ANTHROPOLOGICAL SCIENCE Vol. 000, 000 000, 2005 A new method of stature estimation for forensic anthropological application IZZET DUYAR *, CAN PELIN 2, RAGIBA ZAGYAPAN 2 Institute of Forensic Medicine, Ankara University, Dikimevi, 06590 Ankara, Turkey 2 Department of Anatomy, Baskent University Faculty of Medicine, Baglica, Etimesgut, 06530 Ankara, Turkey Received 7 December 2004; accepted 2 May 2005 Abstract In forensic and anthropological studies, body height is usually estimated from a single regression formula of the population of interest. The aim of this study was to test the accuracy of regression formulae devised for different stature groups (short, medium, tall) within the same population. Our study is based on 242 adult male subjects aged 8. 44.6 years. Body height, tibia length, and ulna length were measured by standard anthropometric techniques. The subjects were randomly divided into a study group (Group, n = 2) and a cross-validation group (Group 2, n = 2). In the first stage of the study, general regression formulae based on ulna length, tibia length, and a multiple equation based on ulna and tibia lengths were created for Group, and these equations were tested using the data and actual heights of the Group 2 subjects. In the second stage of the study, stature group-specific formulae were constructed for the same variable(s) (ulna length, tibia length, and both of them). Since the body height of the victims is unknown in cases for which estimations need to be made, Group 2 was categorized according to long bone (ulna, tibia, and ulna + tibia) lengths, using the 5th and 85th percentiles as cut-off points. Each set of group-specific formulae were tested with the cross-validation sample. The differences between the true and estimated heights were evaluated using the paired t-test, and results of the general formulae were compared with those of each of the stature group-specific formulae. Our results suggest that stature group-specific formulae give more accurate estimates of height, and that this is particularly significant for individuals who are short or tall relative to the average of a population. Key words: forensic anthropology, stature estimation, stature group-specific formulae, ulna, tibia Introduction In forensic cases, stature (or body height) is usually estimated using anatomical and mathematical techniques (Lundy, 985). In the anatomical method, skull height, height of vertebral column, and length of lower limb (including talus and calcaneus) are added, and a correction factor for soft tissues is applied. With mathematical methods, stature is estimated from independent variables, such as long bone lengths, using equations that reflect the linear relationship between stature and the variable(s). The anatomical method yields more accurate results than mathematical methods. However, the former cannot be applied unless almost all components of the skeleton are available. In forensic cases, when mutilated body parts or incomplete skeletal material are available, body height can only be estimated indirectly based on measurements of isolated body parts or bones. In general, mathematical estimates of stature are derived using a single general formula that is specific to the population of interest. Measurements from various bones or body * Corresponding author. e-mail: izduyar@yahoo.com phone: +90-32-39-27-34; fax: +90-32-39-20-77 Published online 30 November 2005 in J-STAGE (www.jstage.jst.go.jp) DOI: 0.537/ase.0427 parts have been used to calculate stature in this way. The most accurate results have been obtained by using regression equations based on long bone lengths, especially those of the lower limb. However, it is well known that a formula that is devised for one population does not necessarily yield reliable results for another (Krogman and Iscan, 986; Rösing, 988). Furthermore, stature estimates based on the classical regression method are not reliable for individuals who are at the height extremes (tall or short) in their population. In general, the height of tall individuals is underestimated and the height of short individuals is overestimated (Trotter and Gleser, 958; Sjøvold, 990, 2000; Duyar and Pelin, 2003). In previous research that aimed to reduce error in stature estimation, we devised separate equations for people in three different categories of stature groups (short, medium, and tall), and found that estimates based on each stature group were more accurate than estimates derived from a single general formula (Duyar and Pelin, 2003). In another study, we tested the value of this new stature group-specific method in forensic cases (Pelin and Duyar, 2003). In both these earlier investigations, the independent variable used for stature estimation was only the length of the tibia. In the present study ulna length was added, and a multivariate regression was evaluated. In the above-cited studies, the devised formulae were tested with a cross-validation sample which was grouped 2005 The Anthropological Society of Nippon
