AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 84:421-426 (1991) Determination of Sex From Arm Bone Measurements DARRYL J. HOLMAN AND KENNETH A. BENNETT Department of Anthropology, The Pennsylvania State University, University Park, Pennsylvania 16802 (D.J.H.1; Department of Anthropology, University of Wisconsin-Madison, Madison, Wisconsin 53706 (K.A.B.1 KEY WORDS Forensic anthropology, Wrist measurements, Bi- styloid breadth ABSTRACT Discriminant function analysis has been applied to numerous dimensions of the cranial and postcranial skeleton for sex determination of U S . blacks and whites and is extended here to five measurements of the arm and wrist. These include maximum lengths of the long arm bones in addition to two measurements that reflect wrist breadth. Our results indicate that whites are more accurately classified than blacks, but seven of the 31 possible measurement combinations common to both groups yield functions with sex prediction accuracies comparable to most, but not all, functions based on other parts of the skeleton. Forensic anthropologists are currently able to assess the sex of unidentified adult skeletal remains with an accuracy approaching loo%, depending on the recovered parts of the skeleton. In many cases, particularly those involving an intact cranium and pelvis, qualitative morphologcal observations are sufficient for accurate sex attribution. In other cases, involving only fragmentary or incomplete remains, sex can be determined by quantitative metric analyses, although with somewhat lower accuracy. Some of these metric techniques have dealt only with absolute size differences, as in Stewart’s (1979) finding that vertical humeral head diameters above 47 mm and below 43 mm “almost certainly” represent males and females, respectively, and Berrizbeitia’s (1989) demonstration of size differences between males and females in maximum and minimum radial head diameters. However, the most widely used statistical technique has been discriminant function analysis of skeletal measurements. Sex determination of US. blacks and whites by this method has a history of about 25 years, beginning primarily with the pioneering work by Giles and Elliot (1963) on the cranium and Giles (1964) on the mandible. Since then, the method has been applied to measurements from other skeletal regions, including a combination of postcranial bones (Giles, 1970), the calcaneus and talus (Steele, 19761,pelvis @ 1991 WILEY-LISS,INC. (Kelley, 1979; .Schulter-Ellis et al., 1983, 19851, tibia (Iycan and Miller-Shaivitz, 1984a), femur (DiBennardo and Taylor, 1979; Iacan and Miller-Shaivitz, 1984b),and sternal rib end (Iycan, 1985). The population-specificnature of the method was recognized early (e.g., Birkby, 19661, which led to the development of functions on populations other thanU.S. blacks and whites (see Igcan, 1988, for a full literature review). Accuracies for sex prediction vary from one measurement set to another, but most generally fall within the middle to upper 80th to low 90th percentile range. Notable exceptions include the studies by DiBennardo and Taylor (1983), who obtained accuracy levels of about 95% with a combination of pelvic and femoral measurements for simultaneous sex and ethnic attribution, and Schulter-Ellis et al. (1983, 19851, who reported accuracies of 96% for black and white sexing from pelvic measurements. The advantages and limitations of discriminant function sexing have been discussed clearly by Giles (1970),and we need not add further comments on this subject. However, it might be noted that the method was validated over a decade ago on a test of 52 forensic cases (Snow et al., 1979) for both sex and ethnic attribution. One of the more important applications of Received October 17,1989; accepted June 29,1990 422 D.J. HOLMAN AND K.A. BENNETT discriminant function sexing occurs when a forensic anthropologist is asked to examine only parts of a dismembered individual, specifically excluding those structures (the cramium and pelvis) upon which sex can be determined visually with a high level of confidence. Such cases may be infrequent, but they do occur; therefore, the development of sexing functions on as many skeletal structures as possible is clearly desirable. Because dismemberment often involves the hands and arms at different points, our purpose here is to develop functions on certain measurements of the upper limb. The feasibility of this was suggested by Jamison’s (1972)study on living Eskimos, in which wrist breadth was the most sexually dimorphic trait among 28 standard anthropometric variables. In addition, an analysis comparing anthropometric sex dimorphism between unlike-sex dizygotic twins and unrelated