AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 79:275-279 (1989) Determination of Adult Stature From Metatarsal Length STEVE BYERS, KAORU AKOSHIMA, AND BRYAN CURRAN Department of Anthropology, University of New Mexico, Albuquerque, New Mexico 87131 KEY WORDS Stature, Metatarsals, Regression ABSTRACT The results of a study to determine the value of foot bones in reconstructing stature are presented. The data consist of length measurements taken on all ten metatarsals as well as on cadaver length from a sample of 130 adults of documented race, sex, stature, and, in most cases, age. Significant correlation coefficients (.58-.89) are shown between known stature and foot bone lengths. Simple and multiple regression equations computed from the length of each of these bones result in standard errors of estimated stature ranging from 40-76 mm. These errors are larger than those for stature calculated from complete long bones, but are approximately the same magnitude for stature calculated from metacarpals and fragmentary long bones. Given that metatarsals are more likely to be preserved unbroken than are long bones and given the ease with which they are accurately measured, the formulae presented here should prove useful in the study of historic and even prehistoric populations. The determination of adult living height is an important part of the evaluation of skeletal remains, including those of early hominids, recent prehistoric populations, and modern forensic cases. The calculation of stature usually involves measurements of complete long bones, a process well known through the work of Manouvrier (1893), Pearson (1899), Stevenson (1929), Dupertius and Hadden (1951), Trotter and Gleser (1952, 1958), Fully and Pineau (1960),and others. However, various studies also have indicated that dimensions of vertebrae (Dwight, 1894), metacarpals (Musgrave and Harneja, 1978),clavicles (Jit and Singh, 1956), scapulae (Olivier and Pineau, 1957), incomplete long bones (Steele and McKern, 1969; Steele, 1970), and more recently, even footprints (Robbins, 1985;Giles and Vallandigham, 1987), provide stature estimations with varying degrees of accuracy. However, the use of foot bones to predict living height has not been examined. Therefore, it is the purpose of this study to determine if metatarsals give useful estimates of adult stature. MATERIALS AND METHODS The sample for this study consists of 130 macerated and dried skeletons; 66 from the Terry Collection at the Smithsonian Institu- @ 1989 ALAN R. LISS, INC. tion and 64 from skeletons housed a t the University of New Mexico’s Maxwell Museum of Anthropology. Demographic information (age, sex, and race) is documented on the majority of these skeletons; however, the ages of 11 individuals from the Maxwell Museum collection are not known and had to be determined by the authors using standard techniques. Stature is recorded on hanging cadavers of the Terry Collection (Trotter and Gleser, 1952),while supine stature is recorded for cadavers of the Maxwell Museum collection. There are 108Euro-Americans (57 males, 51 females) and 22 Afro-Americans (13males and nine females) in all. Grossly normal metatarsals were measured from both sides of the skeleton. Length was taken to the nearest 0.1 mm from the apex of the capitulum to the midpoint of the articular surface of the base parallel to the longitudinal axis of the bone. This measurement corresponds to Mt 1-4 of Martin and Saller (1957) for the first four metatarsals. In some instances, the shaft curved markedly in a dorsal-plantar direction, in which case the base and proximal shaft were taken to be the longitudinal axis. For metatarsal V, measurements included both functional and Rereived March 16, 1988: revision accepted J u l y 20, 1988. 276 S. BYERS ET AL. morphological lengths, with the medial surface of the bone determining the long axis. For the “functional” length, the proximal point was the dorsoplantar midpoint of the intersection between the fourth metatarsal and cuboid facets. This corresponds to Mt 5 of Martin and Saller (1957). The morphological length was measured to the tip of the tuberosity. Two corrections to living stature have been applied. First, as discussed by Trotter and Gleser (1951),maximum stature is attained in humans at around 21 years of age and decreases after age 30 years a t a n average rate of .06 cm per year, irrespective of race or sex. Given this situation, we added .6 (age - 30) mm to the stature of individuals over 30 years of age so that all