Dimensional variation in the proximal ulna Evaluation of a metric method for sex assessment.код для вставкиСкачать
AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 135:469–478 (2008) Dimensional Variation in the Proximal Ulna: Evaluation of a Metric Method for Sex Assessment Lynne S. Cowal1 and Robert F. Pastor1,2* 1 Department of Archaeological Sciences, Biological Anthropology Research Centre, University of Bradford, Bradford, West Yorkshire, BD7 1DP, UK 2 Department of Anthropology, University of Oregon, Eugene, OR 97403-1205 KEY WORDS anthropology sexual dimorphism; discriminant function; Spitalﬁelds; bioarchaeology; forensic ABSTRACT The determination of sex is one of the fundamental assessments in the production of a biological proﬁle for human skeletal remains, and a large number of studies have focused on evaluating sexual dimorphism metrically. A recent study of a contemporary American population presented high classiﬁcation accuracies from discriminant function analysis of the proximal ulna (Grant and Jant, 2003). The present research tests this method using a large sample (223 skeletons: 114 males and 109 females) from two skeletal assemblages of European origin, the documented Spitalﬁelds Cofﬁn-Plate Collection (N 5 171) and the archaeological Raunds Furnells Collection (N 5 52). The three measurements from the original study (Grant and Jantz, 2003), deﬁned as the notch length (NL), the width of the olecranon process (OW), and the height of the coronoid process (CH) were tested, with the addition of a new variable radial notch height (RNH). Signiﬁcant differences (P < 0.001) were found between male and female ulna measurements. Discriminant analysis found the original discriminant equation classiﬁed individuals with accuracies of only 40% for males but 99% for females. New discriminant functions were developed using direct and stepwise analyses of the Spitalﬁelds sample. A direct multivariate function based on four dimensions (NL, OW, CH, RNH) produced an overall classiﬁcation accuracy of 85.4% (males 82.4%; females 88.4%). A second function based on the original three measurements (NL, OW, CH) yielded nearly identical classiﬁcation accuracies (males 81%; females 88.5%). Crossvalidation of the Spitalﬁelds data using the threevariable function yielded an overall classiﬁcation rate of 84.2%. This study indicates that the ulna is sexually dimorphic but its development is population-speciﬁc. Am J Phys Anthropol 135:469–478, 2008. V 2008 Wiley-Liss, Inc. Assessment of sex is one of the fundamental priorities of skeletal analysis, especially in forensic cases where the determination of sex can substantially narrow the biological proﬁle for unidentiﬁed remains. While morphological analysis of complete ossa coxae and crania have suggested accuracies of up to 100%, they are often damaged, making it necessary to ﬁnd methods of assessing sex from other skeletal elements. Many such studies have been developed, a large proportion of which are devoted to metrical analysis of the major weight-bearing bones, such as the femur and tibia (e.g., Singh et al., 1975; Black, 1978; Dibennardo and Taylor, 1979, 1982; Ruff and Hayes, 1983; Iscan and Miller-Shaivitz, 1984a,b; Holland, 1991; Kieser et al., 1992; France, 1998; Stojanowski and Seidemann, 1999). However, the propensity for missing or fragmentary elements in archaeological assemblages and degraded forensic cases has resulted in the compilation of metrical data for a large number of skeletal elements (e.g., Singh and Singh, 1972; Stewart, 1979; Dibennardo and Taylor, 1983; Berrizbeitia, 1988; Holman and Bennet, 1991; Scheuer and Elkington, 1993; Falsetti, 1995; Introna et al., 1997; Steyn and Iscan, 1997, 1999; Iscan et al., 1998; Stojanowski, 1999; Bidmos and Dayal, 2004). A number of studies have focused on the ulna (Godycki, 1957; Maia Neto, 1959; Steel, 1972; Singh et al., 1974; MacLaughlin and Bruce, 1985; Purkait, 2001), of which many have either proven largely inaccurate or required the complete bone for analysis. An early morphological study of the ulna (Godycki, 1957) proposed that the lunar notch of the proximal portion is divided vertically, through the medial portion, in male individuals. Initial ﬁndings indicated that the method had an accuracy of 95% for males and 85% for females. However, a corroborative study by Maia Neto (1959) showed the original ﬁndings to be largely inaccurate. For example, of 204 ulnae without the lunar division and therefore theoretically female, 25% were misclassiﬁed as male. Steel (1972) was one of the ﬁrst researchers to devise a metrical method of assessing sex from the complete ulna. Using a documented shelf collection, discriminant function equations were used to analyze data from three osteometric dimensions taken from complete ulnae. The dimensions included the total length of the bone, the coronoid height, and the width of the distal epiphysis. Although reasonable classiﬁcation accuracies were reported, the study relied upon a relatively small sample. Again, the requirement of a complete bone for this method renders it unusable with fragments. Another study (Singh et al., 1974) developed demarking points relating to the total length, midshaft circumference, and the distal end breadth of the ulna. Nearly 100% accuracy C 2008 V WILEY-LISS, INC. C *Correspondence to: Robert F. Pastor, Department of Anthropology, University of Oregon, Eugene, Oregon 97403-1205. E-mail: firstname.lastname@example.org Received 19 December 2006; accepted 31 October 2007 DOI 10.1002/ajpa.20771 Published online 10 January 2008 in Wiley InterScience (www.interscience.wiley.com). 