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Estimating body height from ulna length: Need of a populationspecific formula

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In forensic work, it is important to be able to estimate body height from a variety of bones. It is well known that estimates based on upper limb long bone measurements are highly accurate. This report describes an equation devised for height estimation in the Turkish population based on ulna length, and compares the results with ulna-based formulae developed for several other populations. Anthropometric measurements were recorded for 254 healthy male subjects aged 18-45 years. The subjects were randomly divided into equal-sized study and control groups. A population-specific formula for height was created based on ulna length of the subjects in the study group. This formula and 14 other formulae reported in the literature were applied to the control group and the mean estimation errors were statistically compared. Analyses indicated that the population-specific equation gave the most accurate results. In addition, the formula devised by Trotter and Gleser for Mongoloids has yielded more reliable results than other for-mulae. The Trotter-Gleser formulae for whites are the ones most frequently used in Turkey today; however, these equations do not yield reliable height estimates for our population.
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Eurasian Journal of Anthropology
Eurasian J. Anthropol. 1(1):1117, 2010
Estimating body height from ulna length: need of a
population-specific formula
İzzet Duyar1 and Can Pelin2
1Department of Sociology, Gaziantep University, Gaziantep, Turkey
2Department of Anatomy, Baskent University, Ankara, Turkey
Received September 15, 2009
Accepted January 12, 2010
Abstract
In forensic work, it is important to be able to estimate body height from a variety of bones. It is
well known that estimates based on upper limb long bone measurements are highly accurate.
This report describes an equation devised for height estimation in the Turkish population based
on ulna length, and compares the results with ulna-based formulae developed for several other
populations. Anthropometric measurements were recorded for 254 healthy male subjects aged
18-45 years. The subjects were randomly divided into equal-sized study and control groups. A
population-specific formula for height was created based on ulna length of the subjects in the
study group. This formula and 14 other formulae reported in the literature were applied to the
control group and the mean estimation errors were statistically compared. Analyses indicated
that the population-specific equation gave the most accurate results. In addition, the formula
devised by Trotter and Gleser for Mongoloids has yielded more reliable results than other for-
mulae. The Trotter-Gleser formulae for whites are the ones most frequently used in Turkey
today; however, these equations do not yield reliable height estimates for our population.
Keywords: Forensic anthropology, stature estimation, ulna length
Introduction
Calculating stature from bones is an important element of forensic science. Of all the
mathematical methods used, regression formulae based on long-bone measurements
yield the most accurate results. Estimates based on long bones of the lower limb are
the most precise, but those based on upper limb long bone measurements are also reli-
able. The ulna is a long bone that is often used for body height estimation. A number
of authors have investigated stature estimation based on measurements of the ulna
and other bones of the upper limb (Rao et al., 1989; Badkur and Nath, 1990; Mall et al.,
2001).
Several authors have offered regression equations based on long bones
(Breitinger, 1937; Telkkä, 1950; Trotter and Gleser, 1958; Muñoz et al., 2001); however it
Corresponding author: Department of Sociology, Faculty of Arts and Sciences, Gaziantep University, Şehitkamil,
27310 Gaziantep, Turkey (e-mail: izduyar@yahoo.com)
ISSN: 2166-7411 Moment Publication ©2010
Duyar and Pelin
12
is well known that formulae that apply to one population do not always give accurate
results for other populations. Pearson first reported this in 1899, stating that a regres-
sion formula derived for one population should only be applied to other groups with
caution. In 1929, Stevenson confirmed the existence of inter-populational differences
with respect to stature estimation (Lundy, 1985). Most studies since that time have
stressed that regression formula for stature estimation should be population-specific
(Krogman and İşcan, 1986).
The formulae derived by Trotter and Gleser (1958) are the ones most frequently
used for stature estimation. In Turkey, the Trotter-Gleser formula for whites has been
most widely used for forensic and anthropological studies; however, the accuracy of
this formula for the Turkish population has not been evaluated in detail. This article
presents a new regression formula based on ulna length for stature estimation in the
Turkish population. Results using this formula were compared to those generated
with other ulna-length-based formulae previously derived for different populations.
