.78
0.06
0.05
1.00
0.16
0.60
0.16
0.08
1.00
0.08
0.65
0.26
0.04
1.00
0.10
0.77
0.08
0.04
1.00
0.16
0.57
0.20
0.08
1.00
0.07
0.66
0.25
0.04
1.00
0.16
0.46
0.30
0.08
1.00
0.07
0.62
0.26
0.04
1
Data for comparative series are from Steele (1970), Steele and McKern (1969), and Jacobs (1992). All measurements are in mm. Max,
maximum.
ences exist in the proportions of segments. Much as
he found that several of Steele’s (1970) White equations performed poorly on Mesolithic Europeans, we
observed little correlation between the success of
Steele’s equations and any a priori expectations
about affinity between the reference populations
and our Maya sample. The Mississippian equations
often estimate Maya bone length with greater error
than the Black and white equations, despite common Native American ancestry, shared maize agricultural subsistence practices, and a similarly warm
climate. Jacobs (1992) proposed that differences in
muscle activity may explain the variation, and suggested that data be collected on populations with
diverse behavioral adaptations. Indeed, we note that
the most evident differences in segment proportion
illustrated in Table 9 are those determined by the
position of landmarks defined by muscle attachment
points. However, if we limit bone length estimation
to those equations defined in Table 5, which exclude
most points defined by muscle action, these population differences in proportion may be less problematic.
While activity differences likely contribute to
these interpopulation differences, it may be significant to note that most of the equations overestimate
bone length when applied to Maya remains. The
diminutive stature of Maya skeletons is perhaps too
far removed from the mean stature of the series on
which these equations were derived to permit an
unbiased estimate of bone length. We suggest that
bone proportions are also significantly constrained
by body size. Regardless of whether the segment
proportion differences are due to activity differences
and/or allometric considerations, it is clear that estimates of bone length of Maya remains cannot be
made with confidence using the majority of the previously published equations.
The equations we have provided here are best
suited to the specific forensic context of Guatemala,
and presumably adjacent Central American nations.
The success of the El Chal tests demonstrates that
the equations perform adequately on the modern
Guatemalan population, even when Maya ethnicity
is not known. We hope that they will aid stature
estimation and the identification of forensic remains
in the ongoing human rights investigations in this
region. We also expect that the equations will perform well on archaeological human remains of the
Maya and other Mesoamerican cultures, many of
whom were taller than are the modern Maya. Additional research might be directed at collecting measurements from other populations, in order to determine whether interpopulation differences in bone
proportions hinder estimation of bone length using
the forensic Maya equations, and whether it would
250
L.E. WRIGHT AND M.A. VÁSQUEZ
be necessary to generate regression equations for
each population to be studied. Before applying our
equations to distant populations, and especially to
significantly taller populations, we recommend that
osteologists verify the results with any complete
long bones that might be available for the population in question. Complementary research on skeletal series with differing behavioral adaptations and
mean statures is needed to provide researchers with
a variety of options for estimating the length of
fragmentary long bones.
ACKNOWLEDGMENTS
We thank the members of the Área de Exumaciones and the Fundación de Antropologı́a Forense de
Guatemala for their kind collaboration in our study.
This research would have been impossible without
the various institutions that have supported their
forensic work, both financially and politically. We
thank Miguel Angel Morales for assistance with
data recording. Last, but not least, we thank Gentry
Steele for inspiration, for his helpful suggestions
during the research, and for his comments on the
manuscript.
LITERATURE CITED
Arzobispado de Guatemala, Oficina de Derechos Humanos. 1998.
Guatemala: nunca más. Informe Proyecto Interdiocesano de
Recuperación de la Memoria Historica. Guatemala: ODHAG.
Bass WM. 1987. Human osteology: a laboratory and field manual
of the human skeleton. Columbia, MO: Missouri Archaeological
Society.
Bogin B, MacVean RB. 1984. Growth status of non-agrarian,
semi-urban living indians in Guatemala. Hum Biol 56:527–538.
Brooks S, Steele DG, Brooks RH. 1990. Formulae for stature
estimation on incomplete long bones: a survey of their reliability. J Forensic Med 6:167–170.
Carmack RM. 1988. Harvest of violence. The Maya Indians and
the Guatemalan crisis. Norman, OK: University of Oklahoma
Press.
Danforth ME. 1994. Stature change in prehistoric Maya of the
Southern Lowlands. Latin Am Antiq 5:206 –211.
Equipo de Antropologı́a Forense de Guatemala. 1997. Las masacres en Rabinal: estudio histórico antropológico de las masacres
de Plan de Sánchez, Chichupac y Rı́o Negro. Guatemala City:
Editorial Serviprensa.
Feldesman MR, Fountain RL. 1996. “Race” specificity and the
femur/stature ratio. Am J Phys Anthropol 100:207–225.
Furbee L, Thomas JS, Lynch HK, Benfer RA. 1988. Tojolabal
Maya population response to stress. Geosci Man 26:17–27.
Genovés S. 1967. Porportionality of the long bones and their
relation to stature among Mesoamericans. Am J Phys Anthropol 26:67–78.
Hens SM, Konigsberg LW, Jungers WL. 2000. Estimating stature
in fossil hominids: which regression model and reference sample to use? J Hum Evol 38:767–784.
Holland TD. 1992. Estimation of adult stature from fragmentary
tibias. J Forensic Sci 37:1223–1229.
