AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 96:315-320 (1995) Brief Communication: Estimation of Adult Stature From the Calcaneus and Talus THOMAS DEAN HOLLAND United States Army Central IdentifKation Laboratory, Hawaii, Hickam AFB, Hawaii 96853-5530 KEY WORDS Hamann-Todd Collection, Tarsals ABSTRACT Calcanei and tali of 100 skeletons in the Hamann-Todd Collection at the Cleveland Museum of Natural History were measured. The skeletons represented 50 males and 50 females distributed equally by race, i.e., whites and blacks. Linear-regression equations, with standard errors ranging from 4.09 to 6.11 cm, were derived from these measurements for the purpose of estimating stature. Two independent control samples, including one comprised of remains of American servicemen lost in World War I1 and the Korea and Vietnam wars, were tested with relatively accurate results. 0 1995Wiley-Liss, Inc. A variety of mathematical techniques for several reasons. First, Steele (1976) has have been developed to estimate living stat- already demonstrated the value of the calcaure from skeletal remains. Probably the neus and talus in assessing sex, thus premost widely used technique in the United senting the potential to determine both sex States is that devised by Trotter and Gleser and stature from the same elements. Secin a series of articles in the 1950s (1951, ond, the calcaneus and talus preserve rela1952, 1958; also Trotter, 1970). A similar tively well (e.g., Pickering, 1986). Finally, technique developed by Genoves (1967) is the required measurements taken from the not uncommonly applied to Native North calcaneus and talus are relatively easy to obtain and replicate. American archaeological samples. As effective as these technique are, howMATERIALS AND METHODS ever, they suffer from a limited applicability A total of 119 calcaneuskalus pairs and to fragmented remains since they require intact long bones. Unfortunately, both ar- one unpaired calcaneus from the Hamannchaeological specimens as well as those of Todd Collection at the Cleveland Museum of forensic interest commonly are recovered Natural History were measured. The elewithout intact or even reparable long bones. ments represented 60 males and 60 females In response, several authors have presented distributed equally by race (American techniques for use in cases where intact limb whites and blacks). The individuals reprebones are not available. Some (e.g., Holland, sented ranged in age a t death from 16 to 81 1992; Steele, 1970; Steele and McKern, years. No element with obvious or suspected 1969; Simmons et al., 1990) have focused on pathology that might have adversely affragmented long limb bones, while others fected the results was used. The Hamann-Todd specimens were di(e.g., Byers et al.,1989; Meadows and Jantz, 1992; Musgrave and Harneja, 1978) have vided into two samples. Sample 1 consisted opted for methods employing alternative el- of 100 calcaneudtalus pairs representing 50 ements such as metacarpals and metatar- males and 50 females distributed equally by race. This sample was used to formulate the sals. The technique presented in this paper was devised for use with the calcaneus Received April 8,1994; accepted September 20,1994. and/or talus. These elements were selected 0 1995 WILEY-LISS, INC. 316 T. D. HOLLAND TABLE 1. Sample-1 statistics Measurement Race Sex Number Mean Standard deviation White White Black Black White White Black Black White White Black Black Male Female Male Female Male Female Male Female Male Female Male Female 25 25 25 25 25 25 25 25 25 25 25 25 81.66 75.38 82.84 75.86 58.64 53.50 60.46 53.09 61.44 56.02 61.96 53.67 4.87 4.15 4.95 4.48 3.58 3.07 2.81 3.56 2.63 2.91 3.59 3.09 ~ MCAL PCAL MTAL regression equations used to estimate stature. The second sample (Sample 2) represented 20 individuals distributed equally by race and sex and consisted of 19 calcaneusl talus pairs and one unpaired calcaneus. The purpose of Sample 2 was to serve as a control group to better gauge the accuracy of the equations derived from Sample 1. Statures for the individuals represented by the Sample 1 and Sample 2 foot bones were taken from the Hamann-Todd files (see Todd and Lindala, 1928, for information on how statures were recorded for this collection) and represent stature a t the time of death. Previously, Dupertuis and Hadden (1951) observed that the statures obtained from the Hamann-Todd cadavers were equivalent to living statures. Given the age range of the specimens used, however, corrections for age-related stature changes were made using the protocol outlined by Giles (1991). Corrected statures range from 56.5-74.4 in. for Sample 1 and 59.2-73.2 in. for Sample 2. A second control sample (Sample 3) consists of 9 calcanei and 10 tali representing 10 American servicemen (mostly aircraft crews) lost during World War I1 (n = 2), the Vietnam War ( n = 6), and the Korean War (n = 5) and subsequently identified at the United States Army Central Identification Laboratory, Hawaii (CILHI). Statures for these individuals were