Subjects and methods
The study involved 254 randomly selected healthy males aged 18-45 years (mean age
23.10 ± 4.72 years, SD). The subjects originated from several cities in Turkey, but all
were living in Ankara at the time of the study. Each subject was randomly assigned to
either the study group (n = 127) or the control group (n = 127). There was a Gaussian
distribution for stature in both groups (Figures 1 and 2). Kolmogorov-Smirnov tests
verified the normality of the distribution of height in the study group (Z = 0.595, P =
0.871) and control group (Z = 0.640, P = 0.808).
Each subject’s body height and forearm (ulna) length were measured using a
Martin-type anthropometer. For height measurement, the subject stood in bare feet
with his back to the anthropometer. The head was adjusted so that the Frankfurt plane
was horizontal, and was then tilted slightly upwards by applying gentle force to the
mastoid processes and zygomatic bones (Cameron et al., 1981). For ulna length, the
subject’s elbow was flexed to 90 with fingers extended in the direction of the long axis
of the forearm, and the distance between the most proximal point of the olecranon and
the tip of the styloid process of the ulna was measured (Martin et al., 1988). All meas-
urements were recorded to the nearest millimeter. The means for age, stature and ulna
length in the study and control groups are listed in Table 1. There were statistically no
significant differences between the groups with respect to these parameters.
Table 1: Comparison of the general characteristics of the study and control groups
Study group
(n = 127)
Control group
(n = 127)
Mean
SD
Mean
SD
F
Sig.
Age (years)
22.96
4.84
23.24
4.62
0.219
0.640
Body height (mm)
1755.07
94.25
1752.28
94.51
0.560
0.814
Ulna length (mm)
275.49
18.12
275.37
18.21
0.003
0.959
Eurasian J. Anthropol. 1(1):1117, 2010
13
Figure 1: Distribution of the stature in study group.
Figure 2: Distribution of the stature in control group.
The scatterplots showing the relationship between the ulna length and stature
both in the study and control groups take place in Figures 3 and 4. We derived the
following linear regression equation for height estimation (in millimeters) using the
measurement data from the study group:
Stature = 3.958 * ulna length + 664.72 83.28
The statistical details of the equation were given in Table 2.
Table 2: Regression equation for stature estimation from ulna length
Unstandardized
coefficients
Standardized
coefficients
t
Sig.
B
Std. error
Beta
Constant
664.721
83.283
7.981
0.000
Ulna
3.958
0.302
0.761
13.120
0.000
Dependent variable: stature
Duyar and Pelin
14
Figure 3: Scatterplot (with 95% confidence interval) for ulna length and stature in study group.
Figure 4: Scatterplot (with 95% confidence interval) for ulna length and stature in control
group.
This new formula was applied to each control subject, and the mean height for
the group was calculated. The mean height estimated by our new formula was com-
pared with the mean of the true heights in the group. In addition, 14 other different
equations for estimating stature from ulna length were also applied to the control
group, and the mean height for each set was calculated. The accuracy of the 15 formu-
lae was evaluated using the paired t-test. All statistical analysis was done using the
software SPSS 11.5.
Results
The means and standard deviations for the subjects’ heights calculated with our new
formula and with the other 14 equations are listed in Table 3. The differences between
Eurasian J. Anthropol. 1(1):1117, 2010
15
true and estimated height with the 15 formulae and the statistical analysis of these
differences are shown in Table 4. The new formula provided the closest estimation of
true height, with a mean overestimation of +0.27 cm. The formula by Sağır yielded the
next most accurate result (+1.30 cm), followed by the Trotter-Gleser formula for Mon-
goloids and the Allbrook formula for the British population, respectively. The estima-
tion error for the later two formulae was close to 2 cm below true height. The Lundy
formula for South Africans gave the least accurate results, with a mean underestima-
tion of 20.71 cm.
