Classification and misclassification in sexing the Black femur by discriminant function analysis.код для вставкиСкачать
AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 58:145-151(1982) Classification and Misclassification in Sexing the Black Femur by Discriminant Function Analysis ROBERT DIBENNARDO A N D JAMES V . TAYLOR Metropolitan Forensic Anthropology Team, Department of Anthropology, Lehman College, City University of New York, Bronx, New York 10468 KEY WORDS Sexing, Black femur, Discriminant analysis ABSTRACT Stepwise discriminant function analysis for sex assessment was applied to 130 North American Black femora. The measurements included femoral length and three midshaft dimensions likely to be preserved in archaeologicallyderived and forensic remains. The method correctly assigned sex for 76.4%of the sample (range 70.8-81.5%).This compares favorably with results achieved with other skeletal parts; it also compares favorably with results using the femur in sexing other racial groups. Among our other conclusions are: (1) a “general size factor” is one of major significance in correct classification and in misclassification of sex, and most misclassified individuals are anomalous for this factor: (2)the inconsistency in the relation between circumference and femoral length, which characterizes the remaining misclassified individuals, suggests that anomalous functional demands of body weightlmusculature are at fault, and affect circumference more than length; and (3) discriminant function analysis of the same variables in Whites produced similar results, suggesting that sex overrides race in sex assessment; this was confirmed by cross-validating the predictive accuracy of Black discriminant function coefficients on White data, and vice versa. Black (1978) suggested and first applied a method for sexing archeologically-derived Amerindian materials using circumference of the femoral shaft, a dimension likely to be preserved in fragmentary skeletal remains. In a recent paper (1979) we tested this method on White dissecting room femora of verified age, race, and sex, using femoral circumference alone and in combination with other more commonly employed femoral mesurements. The overall accuracy of prediction ( 8 2 % ) suggested, first, that femoral circumference might prove equally effective in sexing other groups; and second, that such effectiveness would be especially useful in forensic casework. We are now able to verify these assumptions on the basis of data recently collected on North American Blacks. MATERIALS A N D METHODS Our sample of 130 Black femora was chosen from the Terry Collection of dissecting room skeletons of known age, sex, and race at the Smithsonian Institution. The 65 male and 65 female femora were measured for maximum 0002-948318’215802-0145$02.50r j 1982 ALAN R LISS, INC length and three midshaft dimensions: anteroposterior and transverse diameters, and circumference. Stepwise discriminant function analysis employing these measurements was used to determine the optimal combination of variables for assessing sex of the femur. A number of statistical packages were used to supplement each other, check for accuracy, and derive the maximum amount of information from the data. These were: BMDP, SAS, and SPSS (Dixon and Brown, 1979; SAS Institute, 1979; and Nie et al., 1975). Discriminant function analysis has two broad objectives: (1)analysis - to delineate the dimensions along which populations are maximally differentiated; and ( 2 )classification - to assign individuals to groups on the basis of shared similarities. In analysis, by indicating which variables are highly weighted, the discriminant function coefficients highlight the dimensions along which populations differ most. The stepwise Received June 12. 