adults from New York City (Bennett, unpublished data) indicated that wrist breadth again was the most sexually dimorphic variable among the 38 measurements under study. Given other indications of sex dimorphism in the arm (Stewart, 1979; Hamilton, 1982; Berrizbeitia, 1989), it seemed appropriate to use a modified version of wrist breadth, in combination with maximum lengths of the long arm bones, in an attempt tc develop discriminant functions for sexing U.S. blacks and whites. MATERIALS AND METHODS We took a set of five measurements on each of 302 adult skeletons chosen at random from the Smithsonian Institution’s Terry Collection. The sample consisted of 75 black females, 75 black males, 76 white females, and 76 white males. While an assistant selected the skeletons and recorded the pertinent information from the morgue records, one of us (D.J.H.) took all measurements in order to avoid interobserver error. These were taken without prior knowledge of age at death, sex, or ethnic affiliation of the skeleton. No bones with obvious athologies or healed fractures were include , and all measurements were taken on bones from the left side. Maximum lengths of the humerus, radius, and ulna were measured with an osteometric board according to Wilder (1920) and approximated to the nearest 0.5 mm. The remaining two measurements represent an approximation of bistyloid (wrist) breadth, t; which for convenience may be referred to as the semibistyloid breadth (SBB) of the radius and ulna. The SBB of the radius was measured from the most lateral point on the styloid process t o the deepest point of the ulnar notch, at a right angle to the long axis of the bone. The SBB of the ulna was measured from the most medial point on the head t o the most lateral point on the styloid process, again at a right angle to the long axis. Both were taken with a sliding caliper and approximated to the nearest 0.1 mm. The data were analyzed se arately in three sets, one composed of blac males and females, a second of white males and females, and a third of pooled black and white males and females under the assumption of unknown ethnic affiliation. This allowed us to develop separate discriminant functions for sexing individuals within each group. For the first two groups, data on the first 50 individuals within each sexiethnic group combination were used to develop the discriminant functions, and data on the first 100 individuals in the third group were used for the same purpose. Each analysis was carried out in three stages. First, the STEPDISC procedure (SAS Institute, 1985) was used to generate stepwise entry and terminal statistics for the 31 possible combinations of the five variables. Twelve of these functions satisfied the following selection criteria, although the five that contained only one measurement were subsequently deleted due to their rather poor prediction accuracies: 1)significance of each variable when entered into the function, 2) significance of every variable in the final function, and 3) the requirement that the same function met the first two criteria for each of the three groups. Because of the large number of functions tested, we included this third criterion to reduce the chance of generating a function with meaning only for a certain data set. In the second stage, the unstandardized discriminant function coefficients were enerated with the DISCRIM procedure &AS Institute, 1985).The remaining25 black and 26 white individuals in the first two sex/ ethnic grou combinations and the 51 individuals in t e pooled third grou served as test samples that were classifie in order t o determine accuracy of the method independent of the data used to generate the functions. Finally, structure coefficients were generated with the DSCRIMINANT procedure (SPSSInc., 1988). K R cp 423 DETERMINATION OF SEX FROM ARM BONE RESULTS Tables 1 and 2 contain descriptive statistics for the reference and test samples, respectively, in which female mean values for all measurements were significantly smaller than male values at P < 0.001. In Tables 3-5 are the unstandardized discriminant function coefficients for the seven functions that met the selection criteria given above, for blacks, whites, and pooled blacks and whites. These tables also give percentage accuracies of each function on the test samples, in addition to the structure coefficients associated with each discriminant function. As product-moment correlations between any single variable and the discriminant function, structure coefficients are included to indicate how close the variables are related to their respective functions. The values in Table 6 indicate total discriminating power of each function, as suggested by Klecka (19801,and are arranged in descending order of importance for each of the three groups. These orders, except for minor differences among functions 5 , 6, and 7, are the same for each group. In Table 6 , the percentage values in the ‘relative importance” column were obtained by dividing each eigenvalue by the sum of all eigenvalues. Because the magnitudes of the eigenvalues are directly proportional to the discriminating power of each function, the percentages are the relative power of each function. DISCUSSION From the forensic standpoint, the usefulness of this study rests ultimately with the percenta e accuracies of the seven functions for the t ree groups. In this context, it is discouraging that the functions for blacks provide the lowest discriminating abilities: Only functions 1, 2, 5 , and 6 show accuracy levels of 80% or above for both sexes. Misclassification percentages for these four are also approximately symmetrical by sex, which would be expected under the assumptions of a multivariate normal distribution and equality of group covariance matrices. However, misclassifications for functions 3 and 4 are widely different, as is evident in Table 3. Such distortion in the probabilities of group membership can arise when either or both of the above assumptions are not met, and, indeed, the only significant difference (P < 0.002) in variances between the sexes is for ulna length in blacks. This may explain the sex difference in predictive accuracy for a TABLE 1. Reference sample means and standard deviations (in mm) Variable Blacks N Radius SBB Ulna SBB Radius length Ulna length Humeruslength Whites N Radius SBB Ulna SBB Radius length Ulna length Humerus length Pooled black/white N Radius SBB Ulna SBB Radius length Ulna 1engtYh Humerus length Females Mean S.D. Males Mean S.D. 50 28.53 2.05 18.43 1.35 237.03 13.22 254.66 13.62 309.55 16.43 50 32.82 1.88 21.50 1.75 263.38 16.37 282.18 21.58 339.05 19.79 50 27.88 1.78 18.15 1.90 219.96 13.04 236.48 13.06 300.20 15.21 50 31.78 1.80 21.37 1.85 243.59 14.26 260.44 13.70 326.21 18.06 100 28.21 18.29 228.50 245.57 304.88 100 32.30 1.91 21.44 1.80 253.49 18.23 271.31 21.04 332.63 19.93 1.94 1.65 15.63 16.12 16.43 TABLE 2. Test sample means and standard deviations f i n mmJ Variable Blacks N Radius SRR ~~~.~~ Ulna SBB Radius length Ulna length Humerus-length Whites N Radius SBB Ulna SBB Radius length Ulna length Humerus length Pooled black/white N Radius SBB Ulna SBB Radius length Ulna length Humerus length Females Mean S.D. Males Mean S.D. 25 25 28.40 1.92 2.56 ~~. 32.14 . ~ 18.76 21.79 2.04 1.78 17.41 235.92 15.86 253.48 252.36 16.83 15.35 270.76 306.62 17.74 330.66 19.67 26 28.15 1.85 18.27 1.48 11.49 219.88 237.87 11.69 297.90 14.96 26 31.99-- 2.16 21.12 1.41 243.17 12.05 260.35 12.45 327.63 15.74 51 28.27 1.87 1.64 18.51 227.75 15.88 244.97 15.33 302.18 16.80 51 32.06 2.34 21.45 1.76 248.23 15.66 15.53 265.45 329.12 17.66 function 4 (but not necessarily 3 ) , and, if so, this function should be viewed with considerable caution for both black and pooled black and white samples. The results are far more satisfactory for whites, with all seven functions giving accuracy levels of 85%or better. Misclassification rates, furthermore, are approximately symmetrical. These levels are comparable to ~ 424 D.J. HOLMAN AND K.A. BENNETT TABLE 3. Unstandardized discriminant function coefficients and structure coefficients (in parentheses) for U S . blacks' Measurements 1 Radius SBB 0.827340 (0.807) 0.679517 (0.727) 0.061764 (0.657) Ulna SBB Radius length Ulna length 2 0.883005 (0.848) 0.911964 (0.763) 3 Discriminant function 4 5 0.942549 (0.861) 6 0.936834 (0.886) 0.076352 (0.801) 0.089038 (0.701) 0.998052 (0.904) 0.053734 (0.645) Humerus length Constant Test samole Correctmale (%) Correct female (%I) 7 0.959288 (0.920) 1.025215 (0.924) 0.049033 (0.719) -54.4009 -45.2963 -51.1904 -43.8494 -37.8103 84.0 88.0 84.0 80.0 72.0 92.0 68.0 96.0 80.0 80.0 0.055499 (0.748) -37.9272 -33.6330 80.0 80.0 84.0 72.0 ITotal discriminant scares less than 0 classify as female. TABLE 4. Unstandardized discriminant function coefficients and structure coefficients (in parentheses) for U.S. whites' Measurements 1 Radius SBB 0.814838 (0.860) 0.511105 (0.676) 0.068677 (0.681) Ulna SBB Radius length 2 1.002704 (0.914) 0.557965 (0.718) 3 Discriminant function 4 5 0.994788 (0.917) 6 0.962512 (0.932) 0.743261 (0.786) 0.103340 (0.780) 0.075379 (0.726) 0.764397 (0.820) 0.072218 (0.764) Ulna length -50.3240 92.3 84.6 0.680562 (0.794) 0,103546 (0.828) Humerus length Constant Test sample Correct male (%) Correct female (%) 7 -40.9365 -47.1465 -46.6558 -38.6377 92.3 84.6 92.3 88.5 96.2 88.5 88.5 92.3 0.073635 (0.744) -38.1665 -39.1739 84.6 92.3 84.6 