Statistical analysis with the paired t-test revealed that the estimates from all ex-
cept our new formula were significantly different from true height (p<0.001 for all),
whereas the new formula was very accurate (P = 0.577).
Table 3: Estimated stature in the control group using the 15 different regression formulae
(n=127)
Author/Source
Population
Mean
Std. Deviation
Actual stature
Turkish
175.28
9.45
This study
Turkish
175.49
7.24
Sağır (2000)
Turkish
176.54
6.05
Trotter-Gleser (1958)
Mongoloids
173.31
6.36
Allbrook (Krogman and İşcan, 1986)
British
173.23
5.60
Trotter-Gleser (1958)
Mexicans
172.62
6.51
Trotter-Gleser (1958)
Whites
179.12
6.88
Trotter-Gleser (1958)
Blacks
170.91
5.85
Trotter-Gleser (1958)
Puerto Ricans
170.84
6.04
Shitai (Krogman and İşcan, 1986)
South Chinese
168.34
5.74
Badkur and Nath (1990)
Indians
167.74
2.54
Allbrook (Krogman and İşcan, 1986)
Nilo-Hamit
167.74
5.96
Munoz et al. (2001)
Spanish
186.97
6.04
Allbrook (Krogman and İşcan, 1986)
Nilotic
162.06
6.57
Allbrook (Krogman and İşcan, 1986)
Bantu
161.55
5.93
Lundy (Krogman and İşcan, 1986)
South Africans
154.52
5.38
Table 4: Paired t-test results for comparisons of differences between true height and the heights
estimated by the 15 formulae investigated
Estimated True Height
Population
Mean*
Std. Devia-
tion
t
Sig.
(2-tailed)
Our formula True height
Turkish
0.27
5.39
0.56
0.577
Sağır – True height
Turkish
1.30
5.63
2.63
0.010
Trotter-Gleser True height
Mongoloids
-1.92
5.54
-3.91
0.000
Allbrook True height
British
-2.00
5.79
-3.89
0.000
Trotter-Gleser True height
Mexicans
-2.61
5.51
-5.34
0.000
Trotter-Gleser True height
Whites
3.89
5.44
8.07
0.000
Trotter-Gleser True height
Blacks
-4.31
5.70
-8.53
0.000
Trotter-Gleser True height
Puerto Ricans
-4.39
5.64
-8.78
0.000
Shitai True height
South Chinese
-6.89
5.74
-13.53
0.000
Badkur-Nath True height
Indians
-7.49
7.50
-11.25
0.000
Allbrook True height
Nilo-Hamit
-7.49
5.66
-14.91
0.000
Munoz True height
Spanish
11.74
5.64
23.47
0.000
Allbrook True height
Nilotic
-13.17
5.50
-27.01
0.000
Allbrook True height
Bantu
-13.67
5.67
-27.16
0.000
Lundy True height
South Africans
-20.71
5.88
-39.72
0.000
* Negative values indicate underestimates, and positive values indicate overestimates.
Duyar and Pelin
16
Discussion
Height-estimation formulae based on ulna length show similar levels of accuracy to
calculations based on the length of other upper limb long bones. This is supported by
the standard errors of the estimations reported in several studies. For example, the
standard errors of estimations from formulae that Trotter and Gleser (1958) devised
for several ethnic groups (whites, blacks, Mongoloids and Mexicans) based on
humerus, radius, and ulna length were quite similar (approximately 4-4.8 cm). On the
other hand, the range in estimation error for the Trotter-Gleser equations based on
long bones of the lower limb is 3.0-4.0 cm. Though estimates of body height based on
lower limb long bones are more accurate, the results from formulae based on upper
limb long bones are only slightly less precise. In this study, we developed a new ulna-
based height estimation formula. We chose this bone because, compared to other
bones of the upper limb, it is easier to get a more accurate measure of ulna length in
living subjects.