2 I. DUYAR ET AL. ANTHROPOLOGICAL SCIENCE according to their known stature. In anthropological and forensic applications, however, stature is generally unknown, so it is hard to determine to which stature group an individual belongs. The main aim of this study was therefore to test the functions based on stature group categorizations based on long bone lengths. Subjects and Methods The subjects of the present study were 242 healthy males aged 8. 44.6 years (mean age 23.63, SD 6.58 years). The subjects were from several Turkish cities and a variety of socioeconomic backgrounds, but were living in Ankara at the time of the study. Body height and percutaneous ulna and tibia lengths were recorded for each subject. Ulna and tibia lengths were chosen because their lengths could easily be taken in living individuals, percutaneously by use of an anthropometer. Furthermore, these long bone lengths are known to be strongly correlated to body height. We took all measurements using standard anthropometric equipment and techniques. Stature was measured with the subject standing in bare feet with his back to the anthropometer, and with the head adjusted such that the Frankfurt plane was horizontal (Cameron et al., 98). Ulna length was measured with the forearm flexed at a 90 degree angle, and was recorded as the distance from the most proximal point of the olecranon process to the most distal point of the styloid process (Martin et al., 988). Tibia length was recorded as the distance from the most proximal point of the medial condyle to the most distal point of the medial malleolus (Martin et al., 988). All the measurements were recorded to the nearest millimeter. Each subject was randomly assigned to either the study group (Group, n = 2) or the cross-validation group (Group 2, n = 2) using the Statistical Package for Social Sciences (SPSS) random selection function. Linear regression equations were devised using the measurement data from the study group subjects. Data from the cross-validation group were then used to test these equations. In the first stage of the study, a single formula was devised using the measurements from Group, and its accuracy was tested using the known heights of the Group 2 subjects. The second stage of the study was organized in four steps. In the first step the Group subjects were categorized according to stature, with the 5th and 85th percentiles used as cut-off points. These percentiles were selected since they nearly reflect ± standard deviation of a population showing a normal distribution. Individuals of body height 648 mm or less were identified as short (n = 8), those between 649 and 844 mm were identified as medium (n = 88), and those 845 mm or taller were identified as tall (n = 5). In the second step we devised a separate regression equation for each of these stature groups using the Group measurement data. In the third step, the Group 2 subjects were categorized separately according to tibia length, ulna length, and the sum of the lengths of the ulna and tibia. In the final step the stature group-specific regression equations were tested using the appropriate groups of the cross-validation sample. The regression and other analyses were done using the subroutines of SPSS for Windows, version.5. Results The total combined sample showed a Gaussian distribution of stature. Coefficients of skewness and kurtosis were 0.9 and 0.80, respectively. Kolmogorov-Smirnov s one-sample test also verified the normal distribution of the total sample (Z = 0.808, P = 0.53). Both the study and cross-validation samples were also Gaussian (Group : Z = 0.59, P = 0.876; Group 2: Z = 0.827, P = 0.502). The basic statistics of stature and the long bone lengths are shown in Table. The univariate and multivariate regression equations based on the data from Group are given in Table 2. These equations were then applied to the Group 2 subjects, the results of which are shown in Table 3. It can be seen that the estimates based on the general formulae were quite accurate. The mean difference between the true and predicted heights ranged between. to 2.2 mm, and were not significant according to the paired t-test (P > 0.05). In the second phase of the study, the linear regression equations were constructed for each stature group (short, medium, tall) using the Group measurement data (Table 4). Both standard errors of the estimates (SEE) and R 2 values for the equations for all stature groups were lower than those for the single general formula for each variable (compare Table 2 and Table 4). The stature group-specific formulae were then applied to the cross-validation sample categorized according to the independent variables. Categorization was done based on the available material (ulna and tibia lengths), since the body height of the victim is generally unknown in forensic cases for which stature needs to be estimated. For this categorization, the 5th and 85th percentile values of the long bone lengths were taken as cut-off points; for the ulna, 254 mm and below were categorized as short, 255 294 mm as medium, and 295 mm and above as long; for the tibia 357 mm and below were categorized as short, 358 422 mm as medium, and 423 mm and above as long; for ulna + tibia, Table. General anthropometric characteristics of the study group (Group ), cross-validation group (Group 2), and total sample Variable Group (n = 2) Group 2 (n = 2) Total (n = 242) Mean SD Min Max Mean SD Min Max Mean SD Min Max Body height 743.9 8.82 523 950 756.8 9.7 492 200 750.3 9.28 492 200 Ulna length 273.6.68 283 37 276.5.94 234 326 275.0.82 234 326 Tibia length 389. 2.74 332 467 392.9 3. 326 475 39.0 2.93 326 475 Values are in mm.