470 L.S. COWAL AND R.F. PASTOR was achieved through this method and the technique was found to be applicable to 99.75% of the Indian population used to create it. However, the method has never been validated for accuracy or to determine its applicability to other populations. A recent study by Purkait (2001) focussed on three dimensions of the proximal ulna measured on whole elements from a contemporary documented Indian sample. Accuracies of 80–96% were found from discriminant function analysis of various combinations of variables. It is surprising that little effort has been made to develop a metrical method from the more robust proximal end of the ulna, with the exception of Purkait (2001), since a recent study by Grant and Jantz (2003) indicated high accuracies using a small set of metric variables. Advantages of this method include its applicability to poorly preserved skeletal material, such as in degraded archaeological assemblages or from aircraft crash sites and other mass disasters, and its reputed high accuracy of classiﬁcation (Grant and Jantz, 2003). According to these authors, the proximal ulna is superior to the cranium and other postcranial elements for sex attribution. The original study by Grant and Jantz (2003) used three different documented skeletal samples of known age and sex. The study’s primary aim was to determine if it was possible to determine sex from measurements taken from the proximal ulna. The sample comprised 217 individuals of European–American and African–American descent from three different collections. The initial study was carried out on the William M. Bass Donated Collection, comprising modern individuals of known sex, age, and race, the latter being primarily Americans of European or African ancestry. Skeletal material from two documented collections was used to test the original ﬁndings and develop the method: Terry Collection (NMNH, Smithsonian); and the Joint POW/MIA Accounting Command’s Central Identiﬁcation Laboratory (JPAC/CIL, formerly CILHI). The Terry Collection consists of individuals born in the late 19th and early 20th centuries of known sex and age while the JPAC/CIL test skeletons are all American military casualties from previous conﬂicts. A mixture of left and right-sided bones with no evidence of pathology was used for the Grant and Jantz (2003) study, although left bones were preferred. Three measurements were then taken from the proximal ulna and the ﬁndings were examined by means of discriminant analysis. The results produced an accuracy of 100% for African–American males and European–American females. However, there were four misclassiﬁcations in the sample of European–American males, which resulted in an accuracy of 94.4%. One set of remains in the sample of African–American females was misclassiﬁed, resulting in an accuracy of 97.1%. This discrepancy was attributed to the width of the olecranon process, which was the most strongly weighted variable (Grant and Jantz, 2003). Indeed, the misclassiﬁcation of the males was the result of narrow olecranon widths and the misclassiﬁcation of the single female was due to a wide olecranon width. In the present study, the original discriminant function (equation) devised by Grant and Jantz (2003) is tested on a documented historic European sample of known age and sex. It also tests the method further using a European archaeological sample, where sex has been assessed using morphological analysis of the ossa coxae and crania. The objective is to evaluate whether the proximal ulna is indeed sexually dimorphic and if so, to determine the accuracies of models from the original American Journal of Physical Anthropology TABLE 1. Documented and archaeological samples with sex distribution Skeletal collection Females, N Males, N Total Spitalﬁelds Cofﬁn-Plate Raunds Furnell Total 86 23 109 85 29 114 171 52 223 study and its reliable application to other historical populations. The rationale for this study focused on two principal hypotheses. The null hypothesis states that no signiﬁcant sexual dimorphism is exhibited for dimensions of the proximal ulna. Alternative hypotheses propose that the proximal ulna exhibits systematic and signiﬁcant sexual dimorphism for dimensions of the proximal ulna in European samples, and for which reasonably accurate discriminant equations can be produced. MATERIALS AND METHODS The sample used in the present study comprised two separate osteological collections: the documented Spitalﬁelds Cofﬁn-Plate Sample and the Raunds Furnells archaeological collection. Sample sizes and sex distributions are shown in Table 1. The Spitalﬁelds Cofﬁn-Plate sample, housed at the Natural History Museum in London was the primary focal point of this study. Excavation of the Spitalﬁelds Christ Church Crypt began in November 1984 and resulted in the recovery of 387 sets of postmedieval remains with cofﬁn-plates, documenting the deceased’s names, date of birth and date of death, the latter of which spanned from 1729 to 1852 (Cox, 1996). Subsequently, it was discovered that the majority of the population was of French Huguenot ancestry with only 33% of British origin (Cox, 1996). Because of varied levels of preservation only 171 sets of remains from the cofﬁnplate sample