1981; accepted October 9, 1981 146 R. DIBENNARDO AND J.V. TAYLOR procedure additionally incorporates economy into this search by eliminating variables that contribute only minimally to discrimination. Classification, on the other hand, is based on comparison of an individual's profile with the average profiles of the two or more groups, into one of which he must be assigned. These comparisons are made by computing classification functions for each group, and assigning the individual to the group on whose function he scores highest. We have pursued both of these objectives of discriminant function analysis in the present paper with the following results. remaining variable contributes significantly to group separation. Table 2 presents a summary of the stepwise procedure. There are four steps: the first indicates that circumference alone is the single best discriminator of sex; step two indicates that circumference and length are the best pair of discriminators; step three adds transverse diameter, but this affects the discriminatory power of circumference. The discriminatory power of variables already entered can be altered by their relationships to entering variables; therefore, in step four, circumference is dropped from the discriminant function, because it evidently provides no information not provided by transverse diameter in conjunction with length. The result is an optimal discriminant function for Blacks based on length and transverse diameter. Table 3 presents the discriminant function coefficients for each step. From the standardized coefficients it is apparent that length and transverse diameter are of coequal importance in the discriminant function. Finally, Table 4 presents the prediction matrices for accuracies of prediction at each step in the procedure and Figure 1 presents the histograms for the discriminant function scores of males and females. RESULTS Table 1 presents the descriptive statistics and univariate F's for a one-way ANOVA for each variable. There is a statistically significant sexual dimorphism for all four measurements. In the stepwise procedure, variables are sequentially entered into the discriminant function on the basis of an entrance criterion. The single variable that maximally separates the groups is entered first. The variable with the greatest residual discriminatory power is entered next, and the process is repeated until no TABLE 1. Simple descriptive statistics and uniuariate F-ratios for the differences between Black males and females Variable X Length' 6 475 (450) Q 443 (423) F' S - 31.4 (20.4) 23.6 (22.1) 44.72* Circumference 5.6 15.9) 5.3 (3.9) Anteropos terior diameter 2.4 (2.4) 2.3 (1.7) Transverse diameter 2.1 (2.2) 2.0 (1.7) 45.30* 21.86* 40.71* Data are from the 65 males and 65 females whose values were used in the stepwise discriminant function procedure summarized in Table 2 . Values in parentheses are for U'hitrdatal50 males and 35 temalesl dcscrihed in IXHennardo and'l'aylorl19791 and Taylor and DiHennardoll9821. 'With 1 and 128 degrees of freedom. 'Measurements in millimeters. 'Significant a t a=0.05. TABLE 2. Sumary of the stepwise discriminant function analysis o f male and female Black femora Variable Entered Removed ~ Step 1 2 3 4 . Circum Length Trans. Dia. Circum F t o enter or-remove No. of variables in function F for group differences on function Degrees of freedom 45.30 11.18 6.11 0.42 1 2 3 2 45.30 30.04 22.87 34.25 1,128 2,127 3,126 2.127 147 S E X I N G T HE BLACK FEMUR DISCUSSION Accuracy Although the innominate bone permits the highest accuracy in discriminating sex (above 90%: Washburn, 1948; Hanna and Washburn, 1953; Thieme and Schull, 1957; Genqvese, 1959; Davivongs, 1963; Howells, 1964; Igcan, 1980,1981),the greater resistanceof the femur to insult and decomposition often makes it of greater value in the classification of archeological and forensic remains. This is especially true of the femoral shaft, because it is composed almost entirely of cortical bone. In this regard, it is apparent from Table 3 that sexing the Black femur by discriminant function analysis provides a tolerably high degree of predictive acuracy (76.4%overall, with a range from 70.8-81.5%). This is less than, but comparable to, predictions made with the White femur (80.7% overall, range 72-86%: DiBennardo and Taylor, 1979; Taylor and DiBennardo, 1982, and is virtually as great a predictive accuracy as some investigators have found with the inspectional approach to sexing the skull (7770,Stewart, 1948). Moreover, its range of predictive accuracy substantially overlaps those reported in the literature for sexing the skull and postcranial bones, singly and in combination, by discriminant function analysis (Henke, 1977). There is, however, a notable difference in the relative accuracy of classifying males versus females with the femur, both within and between racial groups. Specifically, in Blacks there is consistently greater accuracy in predicting males (as Black, 