84.6 'Total discriminant scares less than 0 classify a s female. those given b Igcan and Miller-Shaivitz (1984a,b)and teele (1976)for other nonpelvic bones of the postcranial skeleton as well as those given by Giles (1970)for cranial and mandibular measurements. Finally, for the pooled black and white sample, the results are, as expected, intermediate between the black and white groups. All but function 4 show predictive accuracies of 80% or above, with generally symmetrical misclassifications. Functions with the strongest discriminating power (1,2,3, and 4)and contain radius SBB, which, in each case, has the highest structure coefficient of any variable in the function. It would therefore seem that this B dimension is a more biologically significant indicator of sexual dimorphism than any of the other four variables. This is not overly sur rising with respect to bistyloid breadth, in %at radius SBB contributes about 60% to the total breadth in both sedethnic roup combinations (as inferred from corn ined mean values of radius SBB and ulna SBB in Table 1).Ulna SBB is evidently of less biological significance, and none of the long bone lengths would appear to be of comparable utility. Our results suggest that Terry Collection blacks are less sexually dimorphic than whites for the dimensions considered, a finding for which no good anatomical or environ- % 425 DETERMINATION OF SEX FROM ARM BONE TABLE 5. Unstandardized discriminant function coefficients and structure coefficients (in parentheses) for U S . blacks and whites' Measurements 1 Radius SBB 2 0.800243 (0.858) 0.658418 (0.735) 0.032589 (0.593) Ulna SBB Radius length 0.888901 (0.877) 0.721568 (0.751) 3 Discriminant function 4 5 0.956186 (0.947) 0.881177 (0.884) 0.059728 (0.713) 0.870315 (0.875) 0.030833 (0.626) 0.893665 (0.911) 0.046487 (0.686) Humerus length Constant Test sample Correct male (%) Correct female (W) 7 0.982161 (0.971) 0.046121 (0.654) Ulna length 6 -45.1420 -41.2248 -40.0423 -37.6819 -31.8971 86.3 84.3 86.3 80.4 80.4 86.3 76.5 84.3 80.4 82.4 0.058092 (0.729) -35.8044 -29.7653 82.4 84.3 80.4 82.4 ITotal discriminant scores less than 0 classify as female. TABLE 6. Eigenualues, canonical correlations, and relative importance of functions Discriminant function Eiszenvalue Relative imaortance !%) Canonical correlation 1.8516 1.6792 1.6291 1.4261 1.2464 1.1988 1.1466 18.19 16.50 16.01 14.01 12.25 11.78 11.27 0.8058 0.7917 0.7872 0.7667 0.7449 0.7376 0.7309 1.6460 1.4577 1.4456 1.4006 1.2339 1.1924 1.1168 17.34 15.36 15.23 14.75 13.00 12.56 11.76 0.7887 0.7701 0.7688 0.7638 0.7432 0.7375 0.7264 1.5563 1.4925 1.2801 1.2163 1.0983 1.0767 1.0119 17.82 17.09 14.66 13.93 12.58 12.33 11.59 0.7803 0.7738 0.7493 0.7408 0.7235 0.7201 0.7092 Blacks 1 2 3 4 5 6 7 Whites 1 2 3 4 5 7 6 Pooled black/white mental explanation is readily ap arent. This might or mi ht not apply to mo ern individuals, depengng on the extent to which these groups are comparable to Terry Collection skeletons. In this context, Jantz and MooreJansen (1988) have shown convincingly that accuracy in sex prediction is improved considerably with discriminant functions developed from both cranial and postcranial measurements on modern forensic cases now B being registered in the forensic data bank at the University of Tennessee. For example, correct sex classification of whites based on three humeral measurements on these forensic cases approaches 95%. The implication, of course, is that morphological changes due to secular change or differences in nutrition or other environmental variables have occurred between the time of growth and development of Terry Collection individuals 426 D.J. HOLMAN AIVD K.A. BENNETT and today. Although this would render the older anatomical collections less appropriate for the development of sexing discriminant functions for use in modern situations, as Jantz and Moore-Jansen (1988) have stressed, we could not use the University of Tennessee forensic data bank for the simple reason that our distal radius and ulnar measurements have not previously been taken by forensic anthropologists. Substantial improvement in the method might therefore arise with new functions developed from contemporary measurements. Until then, however, the usefulness of this study will await practical testing on forensic cases. ACKNOWLEDGMENTS We thank Douglas Ubelaker for permitting access to the Terry Collection and Kathy Murray for valuable assistance during data collection. We are also grateful to David Steven for skeleton selection and t o Luci Kohn and James Cheverud for their comments. LITERATURE CITED Berrizbeitia EL (1989) Sex determination with the head of the radius. J. 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