Authors have underlined the need for population-specific stature estimation
formulae for more than 100 years. The main reason for this is that the ratios of various
body parts to stature differ from one population to another. In addition to ethnic dif-
ferences, secular trends (Meadows and Jantz, 1995) and even environmental factors,
such as socioeconomic and nutritional status, can influence body proportions (Malina,
1991; Duyar, 1997). Our findings in this study of Turkish males also support the need
for population-specific formulae. When we used equations based on other populations
to estimate stature in our subjects, the lowest underestimation was 20.71 cm and the
highest overestimation was 11.74 cm. In contrast, the new population-specific formula
that we devised yielded a mean overestimation of 0.27 cm, and this difference from
true height was not statistically significant. We also found that another Turkish popu-
lation-specific equation created by Sağır (2000) showed good accuracy for stature esti-
mation in our subjects. This formula resulted in a mean overestimation of 1.3 cm. Alt-
hough the Sağır equation was not as accurate as our new formula, it outperformed all
the other population-based formulae we tested.
In a previous study, we emphasized the importance of population-specific for-
mulae for height estimation from tibia length (Pelin and Duyar, 2002, 2003). In that
report, the mean error with a newly derived equation specific for the Turkish popula-
tion was only +0.1 cm. We found that another Turkish-population-specific formula by
Sağır resulted in 0.06 cm overestimation. When we tested all the other tibia-based
height estimation formulae published in the literature, an error range of -0.65 to +18.94
cm was found, excluding the Trotter-Gleser formula for Mongoloids (-0.01 cm).
Over the years, various authors’ stature formulae have been used in forensic cases and
anthropological studies in Turkey. The first anthropological studies conducted in our
country employed the Pearson formula, and the Trotter-Gleser equation for whites has
been most widely used in recent years. However, in the present study, we calculated a
mean height overestimation of approximately 4 cm with this formula, in comparison
to mean underestimation of approximately 2 cm with the Trotter-Gleser equation for
Mongoloids. The above-mentioned previous report on stature estimation from tibia
length also noted that estimates from the Trotter-Gleser formula for Mongoloids were
more accurate (+0.01 cm) than those for the Trotter-Gleser formula for whites (mean
overestimation of 3.14 cm) (Pelin and Duyar, 2002, 2003). Our present study and this
investigation of tibia-based equations indicate that, for estimating height in Turkish
subjects, the Trotter-Gleser formula for Mongoloids is more accurate than the Trotter-
Gleser formula for whites.
Eurasian J. Anthropol. 1(1):1117, 2010
17
In conclusion, this study shows that the TrotterGleser formula for whites,
which is currently widely used for forensic studies in our country, is not accurate for
the Turkish population. We stress that formulae used for estimating stature based on
long bones should be population-specific.
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... However, there are differences in the relationship between body proportions given to genetic and environmental factors [1,10,11]. Although height estimation from lower limb bones such as the tibia is said to be more precise, the use of the upper limb bones such as the ulna is also reliable [12]. The ulna is the most preferred bone for height estimation in living subjects due to the ease of getting accurate measurements [12]. ...
... Although height estimation from lower limb bones such as the tibia is said to be more precise, the use of the upper limb bones such as the ulna is also reliable [12]. The ulna is the most preferred bone for height estimation in living subjects due to the ease of getting accurate measurements [12]. Previous studies have shown that estimating height using the mathematical method may be fraught with errors, particularly for shorter or taller people [10]. ...
... However, this was not a universal observation since population-specific models from the Amhara region of Ethiopia and Mexican Maya out-performed the current models in estimating the height of Ghanaian males [30,41]. When published ulna-and tibia-based height estimating equations were applied in a Turkish healthy male adults population, it was observed that the study population-specific model equation was more precise, however, a model for a Mongoloid population was as well comparable (bias: ulna= − 1.92 cm, tibia= − 0.01 cm) to the population-specific model [12]. However, a White population-based equation was less precise compared to the Mongoloid's. ...