1978 also found for Amerindians),while in Whites the opposite obtains. Additionally, in Blacks of both sexes, circumference alone is roughly as accurate a TABLE 3.Discriminant function coefficients for the three steps in the stepwise procedure summarized in Table 2 Variable(s) in function Standardized canonical discriminant function coefficients Circumference Uns tandardized coefficients 0.184 1.000 Canonical correlation = Chi-square = Degrees of freedom = 0.51 38.63 1 (constant) -15.823 Group mean for males = Group mean for females = Circumference Length 0.107 0.021 (constant) -18.744 0.590 0.570 Length Transverse diameter 0.660 0.610 0.024 0.300 (constant) -18.744 0.59 -0.59 Canonical correlation = Chi-square = 0.57 49.20 Degrees of freedom = Group mean for males = Group mean for females = 2 0.68 -0.68 Canonical correlation = Chi-square = 0.59 54.78 Degrees of freedom = Group mean for males = Group mean for females = 2 0.73 -0.73 TABLE 4 . Classification results (Yo correctly predicted) of each discriminant function generated zn the stepwise analyszs of sex differences in the Black femur ~ ~ Variables ~ _ in function _ ~ _ ~ _ _ Males (N ~ _ = 65) _ ~~ ~ Females ( N~ = 65) ~ Circumference Circumference and length Length and transverse diameter (Circumference,length and anteroposterior diameter) 75.4 (72) 81.5 (78) 70.8 (86) 75.4 (80) 73.1 (79) 78.4 (79) 78.5 76.9 77.7 Average Across Functions 78.5 (77.3) (82) Values in parenlheses are t o r White data ITayIor a n d DiRennardo. 19821 (86) 74.4 (84) _ Average across sexes (84) 76.4 (80.7) ~ 148 R. DIBENNARDO AND J.V. TAYLOR 4 8 12 16 B-Function Females ' I 2: Circumference, Length 16 12 8 4 4 8 12 16 C-Function Females 3 : Length, Transverse Diameter 16 12 8 Males 12 16 Females Fig. 1. Histograms for the discriminant function scores of males and females for the discriminant functions summarized in Table 2. Hatched areas represent misclassified individuals. predictor of sex as it is in White males, but White females are exceptional in the high degree of predictive accuracy (86%)provided by circumference alone. Overall, therefore, we conclude that the level of sex prediction permitted with the femur indicates a high degree of usefulness in the identification of archeological and forensic materials. Misclassification Our stepwise procedure permits classification of any particular case by three different functions. I t occurred to us that there might be discernible morphological patterns in the misclassified cases, and that such patterns might be revealed by the constancies and inconstancies of misclassifications across discriminant SEXING THE BLACK FEMUR functions. We have designated as constants those cases misclassified by all three functions, and as inconstants, those misclassified by some function(s) but not by all. The constants appear to comprise males with small dimensions for all traits investigated, and, conversely, females with large dimensions overall. This suggests that a "general size factor" is of major significance in correct classification and in misclassification of sex by discrimination function analysis of the femur. It also suggests, that in so far as size is the major component of sexual dimorphism, the constants represent a hard core of cases that will be consistently misclassified by any set of variables chosen for analysis. These constants comprise the larger group of misclassified cases ( 11 of 17 males or 65%, and 12 of 23 females or 52%). The inconstants comprise two subgroups. Most fall into a subgroup (a)anomalous for circumference relative to femoral length (males of normal stature but exceptionally gracile, and females of normal stature but exceptionally robust). As a subgroup, they account for the improved accuracy of classification when length is added to circumference in the second discriminant function. The other subgroup (b) comprises individuals anomalous for length relative to femoral circumference (normal male circumference but exceptionally short, and. normal female circumference but exceptionally tall). These individuals would tend to be misclassified by the second discriminant function, but since their number is small relative to subgroup "a," there is net gain in the second discriminant function over the first. The above analysis is explicable on the premise that stature (and hence long bone length) is largely determined by intrinsic