analyses are based on estimated maximum height attained during life. The second correction accounts for the differences between hanging cadaver stature and living height. Trotter and Gleser (1952) and Trotter (1970) indicate that for the Terry Collection, the average stature of hanging cadavers is 2.5 cm greater than is living height. Dupertius and Hadden (1951) conclude that any difference between living stature and supine cadaver length is insufficient to warrant special consideration. Therefore, we substracted 25 mm from the stature of the individuals from the Terry Collection, whereas those from the Maxwell Museum whose stature was actually supine length remained unchanged. After applying the stature corrections, the following calculations were performed. First, descriptive statistics were calculated for the measurements as a way of noticing deviations from the normal distribution since nonnormality can affect the validity of further computations. Second, Pearson’s Product Moment Correlation Coefficient (r) was calculated between each metatarsal and stature. Third, plots of metatarsal measurements against stature were examined using the technique of Draper and Smith (1966) to determine if the relationship between the measures is linear. Fourth, simple linear regression equations were calculated so that stature could be predicted from metatarsal measurements. Last, multiple regression analysis was performed to determine if better estimates of stature could be generated by using two or more metatarsal lengths. (Model I regression was used in these latter computations because it provides smaller errors of estimate than does Model 11.) For the above calculations, all data first were combined and then broken down into six biological groups: all males, all females, Euro-American males, Euro-American females, Afro-American males, and Afro-American females. Division into the groups is justified because previous work (Trotter and Glesser, 1952,1958; Dupertius and Hadden, 1951; Genoves, 1967; Stevenson, 1929) indicate that the relationship between long bone lengths and stature differ by sex and race. Since the data of this study are composed of measurements from both sides of the same individuals, this factor had to be taken into account during analysis. I n this same situation, Trotter and Gleser (1952) use a n average of the right and left long bones in their regression formulae, Musgrave and Harneja (1978) calculate separate formulae for each side in their study of metacarpals, and Dupertius and Hadden (1951) use only right-side long bones in their analyses. Since a consensus on how to handle sides does not exist in the literature, we use a n average of right and left bones. RESULTS Euro-Americans constitute 82.7% of the sample, while Afro-Americans represent 17.3%;both groups are evenly divided between the sexes. The results of the calculation of descriptive statistics indicate that there are significant deviations (at the .05 level) from the normal distribution for one of the female measurements. Since there is a 92% probability of performing a type I error given the number of tests for skewness and kurtosis, these deviations are considered chance anomalies and their effect on further analyses have been disregarded. All metatarsal lengths are significantly correlated with stature in each biological group. Fairly strong relationships between the metatarsal measurements and stature are indicated by coefficients generally exceeding .60 (see Table 1). Simple linear regression formulae are presented in Table 1 for combined data and the six biological groups. Notice that the standard error of the second and third metatarsals in the formulae for all males and Euro-American males is larger t h a n the errors for the combined data. This is due t o a chance aberration in our sample, which, in all probability, would disappear if more metatarsal data were collected. Also using the techniques of Neter and Waserman (1974), the slopes of the for- 277 STATURE AN11 METATARSAL LENGTH TABLE 1. Simple linear regression of stature calculated from metatarsal measurements (all measurements in mm) Metatarsal/group First Combined data All males All females Euro-American males Euro-American females Afro-American males Afro-American females Second Combined da ta All males All females Euro-American males Euro-American females Afro-American males Afro-American females Third Combined d a t a All males All females Euro-American males Euro-American females Afro-American males Afro-American