were suitable for analysis with regards to this study. The Raunds Furnells Collection, housed at the University of Bradford’s Biological Anthropology Research Centre (BARC), comprises an Anglo-Saxon population from East Northamptonshire. Excavations starting in 1977 led to the discovery of 376 sets of remains buried between the 10th and 12th centuries. Of the 191 adults excavated only 182 could be assessed for sex (Powell, 1996) however, the explosion of a petroleum gas station in 1983 led to the damage and loss of several sets of remains. Subsequently, 52 individuals were available for this study. Because of the absence of documented sex and age information for the Raunds Furnells collection, sex assessment was carried out on this sample by the ﬁrst author using standard morphological indicators of the ossa coxae. In all cases, sex assessment of the skeletons in the sample matched the original assessment reported by Powell (1996). All remains missing the left proximal ulna were excluded from the study as were ulnae showing signs of pathological alteration or erosion to the proximal end. In cases where the left and right ulnae were present, both were measured. However, remains where only the right ulna was present were excluded from the study. All measurements pertaining to the Spitalﬁelds sample were performed ‘‘blind’’ to prevent biasing the results. The resulting sample consisted of 171 (86 females and 85 males) individuals from the Spitalﬁelds Collection and SEXUAL DIMORPHISM IN THE PROXIMAL ULNA Fig. 1. Ulnar notch length (NL) measurement, lateral view. 471 Fig. 2. Ulnar olecranon width (OW) measurement, anterior view. 52 (23 females and 29 males) individuals from the Raunds Furnells Collection. Five measurements were taken from the proximal ulna. The ﬁrst three, classiﬁed as the notch length (NL), olecranon width (OW), and the coronoid height (CH), are those deﬁned and analyzed in the original study by Grant and Jantz (2003) (Figs. 1–3). The fourth and ﬁfth (Figs. 4 and 5) are new measurements chosen for additional analysis during this study: the radial notch height (RNH) and the radial notch width (RNW). All measurements were taken using a set of digital sliding calipers, to the nearest tenth of a millimeter. Notch length The maximum distance between the most proximal point on the lateral articular rim of the olecranon process to the most distal point on the articular rim of the radial notch (see Fig. 1). With the ulna held so that the radial notch faces the individual taking the measurement, the sliding calipers are then positioned parallel to the longitudinal axis of the diaphysis, with the ﬁxed arm of the calipers resting along the proximal surface of the articular rim of the semilunar notch. The calipers are adjusted to meet the most distal point on the articular rim of the radial notch. It should be noted that the shape and position of the radial notch are variable, so the calipers will not always lie neatly across the length of the articular rim. Fig. 3. Ulnar coronoid height (CH) measurement, lateral view. articular rims of the semilunar notch could alter the outcome of the measurement. Olecranon width Coronoid height The maximum distance between the proximal medial articular rim and the proximal lateral articular rim on the semilunar notch of the olecranon process (see Fig. 2). This measurement is taken by holding the ulna so that the semilunar notch faces towards the individual taking it. The ﬁxed arm of the sliding calipers are held parallel to the lateral articular rim of the semilunar notch and the calipers adjusted to meet the most distal point on the medial articular rim. While enthesophytic lipping is common on the most proximal and dorsal surfaces of the olecranon process this should not affect the measurement. However, erosion along the medial and lateral This measurement is the maximum distance between the most ventral aspect on the articular rim of the coronoid process and the point on the dorsal surface of the proximal ulna, perpendicular to the length of the diaphysis (see Fig. 3) (McHenry et al., 1976; Bräuer, 1988). To take this measurement, the ulna is held horizontally with the semilunar notch facing upwards. The sliding calipers are positioned perpendicular to the longitudinal axis of the diaphysis with the ﬁxed arm on the most ventral aspect of the articular rim of the coronoid process. The calipers are then adjusted to meet the dorsal surface of the proximal ulna. It should be noted that osteophytic American Journal of Physical Anthropology 472 L.S. COWAL AND R.F. PASTOR Fig. 4. Ulnar radial notch height (RNH) measurement, lateral view. lipping is common on the ventral aspect of the coronoid process and could alter the measurement. Radial notch height This measurement is the maximum distance between the most proximal aspect on the articular rim of the radial notch and the most distal aspect on the articular rim of the radial notch (see Fig. 4) (similar to ulna measurement 9a in Bräuer, 1988). To take this measurement, the ulna is held so that the radial notch faces toward the individual taking it. With the ﬁxed arm of the sliding calipers on the proximal articular rim of the radial notch the calipers are adjusted to meet the distal articular rim of the radial notch. Radial notch width The maximum distance between the most dorsal point on the articular rim of the radial notch and the most ventral point on the articular rim of the