factors (Osborne and DeGeorge, 1959; Tanner, 1977). On the other hand, as we have argued elsewhere, variation in femoral circumference appears to be largely dependent on the functional demands of weightbearing and/or muscular activity (DiBennardo and Taylor, 1979; see also Schultz, 1953).It follows, then, that (1)the primary basis of sexual dimorphism of the femur appears to be the intrinsic factor of length in combination with commensurable body weight. Anomalous variation in the latter may account for the variations observed in both subgroups of inconstants; in contrast, anomalies in length, accompanied by commensurable variation in weight (and presumably circumference), account for the misclassification of constants. (2) Both Black and White males, and Black and White females, have sim- 149 ilar average circumferences, respectively (Table 1); on the other hand, the four groups differ widely in average lengths. This suggests that the functional demands on long bone circumference (weight bearinglmuscular activity) permit less variability across race in circumference than in length dimensions. Cross-validation The variables utilized in the present study of sexual dimorphism in the Black femur were similarly used in sexing the White femur (DiBennardo and Taylor, 1979; Taylor and DiBennardo, 1982. Some of the similarities and differences in results are worth noting. (1)For both races, circumference is the single best discriminator of sex, and circumference and length, the best pair of discriminators. (2) The best triplet of discriminators, however, is circumference, length, and anteroposterior diameter for Whites, but, circumference, length, and transverse diameter for Blacks. Moreover, in Whites the addition of anteroposterior diameter in the stepwise procedure produces an optimal function with three variables, while in Blacks, the addition of transverse diameter causes circumference to drop out of the function, leaving an optimal function with only two variables. The similarities in results suggests that in sex assessment, sex differences override race differences, a conclusion in accord with those of Giles and Elliot (1963), Giles (1964), and Richman, et al. (1978),for sexing the skeletons of Blacks and Whites by discriminant function analysis. To test this conclusion, we have run a cross validation analysis of our Black classification functions on our White data, and of our White classification functions on our Black data. The accuracies of prediction are given in Table 5. I t is clear from Table 5 that circumference retains a high consistency of predictive accuracy across race (70.8-85.770).Classification functions that include length, on the other hand, are much more variable in predictive success (66-94.170). The latter variability is apparently due to the marked differences in femoral length between Blacks and Whites. Almost all White females have femoral lengths below the average of Black females. Therefore, the Black female classification functions employing femoral length virtually assure a female classification for all White females (94.1 and 91.4%). Conversely, because most White males have femoral lengths below the Black male average, Black discriminant functions using length 150 R. DIBENNARDO AND J.V. TAYLOR TABLE 5. Classification results (% correctly predicted) o f (a)Black discriminant functions on White data and Ib) White discriminant functions on Black data Males Whites ~~ WGes Blacks ~~~ A Cross validation of Black discriminant functions on White data ~ _ _ _ _ _ _ _ ~ ~ ~~~ ~~ Circumference Circumference Length Length Transverse Dia (75 4)* (81 5) 72 0 66 0 68 0 ~ ~~ ~ _ _ _ _ _ _ _ ~ Females Blacks ~~ ~~~ 85 7 94 1 91 4 178 5) ~ ~~~ 176 9) -~ ~~~ ~ B Cross validation of White discriminant functions on Black data Circumference Circumference Length Circumference Length Anteroposterior Diameter 170 7) (75 4) _______ ~__________ 75 4 84 6 172 0) 178 0) 70 8 67 7 (85 7 ) 180 0) 84 6 182 0 ) 69 2 (85 71 *Cdlues in pdrenthezez indicdte accuracies for the datd Iron1 a h i c h thc f u n c t i o n i %eregenerated tend to classify White males as females. This ratifies our earlier conclusion that femoral length is probably a better criterion for racial differentiation than circumference, because it is less responsive to functional demands. At the same time, the contrasting significance of circumference in the