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Whether one population-specific model for sex and height estimation can be extrapolated to another population has been a source of controversy. This study sought to develop and compare models for sex and height estimation from the percutaneous lengths of the ulna and tibia in a Ghanaian population. The study was cross-sectional from January to June 2021 at the University for Development Studies, Tamale. There were 191 (male=89, female=102) participants between 18 and 30 years of age. The standing height, ulna length (UL) and tibial length (TL) were measured following recommended anthropometric techniques. The sample was randomly assigned to training (60%) and holdout (40%) samples. Discriminant models for sex and linear regression models for height estimations were formulated using the training sample. The new models and other population-specific models were tested on the holdout sample for reliability using the Bland-Altmann method, Cohen’s d for height and cross-validation for sex estimations. The observed and the estimated height of males and females using UL (bias, d: male=2.75, 0.46; female= 0.73, 0.13), TL (bias, d: male= 2.74, 0.42; female= 1.50, 0.28) or UL+TL (bias, d: male= 2.76, 0.42; female= 0.86, 0.14) were not statistically different. The average sex estimation accuracy from the holdout sample was better in the multivariable UL+TL (82.9%) than in the univariable UL (76.3%) or TL (55.3%). Models based on UL [bias: 0.50 (95%CI: − 8.10 to 9.09), d: 0.07] from Kumasi-Ghana and TL [bias: − 0.01 (95%CI: − 10.37 to 10.34), d: 0.00] from the Amhara Region-Ethiopia were most reliable for estimating male’s height. For female height estimation, models based on UL [bias: − 0.62 (95%CI: − 12.08 to 10.83), d: 01.2] from Tamale-Ghana and TL [bias: − 3.72 (95%CI: − 16.81 to 9.37), d: 0.76] from the Amhara Region-Ethiopia were most reliable. However, the other models deviated in the range of − 17.09 cm [Khasi tribe-India (UL)] to 0.54 cm [Kumasi-Ghana (UL)] in male height estimation and − 9.86 cm [Barcelona-Spain (TL)] to 1.05 cm [Kumasi-Ghana (UL)] in estimating female height. Cohen’s d was more precise than the Bland-Altmann method in assessing the reliability of height estimation models. Height can be estimated using UL, TL or UL+TL, however, it is recommended to use UL+TL for sex estimation in a Ghanaian population. Although the use of population-specific models (UL and TL) for sex and height estimations is recommended, other models outside the target population may be applicable. Additionally, when measuring the reliability of height estimation models (UL and TL), Cohen’s d should be preferred to the Bland-Altmann method.
... The accuracy rates of generic formulae versus specific equations have resulted in contradictory findings. In some studies, generic equations obtained higher accuracy than specific ones [20,21], whereas others yielded higher estimation accuracy using specific equations [22][23][24][25][26][27]. ...
... However, the SEE values of these generalized equations are remarkably higher than we found in our study, suggesting that calculations specific to stature groups yield more accurate estimates than generic equations. The findings of other studies also support these results [22,[24][25][26][27][28]. Furthermore, while another study in Spanish individuals reported low SEE for stature group regression equations based on multiple long bone lengths [8], our stature-group-specific equations have even lower SEE. ...
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Background Estimation of stature is usually done by measurement of the long bones. Although hand and foot dimensions are useful in predicting stature, they are population-specific. Methods We compared the accuracy of predicting stature by hand and foot dimensions, with long bone (tibia and ulna) lengths, and developed a stature predictive regression formula from the parameters used for the sample population in Kolhapur. We recorded hand and foot measurements and long bone measurements of 1000 consenting participants 18–50 years of age using a stadiometer for height and an anthropometric rod compass for other measurements. Correlation between the variables and stature was determined using Pearson’s correlation analysis (p<0.05). A multiple linear regression formula was derived for the prediction of stature. Results A positive correlation was observed between mean stature and foot length ( r =0.67, p<0.05), tibia ( r =0.66, p<0.05), ulna ( r = 0.75, p<0.05) and hand length ( r =0.69 left, r =0.72 right, p<0.05). There was no correlation between foot breadth and stature. Multiple linear regression analysis of hand and foot dimensions returned R2=62.96 and standard error of estimate 4.689 with comparable computed and experimental measurements. Conclusion The dimensions of the hand and foot can be used to predict stature. The formula derived from the multiple regression analysis incorporating hand and foot dimensions is a good fit to estimate stature in the study population.