radial notch (see Fig. 5) (similar to ulna measurement 9b in Bräuer, 1988). This measurement should be taken while holding the ulna so that the radial notch faces the individual taking it. The sliding calipers are held perpendicular to the longitudinal axis of the diaphysis with the ﬁxed arm of the calipers positioned parallel to the diaphysis along the dorsal articular rim of the radial notch. The calipers are then adjusted to meet the most ventral point on the articular rim of the radial notch. A paired-sample Student’s t test was carried out to test the intraobserver error for all measurements. The ﬁrst 20 individuals with both the left and right ulnae, from the Spitalﬁelds sample, were utilized for this purpose. Each of the ﬁve metric variables (NL, OW, CH, RNH, and RNW) was measured on the left and the right ulnae of each individual during the ﬁrst day of data collection. The same measurements were then repeated 5 days later without reference to the original metrical values. Two-sample Student’s t tests were conducted for all measurements from each individual to compare the left American Journal of Physical Anthropology Fig. 5. Ulnar radial notch width (RNW) measurement, lateral view. measurement to the right. This process was repeated on the ﬁrst twenty individuals with both the left and right ulnae from the Raunds Furnells sample to determine whether different metric variables were affected between the two populations. Finally, where present, the measurements from the right NL, OW, and CH of each individual from the Spitalﬁelds and Raunds Furnells samples were used to assign sex assessments using the original Grant and Jantz (2003) equation. The results were then compared with the sex assessments from the left bone to determine whether asymmetrical variation was great enough to alter the results of the equation. Paired-sample Student’s t tests were done to determine whether there were signiﬁcant size differences between males and females. The left ulnae of the Spitalﬁelds males and females were compared for this purpose, resulting in the comparison of 85 males with 86 females (total sample of 171, see Table 1). The original three measurements (NL, OW, and CH) from both samples were used to test the discriminant function equation devised by Grant and Jantz (2003). All data compilation and statistical analyses were conducted using various subroutines of SPSS version 12.0 (SPSS Science, Inc., 2004). New discriminant function equations were generated for the Spitalﬁelds documented sample using stepwise, univariate, and direct analyses. Unstandardized coefﬁcients were used to create the new discriminant functions using left elements. Functions were developed using the original three measurements (NL, OW, CH) as well as the new variables. In addition, formulae were generated using direct discriminant function analysis of selected combinations of variables for use with fragmentary skeletal remains. New equations were then used to ascribe sex assessments to the left bones from the Raunds Furnells sample. Finally, crossvalidation discriminant analysis of the Spitalﬁelds sample was done in SPSS using a ‘‘leaveone-out’’ classiﬁcation protocol on functions derived from combinations of variables. This type of discriminant 473 SEXUAL DIMORPHISM IN THE PROXIMAL ULNA function subroutine holds one specimen out of the sample in a sequence and then calculates the group variance based on the data from all other specimens. As such, this discriminant analysis approximates a ‘‘jackknife’’ analysis (Aﬁﬁ et al., 2004; Jerwood, personal communication) to derive a truer picture of the error rate for classiﬁcations based on the reference sample. To explore the contribution of shape characteristics, compared with size, for the proximal ulna to any dimorphism present, additional discriminant analyses were conducted using log transformed raw measurements (Darroch and Mosimann, 1985). The log transformations were calculated as the ratio of each individual measurement (e.g., from NL) to the geometric mean for that variable. These ‘‘log shape’’ variables were then used as scale-free indices where shape characteristics of individual variables are given greater statistical weight in the analyses compared with the size characteristics (Holliday, 1997; Powell and Neeves, 1999). Using these variables, separate additional discriminant functions (univariate and multivariate) were generated to test whether there were signiﬁcant shape differences in the proximal ulna between the sexes. RESULTS Results from the intraobserver error analysis indicated that one of the two new measurements (RNW) was unreliable, so this variable was subsequently excluded from the rest of the analyses. All other measurements were found to have negligible intraobserver error (P \ 0.05). Statistical comparison of the left and right ulnae from the two samples indicated signiﬁcant asymmetry (P \ 0.01) for the NL measurement and nearly so (P \ 0.06) for RNH in the Spitalﬁelds sample and OW in the Raunds Furnells sample. From the 129 Spitalﬁelds individuals with both ulnae present, a comparison of sex classiﬁcations from the right ulnae with the left showed that 10 cases were classiﬁed differently, while 92.3% proTABLE 2. Means, standard deviations, univariate F-ratios, and P values for Spitalﬁelds left proximal ulna measurements Males (N 5 85) duced the same sex assessment from both left and right elements. Of these 10 differential