Jacobs K. 1992. Estimating femur and tibia length from fragmentary bones: an evaluation of Steele’s (1970) method using a
prehistoric European sample. Am J Phys Anthropol 89:333–
345.
Konigsberg LW, Frankenberg SR, Walker RB. 1997. Regress
what on what? Paleodemographic age estimation as a calibration problem. In: Paine RR, editor. Integrating archaeological
demography: multidisciplinary approaches to prehistoric population. Carbondale, IL: Southern Illinois University. p 64 – 88.
Konigsberg LW, Hens SM, Jantz LM, Jungers WL. 1998. Stature
estimation and calibration: Bayesian and maximum likelihood
perspectives in physical anthropology. Yrbk Phys Anthropol
41:65–92.
Martorell R. 1995. Results and implications of the INCAP follow-up study. J Nutr 125:1127–1138.
Martorell R, Kettel Khan L, Schroeder DG. 1994. Reversibility of
stunting: epidemiological findings in children from developing
countries. Eur J Clin Nutr 48:45–57.
McCullough JM. 1982. Secular trend for stature in adult male
Yucatec Maya to 1968. Am J Phys Anthropol 58:221–225.
Müller G. 1935. Zur bestimmung der Länge beschädigter Extremitatenknochen. Anthropol Anzeig 12:70 –72.
Simmons T, Jantz RL, Bass WM. 1990. Stature estimation from
fragmentary femora: a revision of the Steele method. J Forensic
Sci 35:628 – 636.
Steele DG. 1970. Estimation of stature from fragments of long
limb bones. In: Stewart TD, editor. Personal identification in
mass disasters. Washington, DC: Smithsonian Institution. p
85–97.
Steele DG, Bramblett CA. 1988. The anatomy and biology of the
human skeleton. College Station, TX: Texas A&M University
Press.
Steele DG, McKern TW. 1969. A method for assessment of maximum long bone length and living stature from fragmentary
long bones. Am J Phys Anthropol 31:215–228.
Whittington SL. 1989. Characteristics of demography and disease
in low status Maya from Classic Period Copan, Honduras.
Ph.D. dissertation, Pennsylvania State University.
Wright LE. 1994. The sacrifice of the earth? Diet, health, and
inequality in the Pasión Maya lowlands. Ph.D. dissertation,
University of Chicago.
251
ESTIMATING LENGTH OF INCOMPLETE LONG BONES
APPENDIX. Additional regression lines for estimation of total bone length, derived from forensic Maya skeletons1
Regression line
A. Humerus (sexes combined)
(H0–4) ⫽ ⫺16.558 ⫹ 0.577 * Humerus length
(H1–4) ⫽ ⫺17.334 ⫹ 0.562 * Humerus length
(H2–4) ⫽ ⫺18.046 ⫹ 0.524 * Humerus length
(H3–4) ⫽ ⫺17.743 ⫹ 0.472 * Humerus length
(H4–7) ⫽ 16.558 ⫹ 0.423 * Humerus length
B. Humerus (males)
(H0–4) ⫽ ⫺17.746 ⫹ 0.579 * Humerus length
(H1–4) ⫽ ⫺17.525 ⫹ 0.561 * Humerus length
(H2–4) ⫽ ⫺28.425 ⫹ 0.556 * Humerus length
(H3–4) ⫽ ⫺30.899 ⫹ 0.513 * Humerus length
C. Femur (sexes combined)
(F0–4) ⫽ ⫺42.021 ⫹ 0.774 * Femur max. length
(F1–4) ⫽ ⫺39.495 ⫹ 0.734 * Femur max. length
(F2–4) ⫽ ⫺43.683 ⫹ 0.606 * Femur max. length
D. Tibia (sexes combined)
(T0–3) ⫽ ⫺21.602 ⫹ 0.675 * Tibia length
(T0–4) ⫽ 17.393 ⫹ 0.623 * Tibia length
(T0–5) ⫽ 1.196 ⫹ 0.757 * Tibia length
(T1–4) ⫽ 14.623 ⫹ 0.594 * Tibia length
(T1–5) ⫽ ⫺1.561 ⫹ 0.729 * Tibia length
(T2–6) ⫽ ⫺16.913 ⫹ 0.644 * Tibia length
(T2–7) ⫽ ⫺25.335 ⫹ 0.732 * Tibia length
1
r2
N
F
SE
0.754
0.766
0.688
0.623
0.622
80
76
79
78
80
239.1
242.3
170.1
125.4
128.4
10.83
10.48
11.64
12.23
10.83
0.685
0.707
0.616
0.598
57
57
56
55
119.5
122.8
86.6
78.0
15.78
15.09
17.77
17.20
0.743
0.726
0.623
96
94
93
271.2
243.6
150.2
19.16
19.16
20.11
0.663
0.714
0.780
0.686
0.769
0.675
0.738
93
95
93
95
93
89
87
178.8
232.2
322.7
202.9
303.8
181.1
239.5
16.80
13.58
14.01
13.87
13.91
15.90
15.76
All measurements, estimated bone lengths, and standard errors are in mm. Max., maximum.
Документ
Категория
Без категории
Просмотров
2
Размер файла
262 Кб
Теги
length, forensic, incomplete, long, guatemalan, standards, estimating, bones
1/--страниц
Пожаловаться на содержимое документа