taken from antemortem medical records on file at CILHI and range from 66.0 to 73.5 in. (in cases where two or more statures were recorded for the same individual, either the mean or the modal value was used). The ages at death for this sample range from 20.0 to 41.0 years. The purpose of Sample 3 was to further gauge the accuracy of the formulas developed and t o provide some insight, albeit limited, into possible problems associated with secular trends in stature. Two measurements for each calcaneus and one for each talus were taken t o the nearest 0.10 mm using a vernier sliding caliper (Sample-l statistics are shown in Table 1). The Sample 2 specimens were measured twice, over a 2-day period, to assess intraobserver error. The low intraobserver rates (0.37-0.50%) attest to the simplicity of the requisite measurements. The measurements are described below (see Fig. 1). 1. Maximum length of the calcaneus (MCAL): maximum length of the calcaneus as taken parallel to the long axis. 2. Posterior length of the calcaneus (PCAL):maximum length between the most anterior point of the posterior talar articular surface and the most posterior point of the calcaneus (on the tuberosity ignoring any extensive exostoses). 3. Maximum length of the talus (MTAL): maximum length between the most anterior point of the head and the posterior tubercle. Note that this measurement differs from the more common measure of talar length in that the posterior landmark is the posterior tubercle rather than the sulcus for the flexor hallucis longus muscle. Simple and multiple linear-regression equations were formulated using the SYSTAT statistical package [version 5.2.1 (Wilk- STATURE FROM THE CALCANEUS AND TALUS 317 Fig. 1. Measurements of the calcaneus and talus utilized in this study. For discussionsee text. erson et al., 1992)l on a Macintosh Classic I1 computer. (Curvilinear equations also were formulated but failed to significantly improve predictive power.) Selected equations and their corresponding standard errors are listed in Table 2. Race- and sex-specific equations that failed to estimate stature as accurately as more general formulas using the same measurement(s) are not presented (eg., the formula derived for white male tali, and not listed on Table 2, has a standard error of 6.23 cm as compared to the standard error of 6.07 cm for the comparable formula derived for use on either white or black males). To use the equations, the selected measurement (in mm) is multiplied by the appropriate coefficient and the product is added to the corresponding constant. The resulting value is the estimated stature (in cm). The equation with the lowest standard error is always preferred. RESULTS As Table 2 shows, race- and sex-specific formulas do not always provide the most accurate results nor the lowest standard errors. This may in fact suggest that the lengths of the calcaneus and talus are linearly related to stature as opposed to the allometric, racially and sexually proportional relations that seemingly characterize long-bone length and body stature. In other words, short bodies generally have short foot bones and tall bodies generally have long foot bones in somewhat disregard for the mitigating influence of sex and race. Certainly the correlations between calcaneal and talar length and stature seem to bear this relation out (correlation coefficients for MCAL,, PCAL, MTAL,, and stature are r = .723, r = .817, and r = .731, respectively). In fact, the efficacy of, and rationale behind, population-generic stature-estimation formulas has been presented elsewhere (e.g., Sj~vold,1990) and is not a novel concept. The standard errors for the formulas presented in Table 2 range from 4.13 to 6.25 cm and are somewhat greater than the standard errors for formulas using intact long bones. The widely used Trotter and Gleser formulas for long bones of whites and blacks, for example, range from 2.99 t o 5.05 cmabout 1.14 cm smaller on average than those presented here. Certainly, the calcaneus or talus should never be used when an intact long bone is available. However, the formulas presented in Table 2 do compare favorably with some of the techniques commonly 318 T. D. HOLLAND TABLE 2. Eauations for estimatinp stature (in em) from the calcaneus and talus Rniiation Standard error ( k 1 Sample-2l Accuracy % 1SE 2SE White Male (mean age 48 years, SD 13 years) 80 100 5.55 80 100 5.75 Black Male (mean age 36 years, SD 17 years) 80 80 4.88 0.710(MCAL) + 118.30 4.81 60 100 1.283(PCAL) + 99.54 80 80 4.69 1.046(MTAL)+ 112.26 0.373(MCAL) + 0.790(PCAL) + 98.38 4.75 80 100 0.362(MCAL) + 0.707(MTAL) + 103.27 4.59 80 80 0.792(PCAL)+ 0.709(MTAL) + 85.28 4.38 80 80 White or Black Male (mean age 42 years, SD 17 years) 5.44 70 100 01.271(PCAL) + 98.47 80 100 6.07 1.045(MTAL)+ 109.66 5.33 90 100 1.039(PCAL) + 0.489(MTAL) + 82.14 White Female (mean age 48 years, SD 17 years) 5.46 100 100 1.159(MCAL)+ 74.59 4.15 40 60 1.932(PCAL) + 58.64 4.22 40 60 O.l41(MCAL)+ 1.785(PCAL)+ 55.87 0.974(MCAL) + O.GOO(MTAL) + 54.94 5.34 80 100 1.780(PCAL)+ 0.347(MTAL) + 47.29 4.13 60 60 Black Female (mean age 37 years, SD 16 years) 100 100 5.52 1.046(MTAL)+ 97.55 4.83 100 100 -0.519(MCAL) + 1.294(PCAL) + 0.556(MTAL) + 103.14 White or Black Female (mean age 42 years, SD 18 years) 0.854(MCAL) + 97.55 5.52 100 100 1.405(PCAL) + 87.27 4.72 70 100 0.951(MTAL) + 109.99 5.89 70 100 5.35 100 100 0.669(MCAL) + 0.543(MTAL) + 81.76 1.275(PCAL)+ 0.252(MTAL) + 80.37 4.72 70 100 White (Sex Unknown) (mean age 48 years, SD 16 years) 1.078(MCAL)+ 82.00 5.81 70 100 1.552(PCAL) + 79.57 5.11 70 90 0.309(MCAL) + 1.220(PCAL) + 73.94 5.06 70 90 0.781(MCAL)+ 0.597(MTAL) + 70.82 5.63 70 100 Black (Sex Unknown) (mean age 37 years, SD 17 years) 90 5.23 70 1.500(MTAL)+ 82.97 0.292(MCAL) + 1.248(MTAL)+ 74.35 5.17 80 90 o.agi(Pcm) + 0 . 