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Do group-specific equations provide the best estimates of stature?
Forensic Science International 261 (2016) 154–158
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Do group-specific equations provide the best estimates of stature? John Albanese *, Stephanie E. Osley, Andrew Tuck Department of Sociology and Anthropology, University of Windsor, Windsor, Ontario, Canada
A R T I C L E I N F O
A B S T R A C T
Article history: Received 20 July 2015 Received in revised form 7 February 2016 Accepted 9 February 2016 Available online 17 February 2016
An estimate of stature can be used by a forensic anthropologist with the preliminary identification of an unknown individual when human skeletal remains are recovered. Fordisc is a computer application that can be used to estimate stature; like many other methods it requires the user to assign an unknown individual to a specific group defined by sex, race/ancestry, and century of birth before an equation is applied. The assumption is that a group-specific equation controls for group differences and should provide the best results most often. In this paper we assess the utility and benefits of using group-specific equations to estimate stature using Fordisc. Using the maximum length of the humerus and the maximum length of the femur from individuals with documented stature, we address the question: Do sex-, race/ancestry- and century-specific stature equations provide the best results when estimating stature? The data for our sample of 19th Century White males (n = 28) were entered into Fordisc and stature was estimated using 22 different equation options for a total of 616 trials: 19th and 20th Century Black males, 19th and 20th Century Black females, 19th and 20th Century White females, 19th and 20th Century White males, 19th and 20th Century any, and 20th Century Hispanic males. The equations were assessed for utility in any one case (how many times the estimated range bracketed the documented stature) and in aggregate using 1-way ANOVA and other approaches. This group-specific equation that should have provided the best results was outperformed by several other equations for both the femur and humerus. These results suggest that group-specific equations do not provide better results for estimating stature while at the same time are more difficult to apply because an unknown must be allocated to a given group before stature can be estimated. ß 2016 Elsevier Ireland Ltd. All rights reserved.
Keywords: Forensic anthropology Stature estimation Long bones Fordisc Secular changes Sex Race/ancestry
1. Introduction An estimate of stature, along with estimates of age and sex, can be used by a forensic anthropologist to assist in the identification of an unknown individual when human skeletal remains are recovered. After Trotter and Gleser [1–3] published a series of papers, the approach for stature estimation has been to develop equations that are group-specific where group membership is based on combinations of sex, race, ancestry, continental origin, nationality, year of birth, and other criteria (for example, [4–13,27– 29]). However, there is some evidence that this group-specific approach can be problematic for various practical and theoretical reasons [14,31–33].
* Corresponding author at: Department of Sociology, Anthropology, and Criminology, 401 Sunset Avenue, University of Windsor, Windsor, Ontario, N9B 3P4 Canada. Tel.: +1 519 253 3000x3973; fax: +1 519 971 3621. E-mail address: [email protected] (J. Albanese). http://dx.doi.org/10.1016/j.forsciint.2016.02.019 0379-0738/ß 2016 Elsevier Ireland Ltd. All rights reserved.
Fordisc is a computer application that can be used to estimate stature, as well as ‘‘race’’ or ancestry, and sex [15]. Fordisc, currently in version 3.1, is an automated version of many of these traditional methods with some changes to the reference samples used to generate equations for constructing a biological profile of an unknown individual. When estimating stature, the software requires the user to select sex-, race- and century-specific options. The rationale is that group-specific equations should provide the most accurate and most useful results most often for stature estimation. An option for non-specific equations is possible in Fordisc but it is described in the Fordisc Help File (Version 1.35, http://math.mercyhurst.edu/sousley/Fordisc/) as a second-best approach that should be used when there are no other options. The most significant practical limitation of this approach is that an unknown individual must first be allocated to one of these sexrace-century groups before the ‘‘correct’’ equation is applied. In this paper we test all the various parameters for group specificity required to estimate stature using humerus and femur data collected from individuals in the Terry Collection for whom stature is documented. We use Fordisc because it allows for the
J. Albanese et al. / Forensic Science International 261 (2016) 154–158
user to easily toggle through a number of group-specific equations, but the goal is not necessarily to test the utility of the software. The goal is to test whether sex-, race- and century-specific stature equations provide the best results when estimating stature.