Vol. 3, 2005 Table 2. General regression equations based on the Group data (in mm) Variable Regression equations SEE R 2 Ulna Stature = 629.83 + 4.072 ulna 55.89 0.60 Tibia Stature = 623.56 + 2.879 tibia 39.42 0.802 Ulna and tibia Stature = 538.66 + 0.984 ulna + 2.405 tibia 38.22 0.85 SEE, standard error of estimate. 65 mm and below were categorized as short, 66 72 mm as medium, and 73 mm and above as long. The mean difference between the actual and estimated heights for each category and the corresponding statistical results are shown in Table 5, together with results of each stature group based on the general formulae. When the stature group-specific formulae were applied to the stature groups categorized by long bone lengths, all the estimations (except for the medium category of tibia) were found to be more reliable than those obtained from the general formulae. With the ulna-based estimations, in individuals with short ulnae, the absolute mean difference between the estimated and true heights decreased by over 22 mm in comparison with that of the general formula. This decrease of mean difference was also observed in individuals with long and medium ulnae (absolute mean difference of 8.3 and 3.8 mm, respectively). The stature group-specific equations of the tibia also gave more accurate results. Contrary to the ulnabased estimations, the most remarkable decrease of mean difference (9.5 mm) was seen in the long tibia category, followed by the short category (mean absolute difference of 2.3 mm). In the medium tibia category, the general formula exhibited a smaller absolute mean difference (.7 mm). STATURE ESTIMATION FROM ULNA AND TIBIA 3 Regarding results of the stature group-specific equations of the tibia + ulna estimations, an increase in accuracy of the estimates was again observed. However, the new method was not as effective as it was with the univariate regressions, and the pattern observed was similar to that seen in the tibia. The paired t-test results also showed improvement in the estimations of the new method. The decrease in t values and increase in P values mean that the estimations are closer to actual height. As seen in Table 5, the t values of the stature group-specific formulae are lower than those of the general formulae, except in the medium category of the tibia. These results indicate that the stature group-specific formulae yield the more accurate results. Discussion Inaccurate stature estimates for individuals at height extremes has always been a major problem in forensic anthropology and skeletal biology. Trotter and Gleser (952, 958) studied stature estimation widely, and highlighted the inaccuracy issue in the 950s. Later, other authors also noted that errors in stature estimation were greater for tall and short subjects in any given population (Olivier, 969; Sjøvold, 990, 2000; Konigsberg et al., 998; Duyar and Pelin, 2003). Different methods involving regression equations, such as Sjøvold s (990) line of organic correlation, were offered as ways of reducing estimation errors for individuals at the extremes of the height range, but this problem has never been solved completely (Konigsberg et al., 998). In this study, we created and tested regression formulae that were specific to individuals in three height categories in a population: the mid-range and the extremes (short and tall). We compared height estimates derived from these specific formulae with estimates derived from the general (non- Table 3. Differences between actual and estimated height in Group 2, with the general formulae (in mm) Variable Estimated height Actual height Mean difference t P Ulna 755.69 756.8.2 0.226 0.82 Tibia 754.65 756.8 2.6 0.626 0.532 Ulna and tibia 755.59 756.8.22 0.369 0.73 Difference = estimated height actual height. Table 4. Stature group-specific regression equations based on the Group data (in mm) Stature groups Regression equations SEE R 2 Ulna Short Stature = 33.48 +.33 ulna 35.07 0.067 Medium Stature = 098.39 + 2.375 ulna 39.54 0.440 Tall Stature = 535.07 +.88 ulna 29.46 0.64 Tibia Short Stature = 753.89 + 2.42 tibia 3.22 0.26 Medium Stature = 942.38 + 2.07 tibia 35.64 0.545 Tall Stature = 389.87 +.42 tibia 26.90 0.303 Ulna and tibia Short Stature = 728.82 + 0.255 ulna + 2.307 tibia 32.9 0.263 Medium Stature = 853.49 +.50 ulna +.490 tibia 33.38 0.606 Tall Stature = 352.9 + 0.342 ulna + 0.997 tibia 27.83 0.32 Sample sizes of stature groups are: n short = 8, n medium = 88, n tall = 5; SEE, standard error of estimate.
