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Eurasian Journal of Anthropology

Eurasian J. Anthropol. 1(1):11−17, 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):11−17, 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):11−17, 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):11−17, 2010

17

In conclusion, this study shows that the Trotter–Gleser 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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