optimal functions for Blacks and Whites, suggests a second major component of femoral variation between Blacks and Whites: the independence of anteroposterior diameter from circumference in Whites may reflect an element of pilastry that is absent in Blacks. This racial difference in pilastry has been attributed to differences in musculature andlor anterior bowing of the shaft (Hooton, 1946; Stewart, 1962; Walensky, 1965 ; Gilbert, 1976). In summary, the functional implications in the present study point the direction to further research emphasizing the analytical rather than classificatory aspect of discriminant function analysis. We are presently expanding our data base to include variables such as femoral bowing, p i l a s t r y , and other dimensions which should throw light on the bases of sexual and racial variation in femoral morphology. ACKNOWLEDGMENTS The authors gratefully acknowledge the help received from Drs. L. Angel and L. St. Hoyme, and the support staff of the NMNH a t the Smithsonian Institution. This research was supported by CUNY-PSC grant 13456. LITERATURE CITED Black TK 111 (1978) A new method for assessing the sex of fragmentary skeletal remains: femoral shaft circumference. Am. J. Phys. Anthrop., 48:227-231. Davivongs, V (1963) The pelvic girdle of the Australian aborigine; sex differences and sex determinations. Am. J. Phys. Anthrop., 21:443-455. DiBennardo, R and Taylor, JV (1979)Sex assessment of the femur: a test of a new method. Am. J. Phys. Anthrop., 503535-638. Dixon, WJ. and Brown, MB (1979)BMDP-79. University of California Press, Berkeley. Genovese. S (1959) L'estimation des differences sexuelles dans l'os coxal; differences metriques et differences morphologiques. Bull. Mem. SOC.Anthrop. (Paris), 10 (X serie):3-95. Gilbert, BM (1976) Anterior femoral curvature: its p r o b able basis and utility as a criterion of race assessment. Am. J. Phys. Anthrop.. 4.2601-604. Giles, E (1964) Sex determination by discriminant function analysis of the mandible. Am. J. Phys. Anthrop., 22129-135. Giles, E, and Elliot, 0 (1963)Sex determination by discriminant function analysis of crania. Am. J. Phys. Anthrop., 21:53-68. Hanna, RE, and Washburn, SL (1953)The determination of the sex of skeletons, as illustrated by a study of the Eskimo pelvis. Hum. Biol.. 2521-27. Henke, K (1977) On the method of discriminant function analysis for sex determination of the skull. J. Hum. Evol., 695-100. Hooton. EA (1946) Up From the Ape. Second ed. MacMillan, New York. Howells, WW (1964) Determination du sex du basin par fonetion discriminante: Btude de material du Docteur Gaillard. Bull Mem. Soc. Anthrop. Paris (11 series), 295-105. Igcan, MY (1980) Differences in pelvic dimension between American Blacks and Whites. Am J. Phys. Anthrop., 52239-240. Igcan, MY (1981) Metrical analysis of pelves of American Indians, Whites and Blacks. AM. J. Phys. Anthrop., 54936. . . S E X I N G THE BLACK FEMUR Nie, NN. Hull, CH, Jenkins, JG, Steinbrenner, K, and Bent, DH (1975) Statistical Package for the Social Sciences. McGraw-Hill, New York. Osborn, DH, DeGeorge, RH, and DeGeorge, FV (1959) The Genetic Basis of Morphological Variation. Harvard University Press, Cambridge. Richman, MS, Michel, ME, Schulter-Ellis, F P and Corruccini, RS 11978) Determination of sex by discriminant function analysis of postcranial skeletal measure ments. J. For. Sci., 23:159-167. SAS Institute Inc. (1979) SAS User's Guide. SAS Institute Inc., Raleigh. Schultz. AH (1953) The relative thickness of the long bones and the vertebrae in primates. Am. J. Phys. Anthrop., 11:277-312. Stewart, TD (1948) Medico-legal aspects of the skeleton. 1. 151 sex, age, race and stature. Am. J. Phys, Anthrop.. 6315-322. Stewart, TD (1962) Anterior femoral curvature: its utility for race identification. Hum. Biol., M49-62. Tanner, J M (1977) In, GA, JS Weiner, J M Tanner, and NA Barnicot (eds):Human Biology (2nd ed.), Harrison, Oxford Oxford University Press. Taylor, J V , and Dibennardo. R (1982) Determination of sex of White femora by discriminant function analysis; forensic implications. J. For. Sci., (in press). Thieme, FP. and Schull. WJ (1957) Sex determination from the skeleton. Hum. Biol., 29242-273. Walensky. NG (1965) A study of anterior femoral curvature in man. Anat. Rec., 151:559-570. Washburn, SL (1948) Sex differences in the pubic bone. Amer. J. Phys. Anthropol. 6199-207.