side comparisons, the majority (7) of correct sex classiﬁcations were from the right side. Only one individual from the Raunds Furnells sample, where both ulnae were present, resulted in an alternate classiﬁcation. The descriptive statistics for each of the four variables for Spitalﬁelds males and females are provided in Table 2. F-test results showed that there were signiﬁcant differences (P \ 0.001) between the metrical values of the male and female ulnae. For all dimensions, male proximal ulnae were signiﬁcantly larger than those of females, indicating that the proximal ulna is sexually dimorphic in this European population. Table 3 presents the results obtained from testing the Grant and Jantz (2003) equation on the complete European sample. All 86 females from the Spitalﬁelds sample were classiﬁed correctly, while a single female from the Raunds Furnells sample was misclassiﬁed. In contrast, 50 males from the Spitalﬁelds sample and nine males from the Raunds Furnells sample were misclassiﬁed as females. Consequently, only 41.2% of males in the Spitalﬁelds sample were correctly classiﬁed and 69% of males in the Raunds Furnells sample using the original equation. The results of the stepwise procedure carried out on the four variables (NL, OW, CH, and RNH) from the Spitalﬁelds sample are listed in Table 4 (Function 1). Of the four measurements entered in the analysis, only NL and width of the olecranon process (OW) were selected as optimal discriminating variables, producing an overall classiﬁcation accuracy of 85.4%. A stepwise analysis of the original three variables, excluding RNH, produced identical results. The canonical discriminant coefﬁcients and other data produced by the stepwise analysis for Function 1, for univariate analyses, and for direct analyses of other combinations of variables are shown in Table 4. Sex assessment of a bone from an unknown skeleton can be achieved by multiplying each measurement by its corresponding coefﬁcient and adding the products together with the constant. For example, for Function 1 the discriminant score (y) is calculated as follows: y ¼ ðNL30:254Þ þ ðOW30:235Þ þ ð14:175Þ Females (N 5 86) Variablea (mm) Mean SD Mean SD F-ratiob P value NL OW CH RNH 36.05 25.08 36.50 11.29 2.97 2.04 2.68 1.34 32.01 21.93 32.43 9.90 1.98 2.22 2.44 1.14 108.79 93.28 107.21 52.99 0.000 0.000 0.000 0.000 a NL, notch length; OW, olecranon process width; CH, coronoid process height; RNH, radial notch height. b Degrees of Freedom 5 169. All signiﬁcant at P \ 0.001. using the dimensions for NL and OW of an ulna of undetermined sex. For a score that is greater than the sectioning point (0.005), the individual can be classiﬁed as male, while for a lower score the individual would be considered female. The raw counts and classiﬁcation frequencies from a direct discriminant function analysis using the original three dimensions (Function 2) are shown in Table 5. For males, 70 ulnae were correctly classiﬁed while 15 were TABLE 3. Classiﬁcation matrix for sex attribution using the original discriminant equationa for proximal ulnae Males Females Skeletal collection Classiﬁed correctly, N Misclassiﬁed, N Total, N Accuracy (%) Classiﬁed correctly, N Misclassiﬁed, N Total, N Accuracy (%) Spitalﬁelds Raunds Furnell Total 35 20 55 50 9 59 85 29 114 41.2 69.0 48.2 86 22 109 0 1 1 86 23 110 100 95.6 99.1 a From Grant and Jantz (2003). American Journal of Physical Anthropology 474 L.S. COWAL AND R.F. PASTOR TABLE 4. Canonical discriminant function coefﬁcients, Wilk’s Lambdas group centroids, structure and sectioning points, and accuracies for Spitalﬁelds males and females Functions and variables Unstandardized coefﬁcient Standardized coefﬁcient Wilk’s lambda Structure point Group centroid Sectioning pointa Accuracy (%) Stepwise analysis 1 NL OW Constant 0.254 0.235 214.175 0.642 0.503 0.608 0.559 0.903 0.836 M 5 0.888 F 5 20.878 0.005 85.4 Direct analysis 2 NL OW CH Constant 3 NL OW CH RNH Constant 4 OW CH RNH Constant 5 OW CH Constant 6 NL CH Constant 7 NL RNH Constant 8 OW RNH Constant 9 CH RNH Constant 0.174 0.184 0.130 214.718 0.145 0.182 0.121 0.127 214.719 0.212 0.200 0.210 214.102 0.228 0.247 213.874 0.218 0.206 214.523 0.341 0.182 213.513 0.360 0.358 212.249 0.320 0.251 213.680 0.440 0.394 0.333 0.547 0.881 0.816 0.875 M 5 0.910 F 5 20.900 0.005 85.4 0.366 0.389 0.311 0.159 0.542 0.873 0.809 0.867 0.610 M 5 0.919 F 5 20.908 0.006 0.453 0.514 0.262 0.557 0.832 0.892 0.627 M 5 0.892 F 5 20.882 0.005 84.8 0.487 0.635 0.571 0.856 0.918 M 5 0.867 F 5 20.857 0.005 84.2 0.552 0.529 0.572 0.928 0.922 M 5 0.864 F 5 20.854 0.005 81.3 0.861 0.227 0.599 0.981 0.685 M 5 0.817 F 5 20.808 0.005 81.3 0.768 0.446 0.598 0.905 0.682 M 5 0.821 F 520.811 0.005 80.7 0.822 0.313 0.592 0.960 0.675 M 5 0.830 F 5 20.820 0.005 78.4 M 5 0.743 F 5 20.734 0.005 85.4 M 5 0.802 F 5 20.793 0.005 81.3 M 5 0.796 F 5 20.787 0.005 77.2 M 5 0.560 F 520.553 0.004 70.8 Univariate analysis 10 OW Constant D.P.c 11 NL Constant D.P.c 12 CH Constant D.P.c 13 RNH Constant D.P.c 0.468 211.011 0.396 213.462 0.389 213.408 0.802 28.496 Females \ 23.51 \ Males Females \ 34.03 \ Males Females \ 34.47 \ Males Females \ 10.60 \ Males (84.2)b 85.4 (83)b a Discriminant scores less than the sectioning point indicate a female while values greater than the sectioning point would be considered male. b Accuracy from cross-validation analysis using ‘leave-one-out’ classiﬁcation. c D.P. 5 Demarking point (in