4 I. DUYAR ET AL. ANTHROPOLOGICAL SCIENCE Table 5. The differences between actual and estimated heights in Group 2, with the general and the stature group-specific regression formulae (in mm) Estimated height Actual height Mean difference t P Ulna, short General formula 660.80 598. 62.69 5.538 0.000 Stature group-specific formula 594.02 634.35 40.33 2.586 0.08 Ulna, medium General formula 754.08 758.73 4.66 0.894 0.374 Stature group-specific formula 75.86 752.7 0.85 0.33 0.895 Ulna, long General formula 854.78 89.65 36.87 3.964 0.00 Stature group-specific formula 895.84 867.24 28.60 2.75 0.02 Tibia, short General formula 620.33 598. 22.22 2.098 0.05 Stature group specific formula 584.87 604.82 9.95.889 0.077 Tibia, medium General formula 756.64 758.73 2.0 0.580 0.564 Stature group-specific formula 755.49 759.26 3.77 0.92 0.364 Tibia, long General formula 867.29 89.65 24.36 2.802 0.0 Stature group-specific formula 893.49 888.67 4.82 0.456 0.654 Tibia + ulna, short General formula 620.7 598. 22.06 2.087 0.052 Stature group-specific formula 589.34 609.94 20.60.929 0.07 Tibia + ulna, medium General formula 756.58 758.73 2.5 0.62 0.542 Stature group-specific formula 753.68 755.74 2.06 0.497 0.620 Tibia + ulna, long General formula 873.36 89.65 8.29 2.274 0.035 Stature group-specific formula 890.87 880.9 9.96.244 0.227 Difference = estimated height actual height. height-specific) formulae. As in previous reports, with the general formula we observed considerable differences between actual height and estimated height in individuals at the extremes of the height range. Applying the stature groupspecific formulae reduced the differences between actual and estimated heights in the short and tall subgroups. In previous studies, we compared stature group-specific formulae based on tibia length with a general formula, and found that the group-specific formulae gave more accurate height estimates (Duyar and Pelin, 2003; Pelin and Duyar, 2003). Since the actual height of victims is generally unknown in forensic cases we focused on this problem in the present study. Thus we applied the stature group-specific formulae on groupings based on long bone lengths. The data from our present investigation show that stature group-specific formulae give more accurate estimates than general formulae. Table 5 indicates that our new method offers no advantage for studies that focus on mean heights in populations, but gains in importance when dealing with individuals at the extreme ends. In forensic cases in which individual stature is important, this new method is a definite improvement over the classic method of height estimation. Another point that we address is whether multivariate regression equations have an advantage over univariate ones. The results of this study indicate that for short and tall individuals, multivariate regression equations do not have an advantage over the univariate equation based on tibia length. Contrarily, the multivariate equations gave better results than the univariate ones based only on ulna length. Some elements of this study affect the conclusions that can be made. First, all our measurements were taken from living individuals as opposed to dry bones. It is well known that measurements of living subjects limbs do not accurately reflect dry bone measurements. However, forensic cases do not always involve dry bones; in some situations, isolated limbs with intact soft tissues are the only body parts available with which to make identifications. In these cases, stature group-specific formulae such as ours (i.e. equations based on living measurements) would definitely give more accurate estimates of the victim s stature. Nevertheless, it is important to underline that, although the differences between living and dry bone measurements for