females Fourth Combined data All males All females Euro-American males Euro-American females Afro-American males Afro-American females Fifth (functional) Combined da ta All males All females Euro-American males Euro-American females Afro-American males Afro-American females Fifth (total) Combined da ta All males All females Euro-American males Euro-American females Afro-American males Afro-American females Formula St = 634 + 16.8 (Metl) S t = 815 14.3 (Metl) S t = 783 13.9 (Metl) S t = 768 15.2 (Metl) St = 656 16.3 (Metl) S t = 556 17.6 (Metl) S t = 796 12.8 (Metl) + + + + + + S t = 675 + 13.4 (Met2) S t = 873 + 11.1 (Met2) St = 791 + 11.5 (Met2) S t = 868 + 11.3 (Met2) St = 712 St = 605 St = 783 + 12.8 (Met2) + 14.0 (Met2) + 10.9 (Met2) St = 720 + 13.6 (Met3) S t = 909 + 11.2 (Met3) St = 836 + 11.6 (Met3) S t = 862 + 12.0 (Met3) St = 732 + 13.3(Met3) S t = 706 + 13.3 (Met3) St = 904 + 9.9 (Met3) S t = 715 + 14.0 (Met4) S t = 910 + 11.6 (Met4) S t = 835 + 11.9 (Met4) S t = 863 + 12.3 (Met4) St = 719 + 13.8 (Met4) S t = 759 + 13.0 (Met4) St = 961 + 9.3 (Met4) St = 782 + 14.7 (Met5m St = 989 + 11.8 (Met5F) S t = 953 + 11.3 (Met5m St = 938 + 12.8 (Met5F) S t = 900 + 12.3 (Met5F) St = 761 + 14.7 (Met5F) St = 979 + 10.2 (Met5F) St = 768 + 12.8 (Met5) S t = 952 + 10.6 (Met5) S t = 922 + 10.2 (Met5) St = 912 + 11.2 (Met5) S t = 905 + 10.6 (Met5) S t = 846 + 11.5 (Met5) St = 891 + 10.2 (Met5) mulae for all males, all females, EuroAmerican males, Euro-American females, Afro-American males, and Afro-American females are different (at the .05 level and beyond) whereas intercepts are not. Therefore, it should be assumed that the lines representing the relationship between stature and metatarsal lengths differ for the sexes and races. Table 2 presents multiple regression formulae for stature against all five metatarsal measurements. The level for inclusion of a n independent variable is a calculated F-value Standard error No. r 130 70 .79 .72 .71 .72 .79 .87 .70 65.4 64.2 56.1 63.2 49.6 I .78 .66 .73 .63 .77 .86 .83 65.4 69.8 54.8 70.1 52.0 56.8 39.9 128 69 57 57 48 10 7 .76 .66 67 .65 .71 .89 .78 67.6 68.1 59.7 68.9 57.5 42.2 44.9 126 68 56 57 47 9 7 .76 .67 .67 .65 .72 .88 .76 68.5 68.0 59.9 68.5 57.5 46.5 46.5 128 68 58 57 49 9 7 .69 .59 .61 .60 .72 .75 76.0 73.8 63.3 72.2 63.3 68.0 47.4 .73 .63 .61 .63 60 .76 .78 71.2 70.9 63.6 70.3 64.9 64.2 45.2 58 57 49 11 7 129 69 58 57 49 10 128 68 58 57 49 9 7 63 51.0 50.8 with a probability less than or equal to .05; the residual plots indicate t h a t the relationship between independent a n d dependent variables is linear. Only metatarsals 2 and 4 provide a significant contribution to the accuracy of calculated stature when included with metatarsal 1. Finally, there are no formulae for all females, Euro-American males, Afro-American males, and Afro-American females. This is because the inclusion of other metatarsal measurements in the formulae for stature predicted by second metatarsal in all females, and stature predicted 278 S. BYERS ET AL. TABLE 2. Multiple regression formulae for stature from metatarsal measurements (all measurements in mm) Group Standard error Formulae Combined da ta All males Euro-American females St = 573 S t = 737 S t = 558 + 10.9 (Metl) + 6.3 (Met4) + 10.4 (Metl) + 4.6 (Metl) + 9.1 (Metl) + 7.4 (Met2) by first metatarsal in Euro-American males, does not reduce the predictor error significantly. Multiple regression formulae are not computed for the Afro-Americans because the number of independent variables too closely approximates the number of data points. DISCUSSION The standard errors for the simple linear regressions between various bones and stature are presented in Table 3. Notice that those for metatarsals are not as small as those for long bones; however, they are of the same order of magnitude a s those for fragmentary long bones and metacarpals. Considering the small amount of error involved in measuring and the greater probability of being perserved unbroken, metatarsals along with metacarpals should provide the most easily attained and accurate estimates of stature when long bones are absent or fragmentary. The standard errors listed in Tables 1 and 2 indicate that the best estimates of stature are obtainable from the multiple regression equations, followed (generally) by the simple linear regression equations for metatarsals 1, 2, 3, 4, 5, and 5 (functional), respectively. If the first and fourth or first and second metatarsals are available, the multiple regression equations provide the best