mm). classiﬁed as female, resulting in an accuracy of 82.4%. Ten females from the original sample of 86 ulnae were incorrectly classiﬁed. As such, Function 2 produced an accuracy of 88.4% for females. Overall, 85.4% of the original grouped cases were correctly classiﬁed (Tables 4 and 5). Combined accuracies for both sexes using direct analysis of select combinations of two to four variables ranged from 78.4 to 85.4% (Table 4). The best separations from the multivariate analyses (85.4%) were produced by Functions 2 and 3, followed closely by Functions 4 and 5 (84.8 and 84.2%, respectively). The structure points and Wilk’s Lambda scores shown in Table 4 for these functions indicate that, as with the stepwise procedure (Function 1), notch size (NL) and/or OW were responsible for the majority of the variance in these functions. American Journal of Physical Anthropology The univariate analyses produced a wider range of classiﬁcation accuracies (70.8–85.4%) with the highest contribution from OW alone followed by notch size. The RNH provided the lowest separation (70.8%) for a single variable. The high classiﬁcation accuracies for Functions 2 to 5 where OW is included, and as the sole variable in Function 10, provide further evidence for the importance of this dimension for sex assignment compared with CH and RNH. High accuracies were achieved when applying the new functions to the Raunds Furnells archaeological sample. Only two males were misclassiﬁed resulting in an accuracy of 93.1% and four females were misclassiﬁed resulting in an accuracy of 82.6%. The new functions correctly classiﬁed six Raunds Furnells males that were originally misclassiﬁed by the Grant and Jantz (2003) equation. It 475 SEXUAL DIMORPHISM IN THE PROXIMAL ULNA TABLE 5. Classiﬁcation results for discriminant Function 2 using three variables (NL, OW, CH) from Spitalﬁelds sample Predicted group membership Original analysisa [Count (N)] Percent (%) Cross-validatedb [Count (N)] Percent (%) a b Sex Female Male Total Female Male Female Male Female Male Female Male 76 15 88.4 17.6 74 15 86.0 17.6 10 70 11.6 82.4 12 70 14.0 82.4 86 85 100 100 86 85 100 100 85.4% of original grouped cases correctly classiﬁed. 84.2% of crossvalidated grouped cases correctly classiﬁed. is likely that the two males and one female that remained misclassiﬁed when using the new equations were the result of particularly gracile males and a robust female. For ease of classiﬁcation when single variables are used with fragmentary remains, demarking points are also provided in Table 4 for comparison of the dimension of a specimen in question. A bone measurement for one of the four variables is simply compared with the demarking point listed in Table 4 for that variable to determine the sex of the element. For example, a proximal ulnar fragment where OW was available would be considered male if the measurement was greater than the demarking point of 23.51 mm but female if below this threshold. The crossvalidation discriminant analysis for Functions 2 and 3 yielded only slightly lower overall classiﬁcation rates than the direct analyses (Table 4). The ‘‘leave-one-out’’ protocol using the combination of four variables including RNH (Function 3) yielded a classiﬁcation rate of 83%, whereas the accuracy for the standard direct analysis was 85.4%. A slightly higher overall classiﬁcation rate (84.2%) was obtained from crossvalidation of the original set of three variables (Function 2) compared with the 85.4% accuracy from the standard direct analysis. Table 5 lists the complete classiﬁcation results (counts and percentages) for the crossvalidated analysis using these three variables. For females, 74 of 86 ulnae (86%) were classiﬁed correctly when subjected to crossvalidation compared with the 88.4% accuracy obtained with the original discriminant analysis. A slightly lower classiﬁcation rate was obtained from crossvalidation of male ulnae (70 of 85 specimens, 82.4%), an accuracy identical to that for the original direct analysis. Table 6 shows the descriptive statistics (means, standard deviations) for the log shape variables and the results of univariate discriminant function analyses for each of the four transformed variables. The very low F-ratios and high probability values (P 5 0.882–0.994) indicated that none of these univariate analyses, nor any of the various combinations of variables from multivariate analyses (not shown), yielded signiﬁcant differences between Spitalﬁelds males and females for shape characteristics of the proximal ulna. DISCUSSION A number of previous studies have developed discriminant function models for ulnar dimorphism, although fewer have focussed on proximal dimensions. For exam- TABLE 6. Descriptive statistics and univariate discriminant function analysis of log shape variables for Spitalﬁelds left proximal ulna measurements Males (N 5 85) Females (N 5 86) Variablea Mean SD Mean SD F-ratio P value NL OW CH RNH 1.003 1.003 1.002 1.006 0.082 0.081 0.073 0.119 1.001 1.004 1.002 1.006 0.062 0.101 0.075 0.115 0.022 0.006 0.000 0.000 0.882 0.936 0.994 0.991 a Log shape variables (Darroch and Mosimann, 1985) calculated as the ratio of each individual measurement (e.g., from NL) to the geometric mean for that variable. All Wilk’s Lambdas equal 1. Degrees of Freedom 5 169. ple, Mall et al. (2001) conducted discriminant analyses on arm bones from a contemporary German autopsy sample. Ulnar length alone provided 