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Latar Belakang: Penilaian status gizi pasien rawat inap di rumah sakit di Indonesia saat ini masih sulit dilakukan karena kondisi pasien yang harus berbaring di tempat tidur. Pengukuran antropometri menjadi bagian dari penilaian status gizi sebagai dasar perhitungan kebutuhan gizi pasien dan untuk menentukan risiko timbulnya masalah gizi. Penelitian di Amerika, Eropa, India dan Thailand menunjukkan bahwa panjang tulang ulna telah terbukti reliabel dan presisi dalam memprediksi tinggi badan seseorang. Tujuan: Penelitian ini bertujuan untuk menganalisis perbedaan hasil tinggi badan berdasarkan panjang tulang ulna dengan tinggi badan aktual pada pria dan wanita dewasa di Kota Semarang.Metode: Penelitian ini merupakan penelitian cross sectional. Jumlah sampel dalam penelitian ini adalah 103 orang yang terdiri dari 55 wanita dan 48 usia 19 – 29 tahun. Data yang diambil yaitu data karakteristik subjek, tinggi badan dan panjang ulna. Subjek penelitian diambil secara consequtive sample yang diberikan informed consent secara verbal. Data panjang ulna subjek kemudian dimasukkan dalam tiga formula estimasi tinggi badan dari penelitian sebelumnya.Hasil: rerata tinggi badan aktual pria 167,9 cm dan wanita 156,9 cm. Rerata estimasi tinggi badan rumus Ilayperuma et al, Thummar et al, dan Pureepatpong et al berturut – turut adalah untuk pria 168,24 cm, 166,28 cm, dan 167,61 cm; dan untuk wanita 157,77 cm, 153,79 cm, dan 155,88 cm. Selisih tinggi badan aktual dengan estimasi tinggi badan berturut-turut adalah untuk pria 0,35 cm, -1,62 cm, dan -0,28 cm; dan wanita 0,86 cm, -3,12 cm, dan -0,28 cm. Selisih terbesar terdapat pada rumus estimasi Thummar et al yaitu pada pria -1,62 cm dan pada wanita -3,12 cm. Tidak ada perbedaan antara tinggi badan aktual dengan estimasi tinggi badan dari panjang ulna rumus Ilayperuma et al dan Pureepatpong et al pada pria dan wanita (p>0,05) dan ada perbedaan antara tinggi badan aktual dengan estimasi tinggi badan dari panjang ulna rumus Thummar et al pada pria dan wanita (p<0,05). Penelitian ini menghasilkan formula regresi linier dari tinggi badan dan panjang ulna subjek, yaitu untuk pria = 76,053 + 3,405 x ulna lengan kiri; untuk wanita = 81,927 + 3,034 x ulna lengan kiri.Kesimpulan: rumus Ilayperuma et al (pria= 97,252 + 2,645 x panjang ulna dan wanita= 68,777 + 3,536 x panjang ulna) dan Pureepatpong et al (pria= 64,605 + 3,8089 x panjang ulna dan wanita= 66,377 + 3,5796 x panjang ulna) dapat diterapkan di Semarang.