2. Materials and methods A sample (n = 28) was selected from the Terry Collection to include only White males with years of birth before 1870. The birth years were selected so that the entire growth and development period was completed before the start of 20th century. There are 134 individuals in the Terry Collection within these parameters for whom there are stature data. Approximately 20% of these 134 individuals were randomly selected to be included in this research. The maximum length of the humerus and the maximum length of the femur were collected from the left side by two of us on two separate occasions following the measurement description recommended for Fordisc [16]. Testing was conducted to ensure that data were collected consistently. Intra- and inter-observer measurement errors were assessed using the absolute differences between measurements. In over 95% of the cases, the absolute difference for each observer and between observers was less than 1 mm or 0.5%. In a few cases where the bone on the left side was damaged or was affected by trauma, data were collected from the right side. Both femur and humerus data were used to assess any differences between the upper and lower limb. Data for this research were collected from the Terry Collection because it is one of the few identified skeletal collections with reliable, documented stature for a large number of individuals [17]. Stature data were collected by Robert Terry and his assistants using a standardized protocol for positioning, measuring and photographing the cadaver in a ‘‘standing’’ position that closely approximated living stature [1,34]. For some cases it was not always possible to accurately reproduce living stature from the cadavers. Those cases were easily excluded from our sample using Terry’s detailed notes and photographs of cadavers. The humerus and the femur data for our sample of 19th Century White males were entered into Fordisc and stature was estimated using 22 different equation options for a total of 616 trials: 19th and 20th Century Black males, 19th and 20th Century Black females, 19th and 20th Century White females, 19th and 20th Century White males, 19th and 20th Century Any, and 20th Century Hispanic males. There is no 19th Century Hispanic option. The ‘‘Any’’ option is better described as ‘‘all’’ because it includes all
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racial groups and both sexes in a century-specific equation. The 90% confidence interval was used for this analysis. If the race, century and sex assumptions are true, then the 19th Century White male equation should consistently provide the best predictions of stature for the test sample of 28 White males who were born and had their entire growth and development period in the 19th century. The latest version of Fordsic was used: Version 3.1, build 307, released October 16, 2015. The accuracy and utility of the equations were assessed several ways. First, we assessed the equations using a simple count to determine the utility of the equations for providing useful information in a forensic investigation. We counted the number of times the actual stature was bracketed by the predicted range calculated using the 90% confidence interval, which provides the narrowest estimated range. We calculated the mean difference (MD) and mean absolute deviation (MAD). The MD is the average of the difference of the estimated stature minus the documented stature. One limitation of the MD is that some positive and negative errors may cancel each other out. One clear benefit of the MD is that it can be used to identify a tendency or bias to overestimate or underestimate stature using a specific equation. When calculated as the estimated stature minus the documented stature as in this research, a positive MD suggests a tendency to overestimate documented stature and a negative MD suggests a tendency to underestimate documented stature. The MAD is the mean of the absolute value of the documented stature minus predicted stature. In contrast to the MD, which is always equal to or lower than the MAD, the MAD is a better measure of overall error because it is the mean of the absolute difference, and positive and negative errors do not cancel each other out. Together the MAD and MD provide a good measure of precision (how close the estimate is to the documented stature), and bias (trend towards overestimation or underestimation), respectively. Both the MDs and MADs for each equation were tested using a one-sample t-test to assess whether they are significantly different than zero. The MADs for each equation were also tested for significant differences from each other using 1way ANOVA. Finally, the estimated mean for each equation was tested for significant differences from the mean of the documented statures using 1-way ANOVA and Tukey HSD post hoc to group means into homogeneous subsets.
3. Results The MAD and MD are listed for each equation for the humerus and the femur in Table 1. The equations are listed from best to
Table 1 Mean difference (MD) and mean absolute difference (MAD) for equations using the humerus and femur ranked by overall utility. The 19th Century White male equations calculated by Fordsic 3.1 do not provide the best results when tested on a sample (n = 28) of 19th Century White males from the Terry Collection. Humerus No 20th 20th 20th 20th 20th 20th 19th 19th 19th 19th 19th * & ^ # **
Century Century Century Century Century Century Century Century Century Century Century
Black Male Black Female White Female Any (All) White Male Hispanic Male Any (All) White Male Black Male White Female Black Female
0 0 0 0 1 1 1 2 2 2 8
Yes 28 28 28 28 27 27 27 26 26 26 20
Femur % 100 100 100 100 96.4 96.4 96.4 92.9 92.9 92.9 71.4
MAD* 3.58 3.73 3.66 3.68 3.89 3.58 3.95 3.64 3.83 3.84 4.84
All MADs are significantly different from zero at p < 0.0001 level. Significantly different from zero at p < 0.05 level. Significantly different from zero at the p < 0.01 level. Significantly different from zero at p < 0.001 level. Significantly different from zero at the p < 0.0001 level.