8 2 5 ~ +~71.44 ~ ~ ~ ) 4.66 90 90 White or Black (Sex Unknown) (mean age 42 years, SD 17 years) 1.150(MCAL) + 77.37 6.25 80 100 70 95 1.617(PCAL) + 76.91 5.22 1.411(MTAL) + 85.95 75 100 6.18 O.lGO(MCAL) + 1.448(PCAL)+ 73.84 5.22 70 95 90 100 0.644(MCAL) + 0.836(MTAL) + 68.56 5.69 70 100 1.230(PCAL) + 0.495(MTAL) + 69.89 5.02 1.003(PCAL) + 112.42 0.674(MCAL) + 116.24 Sample-3' Accuracy % 1SE 2SE 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 86 80 86 100 100 100 83 67 83 80 100 100 100 100 100 100 100 100 100 100 100 75 91 63 86 71 100 100 100 100 100 100 'Percentage of applicable Sample-2 individuals whose estimated stature falls within one standard error USE) and two standard errors (2SE). Percentage of applicable Sample-3 individuals whose estimated stature falls within one standard error (1SE)and two standard errors (2SE). employed in cases where no intact long bones are present; the Simmons et al. (1990) and Steele (1970) formulas for incomplete long bones range from 5.47 to 7.16 cm and 3.99 t o 7.06 cm, respectively, while the Byers et al. (1989) equations for metatarsals range from 3.99 to 7.60 cm, and the Meadows and Jantz (1992) metacarpal equations range from 5.10 to 5.67 cm. Analysis of residuals reveals an overall random pattern of values. There is a slight tendency to underestimate taller statures (>180 cm) and overestimate shorter statures (<160 cm), though both trends are rather weak. Furthermore, the results obtained for the two control samples suggest that the formulas presented in Table 2 provide reasonably accurate results when STATURE FROM THE CALCANEUS AND TALUS applied to bones not directly involved in the creation of the regression models, i.e., they can be used on independent samples. For the most part, Sample 2 was accurately estimated (defined as an estimate within one standard error of the known stature) approximately 70-100% of the time. Some of the equations applicable to white females had the lowest accuracy rates due to the inclusion of what appear to be two statistical outliers (one female with unusually large and one female with unusually small foot bones for their statures) within the randomly selected sample of five individuals. The results obtained for Sample 3 are particularly encouraging, however, since the biological and socioeconomic profiles of this group no doubt differ markedly from that of the Hamann-Todd dissection-room population. In addition, the accuracy (generally 70-100%) with which the Sample-3 statures were estimated suggests that the calcaneus and talus may not be as affected as the long bones by recent secular increases in stature. CONCLUSIONS The calcaneus and talus are solid, relatively compact elements that commonly are recovered in contexts where intact long bones may not be, and the measurements of these elements needed to estimate stature are simply and reliably obtained. While any set of formulas derived from an early twentieth-century dissection-room population will suffer from some degree of population specificity, the equations presented in Table 2 would appear to have some utility in providing stature estimates in cases where other methods are not applicable. Unfortunately, the technique presently is restricted to use on whites and blacks, as its applicability to mongoloid remains is undocumented. Certainly, common sense should be exercised in determining when, where, and under what circumstances to employ these equations. ACKNOWLEDGMENTS The measurements used in this study were obtained by William Mayhew, who declined to be listed as a coauthor, but whose contribution was no less essential. I thank the Cleveland Museum of Natural History, 319 in particular Bruce Latimer and his staff, for allowing us access to the Hamann-Todd Collection. I also thank Bruce Anderson, William Grant, Kim Schneider Kimminau, Robert Mann, William Maples, and Ted Rathbun for reading and commenting on early drafts of the manuscript. The assertions contained in this work are those of the author and should not be construed to represent those of the United States Army or the Department of Defense. LITERATURE CITED Byers S, Akoshima K, and Curran B (1989) Determination of adult stature from metatarsal length. Am. J. Phys. Anthropol. 79:27%279. 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