87% accuracy but for their ‘‘proximal ulnar width,’’ the dimension closest to OW in this study, a much lower classiﬁcation accuracy of 72.14% was obtained. Ulnar length combined with the proximal and distal widths yielded a higher accuracy (90.58%). France (1998) reported that two diameters of the ulnar diaphysis provided 91% correct classiﬁcation on a European–American sample. For the humerus a combination of three dimensions, including epicondylar breadth, yielded 92% accuracy from the same sample. Interestingly, use of a single distal humeral measurement alone (articular width) provided 93% correct classiﬁcation. This articular dimension is probably most closely associated with the two ulnar variables, OW and NL, which provided 85 and 81% accuracy, respectively, in the present study and which comprise much of the ulnar portion of the ulna–humerus articulation. A recent metric study of humeri from a Guatemalan forensic sample (Frutos, 2005) also noted classiﬁcation accuracies greater than 90% for the epicondylar breadth, and similar accuracies were found for this single humeral dimension in several documented Asian skeletal samples (Iscan et al., 1998). A recent study of long bone circumferences from a Late Roman archaeological sample (Safont et al., 2000) revealed that arm bone circumferences produced higher sex classiﬁcation accuracies than those of the leg. Univariate discriminant analyses of ulnar circumferences yielded 91.1% accuracy compared with the slightly more dimorphic humerus (92.6%). However, with this and many of the other methods a complete element is preferable to obtain measurements in the desired locations. For example, it is difﬁcult to determine the exact point of the midshaft in a fragmented bone (MacLaughlin and Bruce, 1985), while the distal epiphysis is the least likely section of the ulna to survive. Purkait (2001) devised a method to assess sex speciﬁcally from the proximal ulna using discriminant functions. Three measurements were taken from bones in a contemporary Indian collection: the olecranon–coronoid angle, and the length and width of the inferior medial trochlear notch. When all three variables were used, the method reached an accuracy of 96% for males and 80% for females. The single best discriminator was the olecranon coronoid angle with an accuracy of 85% and when combined with the trochlear NL an accuracy of 90.6% was obtained. Despite having seemingly good accuracies, this study is not without its problems. Although the method was designed to speciﬁcally use the proximal American Journal of Physical Anthropology 476 L.S. COWAL AND R.F. PASTOR ulna, determination of the olecranon-coronoid angle is complicated and requires the ulna to be nearly intact making the method difﬁcult to use with fragmentary elements. Grant and Jantz (2003) determined that the OW was weighted most heavily in determining sex, followed by the CH and ﬁnally the NL. However, the European discriminant functions indicated that the NL was the greatest contributor followed by the OW, the CH and ﬁnally the RNH. It is therefore evident that different variables will have more of an impact in assessing sex within different populations. Similar population differences have been reported in a variety of studies focused on the metric assessment of sex and as such this result is not entirely surprising. (e.g., Stewart, 1948; MacLaughlin and Bruce, 1985). The fact that Function 3 with RNH present has a slightly lower crossvalidated classiﬁcation rate (83%) than for Function 2 where this dimension is not included argues that the RNH contributes less to the overall variance than the other variables (Table 4). This is also conﬁrmed by the comparatively low single dimension classiﬁcation accuracy for RNH (70.8%, Function 13). The two dimensions (NL and OW) exhibiting side asymmetry in the Spitalﬁelds and Raunds Furnells samples, respectively, are both directly associated with the size of the distal humerus. Many studies have indicated that the humerus is prone to developmental changes from physical activity, leading to increased cortical bone thickness as a result of mechanical loadings on the bone. This can be caused by a number of factors including body mass, muscle attachments, and body proportion (Ruff, 1992; Knüsel, 2000). Consequently, if an arm bone is used repetitively over a long period of time, for example, from a work-related activity, the cortical bone thickness will increase (Claussen, 1982; Mays, 1998). It is likely that the bilateral asymmetry in proximal ulna size for the European samples is associated with functional alterations of the distal humerus due to activity related movement in the dominant arm (Claussen, 1982; Ruff, 1992; Mays, 1998). The fact that the sizes of male ulnae were generally more variable than those of females (Table 2), which were in general uniformly small, is consistent with the ﬁndings of Grant and Jantz (2003) and may be further evidence for the effects of activity-related movement. It is evident from the analyses using the original equation (Grant and Jantz, 2003) that assessing sex from the proximal ulna produced unsatisfactory results when applied to the European groups. The results indicate that Spitalﬁelds and Raunds have smaller proximal ulna dimensions than the American samples analyzed in the original study. The less robust dimensions of the European samples result in all the females being correctly classiﬁed because they