Humerus and Femur MD 0.78 0.23 1.97& 1.01 2.32# 1.23 2.35^ 1.49 2.10& 1.95& 4.45**
No 0 0 0 0 0 1 1 1 1 3 12
Yes 28 28 28 28 28 27 27 27 27 25 16
% 100 100 100 100 100 96.4 96.4 96.4 96.4 89.3 57.1
MAD* 4.31 4.02 3.56 2.55 2.74 2.66 3.68 2.43 3.24 4.20 5.96
MD **
3.90 3.78** 3.08** 0.93 1.20& 0.39 3.02** 0.54 2.64** 3.95** 5.89**
No
Yes
%
0 0 0 0 1 2 2 3 3 5 20
56 56 56 56 55 54 54 53 53 51 36
100 100 100 100 98.2 96.4 96.4 94.6 94.6 91.0 64.3
J. Albanese et al. / Forensic Science International 261 (2016) 154–158
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worst by overall utility for both bones. For the first four groups (eight equations) estimated range bracketed the documented stature 100% of the time for both the femur and the humerus: 20th Century Black male, 20th Century Black female, 20th Century White female, 20th Century Any. The 19th Century White male equation did not bracket documented stature twice using the humerus and once using the femur, but performed well by bracketing the documented stature 94.6% (53 out of 56). Twenty out of the 22 group-specific equations bracketed the documented stature of the 19th Century White males over 90% of the time. The exceptions to the trend in utility were the 19th Century Black female equations which performed poorly using both the femur and the humerus. The one-sample t-tests indicate that the MADs, which range from 2.43 cm for the 19th Century White male femur equation to 5.96 cm for the 19th Century Black female femur equation, are all significantly different (p < 0.0001) than zero. The 1-way ANOVA of the MADs indicates that (1) although the 19th Century White male femur equation has the lowest MAD, that MAD is not significantly different than any other MAD except for the 19th Century Black female humerus equation and the 19th Century Black female femur equation; and (2) The MAD for the 19th Century White male humerus equation is in the middle of the range of MADs and is not significantly different than any other MAD (Table 2). Six of 11 humerus equations and eight of the 11 femur equations have MDs that are significantly different than zero (significance varies in level from p < 0.05 to p < 0.0001). Statistically, significance of MDs in these cases suggests a bias in error rather than a random distribution of error. With the way MDs were calculated in this study, a positive MD suggests a tendency to overestimate stature and a negative MD suggests a tendency to underestimate stature. Of the 14 MDs that are significantly different from zero, only one has a tendency to overestimate stature: the 20th Century White male humerus equation. For most equations with a significant bias, the MDs are absolutely small and relatively small when compared to the 90% prediction interval generated by Fordisc which ranged from a low of 5.2 cm for 20th Century Hispanic male femur equations to high of 11.4 cm for 19th Century Black female humerus equations.
Table 2 Homogeneous subsets, grouped using Tukey HSD post hoc, of MAD for various equations using the humerus and the femur. Equation
n
1
Femur White Male 19th C Femur Any 20th C Femur Hispanic Male 20th C Femur White Male 20th C Femur Black Male 19th C Femur White Female 20th C Humerus Black Male 20th C Humerus Hispanic Male 20th C Humerus White Male 19th C Humerus White Female 20th C Femur Any 19th C Humerus Any 20th C Humerus Black Female 20th C Humerus Black Male 19th C Humerus White Female 19th C Humerus White Male 20th C Humerus Any 19th C Femur Black Female 20th C Femur White Female 19th C Femur Black Male 20th C Humerus Black Female 19th C Femur Black Female 19th C
28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28
2.43 2.55 2.66 2.74 3.24 3.56 3.58 3.58 3.64 3.66 3.68 3.68 3.73 3.83 3.86 3.89 3.95 4.02 4.20 4.31
Sig.