the tibia and ulna are only millimeters, formulae based on measurements from living subjects cannot be used with dry bones. We recognize this limitation and conclude that, since our stature group-specific formulae based on measurements from living individuals gave more accurate results, similar equations could be developed for skeletal measurements. The aim of our study was not to establish standard formulae, but to offer a new method of stature estimation. The second point relating our findings to forensics is that, in order to use stature group-specific formulae, one must determine whether the available bones belong to an individual who is tall, medium-height, or short for a given population. To eliminate this problem we categorized the sample according to long bone length as short, medium, and long. Later we applied the stature group-specific equations to these categories and reached better results. In summary, this study revealed that stature group-specific regression equations give more reliable estimates than
Vol. 3, 2005 general formulae for the individuals at the extreme ends of variation. This can be done by categorizing long bone length on a population-by-population basis. In order to apply stature group-specific formulae to a broader extent in the fields of forensic anthropology and skeletal biology, the accuracy of equations based on humerus and femur lengths should also be evaluated. Acknowledgments We would like to express appreciation to the anonymous reviewers for their helpful comments on the earlier draft of this paper. References Cameron N., Hiernaux J., Jarman S., Marshall W.A., Tanner J.M., and Whitehouse R.H. (98) Anthropometry. In: Weiner J.S. and Lourie J.A. (eds.), Practical Human Biology. Academic Press, London, pp. 25 52. Duyar I. and Pelin C. (2003) Body height estimation based on tibia length in different stature groups. American Journal of Physical Anthropology, 22: 23 27. Konigsberg L.W., Hens S.M., Jantz L.M., and Jungers W.L. (998) Stature estimation and calibration: Bayesian and maximum likelihood perspectives in physical anthropology. Yearbook of Physical Anthropology, 4: 65 92. Krogman W.M. and Iscan M.Y. (986) The Human Skeleton in Forensic Medicine. Charles C. Thomas, Springfield, Illinois, STATURE ESTIMATION FROM ULNA AND TIBIA 5 pp. 302 35. Lundy J.K. (985) The mathematical versus anatomical methods of stature estimate from long bones. American Journal of Forensic Medicine and Pathology, 6: 73 76. Martin A.D., Carter J.E.L., Hendy K.C., and Malina R.M. (988) Segment lengths. In: Lohman T.G., Roche A.F., and Martorell R. (eds.), Anthropometric Standardization Reference Manual. Human Kinetics, Champaign, Illinois, pp. 9 26. Olivier G. (969) Practical Anthropology. Charles C. Thomas, Springfield, Illinois, p. 287. Pelin C. and Duyar I. (2003) Estimating stature from tibia length: a comparison of methods. Journal of Forensic Sciences, 48: 708 72. Rösing F.W. (988) Körperhöhenrekonstruktion aus Skelettmassen. In: Knussmann R. (ed.), Anthropologie: Handbuch der Vergleichenden Biologie des Menschen. Gustav Fischer, Stuttgart, pp. 586 600. Sjøvold T. (990) Estimation of stature from long bones utilizing the line of organic correlation. Human Evolution, 5: 43 447. Sjøvold T. (2000) Stature estimation from the skeleton. In: Siegel J.A., Saukko P.J., and Knupfer G.C. (eds.), Encyclopedia of Forensic Sciences, Volume. Academic Press, London, pp. 276 283. Trotter M. and Gleser G.C. (952) Estimation of stature from long bones of American whites and negroes. American Journal of Physical Anthropology, 0: 463 54. Trotter M. and Gleser G.C. (958) A re-evaluation of estimation of stature based on measurements of stature taken during life and long bones after death. American Journal of Physical Anthropology, 6: 79 23.