are in the female range, but many males are misclassiﬁed because of their smaller size and resemblance to the American female ulnae. Conversely, classifying the American groups on a Spitalﬁelds function would result in getting males correct but with the result of missing many of the females because they fall in the size range of Spitalﬁelds males. Nevertheless, it is somewhat surprising that the method presented here for the proximal ulna, although providing reasonably good accuracies with the European samples, did not yield the extremely high accuracies reported by Grant and Jantz (2003) for their American samples. Previous studies have documented secular American Journal of Physical Anthropology changes between the 19th and 20th centuries in the size and proportion of long bones (e.g., Meadows and Jantz, 1995). The differences observed here may be due to secular changes (e.g., Boldsen, 1995; Meadows and Jantz, 1995) for the American samples whereby male elbows are more robust than females due to nutritional or developmental differences, or from genetic differences between the samples. It is possible the relatively lower dimorphism in the Spitalﬁelds population is a result of similar occupations (i.e., artisans primarily in the weaving trade) shared by men and women in this London group (Cox, 1996), which might limit the developmental differences such as musculature. In addition, this population was likely under low but chronic nutritional and environmental stress due to the cramped and polluted living conditions in London during the post-Medieval industrial era (Molleson and Cox, 1993; Lewis, 2002). It is a well-known phenomenon that a population under severe environmental stress will have diminished sexual dimorphism (e.g., Stinson, 1985) but after amelioration of the stressors that the males in the population often then experience augmented growth and development compared with females (Frisancho, 1993; Boldsen, 1995; Bogin, 1999). This could explain some of the differences seen between the populations examined in the present study and the contemporary groups used in the Grant and Jantz (2003) study. However, it is apparent from this study that the method can produce relatively high standards of accuracy when assessing sex, although it is evident that one equation cannot be applied universally. Original data obtained by Grant and Jantz (2003) were unavailable for examination, making comparison of the two studies purely based on their central tendencies. However, results from this comparison have highlighted that dimensions of the proximal ulna are not consistent throughout different populations. The method appears to be highly size sensitive and therefore it would be inadvisable to extend results from one sample to another unless the ulna dimensions can be shown to be similar. This point is echoed by the fact that the comparisons between size information and shape information revealed no signiﬁcant shape differences in the proximal ulna between the sexes. CONCLUSIONS This study tests the original work of Grant and Jantz (2003) on two European populations, the documented Spitalﬁelds Cofﬁn-Plate sample and a British archaeological sample (Raunds Furnells). The study conﬁrms that the proximal ulna is sexually dimorphic and that the three metric traits devised in their study are easily undertaken and repeated. Two new metric variables were tested, one of which (RNH) provided reasonable univariate classiﬁcation accuracy but performed better when combined with other variables. The Grant and Jantz (2003) equation was found to be highly inaccurate when applied to European males, with correct classiﬁcations dropping to 50%. Several new discriminant functions were developed using the documented Spitalﬁelds sample and produced good accuracies when applied to both European populations. Results from this study demonstrate that the size of the proximal ulna is associated to its direct articulation with the distal humerus and subsequent developmental change due to mechanical loadings on the bone. This SEXUAL DIMORPHISM IN THE PROXIMAL ULNA method and the derived equations are inherently population-speciﬁc, as shown previously in numerous metric analyses of other skeletal elements demonstrating sexual dimorphism as well as associations with stature (e.g., Trotter and Gleser, 1952a,b; Stewart, 1979; Krogman and Iscan, 1986; King et al., 1998; Bidmos and Asala, 2003, 2005). Consequently, the optimism expressed in the original study (Grant and Jantz, 2003) for ranking the proximal ulna ahead of the cranium and most other postcranial elements for sex assignment is tempered by the lower overall accuracy (85.4%) for formulas developed from the 18th and 19th century European sample. Results from this study indicate that while the method provides good accuracies and a quick and easy manner of assessing sex, care should be taken when applying it to populations of alternate origin. While the equations presented here would be applicable to other European historical and archaeological groups, tests of the method on other populations especially modern samples would be beneﬁcial in the application to medico-legal investigations and for the classiﬁcation of other archaeological series. ACKNOWLEDGMENTS Appreciation is extended to Louise Humphrey and Rob Kruzynski (The Natural History Museum, London) for access to the Spitalﬁelds Collection. 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