.366
2 2.55 2.66 2.74 3.24 3.56 3.58 3.58 3.64 3.66 3.68 3.68 3.73 3.83 3.86 3.89 3.95 4.01 4.20 4.31 4.84
.077
3
3.58 3.58 3.64 3.66 3.68 3.68 3.73 3.83 3.86 3.89 3.95 4.01 4.20 4.31 4.84 5.96 .051
These small but significant biases do not necessarily translate into poorer estimates of stature. For example, the femur MD for the 20th Century Black female equation is negative and significantly different than zero suggesting a bias to underestimate stature, but the estimated range brackets the documented stature 100% of the time. The MD indicates a slight significant bias for the 20th Century Black females, but the MAD is not significantly different from the 19th Century White male MAD. The pattern is the same for all the equations with the best utility and an MD that is significantly different from zero: 20th Century Black male femur, 20th Century White female femur and 20th Century White female humerus. The small but significant bias has no impact on utility. The obvious outliers that do not follow the overall pattern are the 19th Century Black female equations for the humerus and the femur which have the highest MDs that are significantly different from zero. For the humerus, 24 of 28 cases are negative and for the femur 27 of 28 cases are negative. This tendency is evident in how similar the MD is to the MAD for each equation, respectively (last row of Table 1). Furthermore, the 19th Century Black female MADs are the only MADs that are significantly different than the MADs for 19th Century White male femur equations. Both 19th Century Black female equations are excluded from group 1 in Table 2. The 1-way ANOVA results for the mean documented stature and the means of estimated stature for each group-specific equation for both the humerus and the femur are presented in Table 3. The means are listed from lowest to highest and are grouped into statistically significant homogenous subsets. Although there are three statistically significant groups, (1) there is no pattern to the grouping by sex, race, century or bone, and (2) the documented mean clusters with all three subsets, and there is no significant difference between the mean of the document stature and the means of the estimated stature using any of the equations for either bone (Table 2). 4. Discussion Almost all the equations regardless of group specificity would have provided information that would have been useful in a
Table 3 Homogeneous subsets, grouped using Tukey HSD post hoc, of mean documented stature and of mean stature estimates using various humerus and femur equations. None of the means are significantly different than the mean of the documented stature (in bold). Equation
n
1
Femur Black Female 19th C Humerus Black Female 19th C Femur White Female 19th C Femur Black Male 20th C Femur Black Female 20th C Femur White Female 20th C Femur Any 19th C Femur Black Male 19th C Humerus Any 19th C Humerus Black Male 19th C Humerus White Female 20th C Humerus White Female 19th C Humerus White Male 19th C Femur Any 20th C Femur White Male 19th C Documented Stature Humerus Black Female 20th C Femur Hispanic Male 20th C Humerus Black Male 20th C Humerus Any 20th C Femur White Male 20th C Humerus Hispanic Male 20th C Humerus White Male 20th C
28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28
164.6 166.0 166.5 166.6 166.7 167.4 167.4 167.8 168.1 168.4 168.5 168.5 169.0 169.5 169.9 170.5
Sig.
2
.051
3
166.0 166.5 166.6 166.7 167.4 167.4 167.8 168.1 168.4 168.5 168.5 169.0 169.5 169.9 170.5 170.7 170.9 171.2 171.5 171.7 171.7
.077
167.4 167.4 167.8 168.1 168.4 168.5 168.5 169.0 169.5 169.9 170.5 170.7 170.9 171.2 171.5 171.7 171.7 172.8 .126
J. Albanese et al. / Forensic Science International 261 (2016) 154–158
forensic investigation over 90% of the time, and the ‘‘Any’’ option was not a second best choice for estimating stature. Considering the group-specific equation that is opposite in every parameter for group membership, the 20th Century Black female equations produce results that are not significantly different (MAD, mean stature and humerus MD) than the 19th Century White males, but provide a higher utility by bracketing the documented stature 100% (versus 94.6%). The 19th Century White male equations provide good results but they do not provide any improvement in stature estimates when compared to other group-specific equations with two exceptions. An unexpected result of the uniformity of the results is that the MDs, MADs, 1-way ANOVA, and utility results from this study suggest that the humerus can provide comparable, consistent results if the femur is not available for analysis. The results for the 19th Century Black female equations seem to be the exception to the pattern, but are not necessarily inconsistent with the overall results when the source of the data used by Fordisc is considered. As Komar and Grivas [18] have noted, not enough attention has been paid to the impacts on research of the biased nature of all reference collections. There is some information about the sources of the reference sample used by Fordisc to calculate various equations in the Fordisc Help File (Version 1.35, http://math. mercyhurst.edu/sousley/Fordisc/): generally ‘‘a good number [of American Blacks] come from the Terry Collection’’ (page 4), and specifically with respect to stature, there are 41 Black females in the 19th Century reference sample from the Terry Collection (page 45). Although individuals from the Terry Collection are likely included in all the 19th and 20th Century Black and White groups, the most problematic group is 19th Century Black female. The anomalous results of the 19th Century Black female equations are likely due the nature of this reference sample. Black females from the Terry Collection are the most biased sub-sample in the collection [19]. In the past, this bias has been misinterpreted as ‘‘racial’’ differences in Black females, but is due to physiological stress resulting in compromised growth during the post-civil war segregationist period in the USA. Furthermore, the bias was magnified by how the Terry Collection was amassed. When compared to other groups, there is a disproportionate number of younger Black females which resulted in a significant mortality bias in a group originally described as ‘‘Negro’’ females by Robert Terry and Mildred Trotter. The uniformity of results from the current study is not entirely unexpected. Several studies have concluded that race-specificity is not required and in fact could be a liability for estimating stature [14,30–33]. Feldesman and Fountain [14] found that ‘‘races’’ formed statistical groups but with limited group cohesion, and while there may be a statistical benefit to using a group-specific approach, the cost of selecting the wrong group-specific equation outweighs the benefit of the consistency in estimates that were provided by a generic equation. As Feldesman and Fountain [14] note, there are problems with how they combined data in their meta-analysis since it is possible that the statistically significant differences they found are an artifact of group construction. On a practical level, it may be possible to estimate sex with some certainty even if no method is 100% accurate, but determining race or ancestry can be particularly problematic (see [19] for a critical review of race/ancestry determination methods). Although sex is part of identification in most jurisdictions and race/ancestry is part of identification in some jurisdiction, the results from the current study demonstrate that race- and sex-specific methods are more difficult to apply because the unknown must be allocated to a given group, but this group-specific approach does not provide better results when estimating stature. In fact, the group-specific approach provides results that are worse than expected. Both the 19th and 20th Century ‘‘Any’’ option which include all groups
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in large century-specific reference samples provide results that are as good or better than sex- and race-specific groups. The current study which used the latest build of Fordisc 3.1 is also consistent with previous results that found there was no statistically significant benefit of using century-specific equations when estimating stature using Fordisc 3.0 [20]. An update to the software which includes some changes the 20th Century reference samples has not resulted in any difference in results. Although there may be clear secular trends in stature throughout the 19th and 20th Centuries in much of North America and other parts of the world [21,22–26], there is no clear threshold effect at the start of the 20th century or at any other arbitrary year. Furthermore, secular changes represent population trends while a forensic anthropologist must consider an unknown individual lacking population context. At any given point in a secular trend, there will always be taller and shorter individuals. As with sex and race, the need to choose between centuries in Fordisc complicates stature estimation without providing any improvement in stature estimates. The approach in Fordisc follows the research of [1–3] where the general practice has been to develop group-specific equations. This approach is not unique to Fordisc. Many other methods have developed group-specific methods where the parameters for group membership are based on various combinations of sex, race/ ancestry, continental origin, nationality, year of birth and other criteria (for example, [4–13,27,28]). The basic assumption of all these methods is that group-specific methods should be more accurate because they account or control for variation in body proportions. The results from this study are not consistent with this group-specific methodology for developing stature estimation equations. Twenty out of 22 group-specific equations tested provided very good results regardless of sex, race or century of birth. The fundamental problem is likely the problematic approach to defining the parameters of group membership. For every parameter – sex, race, century – continuous and overlapping human variation is forced into arbitrary categories. Group-specific equations are more difficult to apply because the unknown has to be allocated to a specific group, but these methods do not provide any increase in accuracy or precision.