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Most forensic and biological anthropological studies use the stature-estimation formulae developed by Trotter and Gleser (1). In recent decades, studies of morphological differences between populations have indicated that population-specific formulae are necessary to obtain accurate estimates. A number of equations have been devised for the Turkish population. Previously, we introduced a “general formula” and three “stature-group-specific formulae” based on tibial length. The purpose of the present study was to determine whether formulae in the literature are suitable for estimating height in the Turkish population. To make this assessment, we compared the accuracy of formulae designed for Turkish people to the accuracy of formulae devised for other populations. We also evaluated the accuracy in short, medium, and tall height groupings. The formulae were tested on 110 healthy Turkish male adults, with estimated height compared to true height in each case. Analysis showed that the Trotter-Gleser formula for Mongoloids was most accurate for estimating stature in the study group as a whole. The formulae of Sag ˘ır (9) for the Turkish population and our previously published (6) “general formula” were the next most accurate methods, respectively. When the 110 subjects were categorized as short (1652 mm and below), medium (1653 to 1840 mm), and tall (1841 and above), the stature-group-specific formulae calculated in the present study were more accurate than all other equations for subjects at the height extremes. The results of this study indicate that staturegroup-specific formulae are more reliable for forensic cases.
Conference Paper
Most forensic and biological anthropological studies use the stature-estimation formulae developed by Trotter and Gleser (1). In recent decades, studies of morphological differences between populations have indicated that population-specific formulae are necessary to obtain accurate estimates. A number of equations have been devised for the Turkish population. Previously, we introduced a "general formula" and three "stature-group-specific formulae" based on tibial length. The purpose of the present study was to determine whether formulae in the literature are suitable for estimating height in the Turkish population. To make this assessment, we compared the accuracy of formulae designed for Turkish people to the accuracy of formulae devised for other populations. We also evaluated the accuracy in short medium, and tall height groupings. The formulae were tested on 110 healthy Turkish male adults, with estimated height compared to true height in each case. Analysis showed that the Trotter-Gleser formula for Mongoloids was most accurate for estimating stature in the study group as a whole. The formulae of Sagur (9) for the Turkish population and our previously published (6) "general formula" were the next most accurate methods, respectively. When the 110 subjects were categorized as short (1652 mm and below), medium (1653 to 1840 mm), and tall (1841 and above), the stature-group-specific formulae calculated in the present study were more accurate than all other equations for subjects at the height extremes. The results of this study indicate that stature-group-specific formulae are more reliable for forensic cases.
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The mathematical and anatomical methods of estimating living stature from long limb bones are discussed. In forensic cases, when one has a nearly complete skeleton, the anatomical method is preferable to the mathematical method. The anatomical method may also be used to derive stature estimation equations in samples where living statures or cadaver lengths are unavailable, such as some dissection hall and museum collections.
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Allometric secular changes in the six long limb bones for White and Black males from the mid 1800s to the present are examined. Long bone lengths are available from the Terry collection and WWII casualties. We conducted two types of analysis to reveal secular changes. First, allometry scaling coefficients were derived by regressing log bone length onto log stature. These showed that the femur, tibia and fibula were positively allometric with stature, while the humerus, radius and ulna were isometric. The lower limb bones were more positively allometric in the WWII sample than in the Terry sample. Second, secular changes in length of femur and tibia and in the tibia/femur ratio were evaluated, using modern forensic cases in addition to the Terry and WWII samples. This analysis shows that secular increase in lower limb bone length is accompanied by relatively longer tibiae. Secular changes in proportion may render stature formulae based on nineteenth century samples, such as the Terry collection, inappropriate for modern forensic cases. The positive allometry of the lower limb bones argues against using simple femur/stature ratio, which assumes constant proportionality, as an alternative to regression equations.
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The estimation of stature from of a variety of bones is an important aspect of forensic work. In order to obtain reliable results, it is important to have comparative data obtained from the same population group as the skeletal remains. However, lack of up to date information on the population groups of Southern Europe makes the estimation of stature from bones in this area subject to possible error. In this study, the stature of 104 healthy adults from Spain was measured, and an anteroposterior teleradiograph of the right lower and the right upper limb of every subject in the study was made in order to measure the lengths of the femur, tibia, fibula, humerus, cubitus and ulna. Pearson's regression formulae were obtained for both limbs. In males, we found the femur to be the most accurate predictor of stature (R = 0.851), whereas in females best results were obtained with the tibia (R = 0.876).