stature estimates. If any of these bones are absent, the appropriate formula from Table 1 with the lowest standard error should be used. It is not recommended that the results for different formulae be averaged since this treats all equations as though they are equally accurate (the standard errors indicate that they are not). If sex is known, the formulae for the identified sex should be used since these will provide statures with lower error estimates. Similarly, if it is known or caq be inferred, the proper biological group formula should be used to produce estimates w3h even lower errors. Two modifications to calculated stature deserve consideration. First, since the formulae of this study are based on greatest 61.8 61.3 48.4 TABLE 3. Standard errors (in em) of simple linear regression equations for stature calculated from various bones Bone' Complete Humerus Radius IJlna Femur Tibia Fibula Fragmentary Humerus Femur Tibia Metatarsal 1 2 3 4 5 (functional) 5 (total) Metacarpal 1 2 3 4 5 Euro-American Afro-American Male Female Male Female 4.1 4.3 4.3 3.3 3.3 3.3 4.5 4.2 4.3 3.7 3.7 3.6 4.4 4.3 4.4 3.9 3.8 4.1 4.3 4.6 4.8 3.4 3.7 3.8 4.8-5.3 3.9-4.4 4.2-5.5 5.1-5.4 4.8-4.9 4.7-5.7 4.6-5.0 3.7-3.7 3.9-4.5 4.8-4.9 5.8-6.2 4.5-5.0 6.3 7.0 6.9 6.9 7.2 7.0 5.0 5.2 5.7 5.8 6.3 6.5 5.1 5.7 4.2 4.7 6.8 6.4 5.1 4.0 4.5 4.7 4.7 4.5 5.5-5.8 5.8-5.8 5.8-6.0 5.8-6.0 6.3-6.3 7.2-5.5 5.6-4.7 6.6-4.7 7.6-5.0 8.3-4.7 - - - - - - 'Data for complete long bones from Trotter and Gleser (1952); range of standard errors for incomplete long bones from Steele (1970); right and left metacarpal standard errors from Musgrave and Harneja (1978). height attained in life, calculated stature should be adjusted for age (if possible) by subtracting the factor that we added [i.e., (age - 30) X 61. Second, Trotter and Gleser (1952) discuss the differences between dry and wet bone lengths. They conclude that long bones may shrink a s much as 2 mm during drying. This shrinkage causes a calculated stature difference of 4-8 mm. Since long bones are known to shrink with drying, it is logical to assume that metatarsals would shrink in proportion to their size and that this proportional shrinkage would affect calculated stature to approximatelythe same degree a s it does long bone shrinkage. This should be considered when reconstructed heights are reported. It is important to note t h a t the bias introduced by age and shrink- STATURE AND METATARSAL LENGTH age is always smaller t h a n the standard error of the formulae; however, by considering their effect, a beneficial increase in accuracy might be obtained. CONCLUSIONS Regression formulae of stature on metatarsal lengths are calculated from the average of the left and right metatarsals of 130 EuroAmericans and Afro-Americans of both sexes. The majority of Pearson’s Product Moment Correlation Coefficients for the relationship between the foot bones and height range from .58 to .79. The errors of estimating stature from metatarsals are greater than those of estimates of stature from long bones; however, they are approximately the same size as those for fragmentary long bones and metacarpals. Given this situation, the equations from this study should prove to be useful for calculating stature from fragmentary human remains of historic or prehistoric origin. ACKNOWLEDGMENTS The authors thank the Smithsonian Institution and the Maxwell Museum a t the University of New Mexico for allowing access to their skeletal collections. Stan Rhine, Erik Trinkaus, and Jeff Long also are thanked for their review and comments of earlier versions of this paper. The authors accept full responsibility for any errors or omissions in this text. LITERATURE CITED Draper NR, and Smith H (1966) Applied Regression Analysis. New York: John Wiley & Sons, Inc. Dupertius CW, and Hadden J A (1951) On the reconstruction of stature from long bones. Am. J. Phys. Anthropol. 9:15-54. Dwight T (1894) Methods of estimating the height from parts of the skeleton. Med. Res. Rev. 46.293-296. Fully G, and Pineau H (1960) Determination de la stature au moyen du squette. Ann. Med. Leg. 40:145-154. 279 Genoves S (1967) Proportionality of the long bones and their relation to stature among Mesoamericans. Am. J . Phys. Anthropol. 26:67-78. Giles E, and Vallandigham P (1987) Error estimates in calculating stature from foot and shoe lengths (abstract). J. Can. SOC.Forensic Sci. 20(3):172. Jit I, and Singh S (1956)Estimation of stature from clavicles. 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