5. Conclusion The 19th Century White male equation provided good results for estimating stature for 19th Century White males, but it did not provide the best results. Other group-specific equations including 20th Century Black male, 20th Century Black female and 20th Century White female equations provided better results. The results from this study demonstrate that however a group is defined, group-specific equations do not provide better estimates of stature. Two female-specific equations outperformed the malespecific equation which should have worked best on the test sample. Additionally, race-specific equations do not provide any increase in accuracy and precision. Two equations, for Black males and Black females, outperformed the equations for White males when tested on White males. Regardless of the reader’s position on the race concept or the inclusion of race or ancestry as part of identification in some jurisdictions, on a practical level there is no benefit to attempting to determine ‘‘race’’ or ancestry before estimating stature. Race-specific stature estimation methods are at best unnecessary, or at worst a liability because they are more difficult to apply. Lastly, while there are clear secular changes in stature and long bone lengths, century-specific equations provide no benefit when estimating stature. Overall, the results from this study demonstrate that group-specific methods do not provide the best results when estimating stature, and that alternative
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Do group-specific equations provide the best estimates of stature? John Albanese *, Stephanie E. Osley, Andrew Tuck Department of Sociology and Anthropology, University of Windsor, Windsor, Ontario, Canada
A R T I C L E I N F O
A B S T R A C T
Article history: Received 20 July 2015 Received in revised form 7 February 2016 Accepted 9 February 2016 Available online 17 February 2016
An estimate of stature can be used by a forensic anthropologist with the preliminary identification of an unknown individual when human skeletal remains are recovered. Fordisc is a computer application that can be used to estimate stature; like many other methods it requires the user to assign an unknown individual to a specific group defined by sex, race/ancestry, and century of birth before an equation is applied. The assumption is that a group-specific equation controls for group differences and should provide the best results most often. In this paper we assess the utility and benefits of using group-specific equations to estimate stature using Fordisc. Using the maximum length of the humerus and the maximum length of the femur from individuals with documented stature, we address the question: Do sex-, race/ancestry- and century-specific stature equations provide the best results when estimating stature? The data for our sample of 19th Century White males (n = 28) were entered into Fordisc and stature was estimated using 22 different equation options for a total of 616 trials: 19th and 20th Century Black males, 19th and 20th Century Black females, 19th and 20th Century White females, 19th and 20th Century White males, 19th and 20th Century any, and 20th Century Hispanic males. The equations were assessed for utility in any one case (how many times the estimated range bracketed the documented stature) and in aggregate using 1-way ANOVA and other approaches. This group-specific equation that should have provided the best results was outperformed by several other equations for both the femur and humerus. These results suggest that group-specific equations do not provide better results for estimating stature while at the same time are more difficult to apply because an unknown must be allocated to a given group before stature can be estimated. ß 2016 Elsevier Ireland Ltd. All rights reserved.
Keywords: Forensic anthropology Stature estimation Long bones Fordisc Secular changes Sex Race/ancestry
1. Introduction An estimate of stature, along with estimates of age and sex, can be used by a forensic anthropologist to assist in the identification of an unknown individual when human skeletal remains are recovered. After Trotter and Gleser [1–3] published a series of papers, the approach for stature estimation has been to develop equations that are group-specific where group membership is based on combinations of sex, race, ancestry, continental origin, nationality, year of birth, and other criteria (for example, [4–13,27– 29]). However, there is some evidence that this group-specific approach can be problematic for various practical and theoretical reasons [14,31–33].
* Corresponding author at: Department of Sociology, Anthropology, and Criminology, 401 Sunset Avenue, University of Windsor, Windsor, Ontario, N9B 3P4 Canada. Tel.: +1 519 253 3000x3973; fax: +1 519 971 3621. E-mail address: [email protected] (J. Albanese). http://dx.doi.org/10.1016/j.forsciint.2016.02.019 0379-0738/ß 2016 Elsevier Ireland Ltd. All rights reserved.
Fordisc is a computer application that can be used to estimate stature, as well as ‘‘race’’ or ancestry, and sex [15]. Fordisc, currently in version 3.1, is an automated version of many of these traditional methods with some changes to the reference samples used to generate equations for constructing a biological profile of an unknown individual. When estimating stature, the software requires the user to select sex-, race- and century-specific options. The rationale is that group-specific equations should provide the most accurate and most useful results most often for stature estimation. An option for non-specific equations is possible in Fordisc but it is described in the Fordisc Help File (Version 1.35, http://math.mercyhurst.edu/sousley/Fordisc/) as a second-best approach that should be used when there are no other options. The most significant practical limitation of this approach is that an unknown individual must first be allocated to one of these sexrace-century groups before the ‘‘correct’’ equation is applied. In this paper we test all the various parameters for group specificity required to estimate stature using humerus and femur data collected from individuals in the Terry Collection for whom stature is documented. We use Fordisc because it allows for the
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user to easily toggle through a number of group-specific equations, but the goal is not necessarily to test the utility of the software. The goal is to test whether sex-, race- and century-specific stature equations provide the best results when estimating stature.
2. Materials and methods A sample (n = 28) was selected from the Terry Collection to include only White males with years of birth before 1870. The birth years were selected so that the entire growth and development period was completed before the start of 20th century. There are 134 individuals in the Terry Collection within these parameters for whom there are stature data. Approximately 20% of these 134 individuals were randomly selected to be included in this research. The maximum length of the humerus and the maximum length of the femur were collected from the left side by two of us on two separate occasions following the measurement description recommended for Fordisc [16]. Testing was conducted to ensure that data were collected consistently. Intra- and inter-observer measurement errors were assessed using the absolute differences between measurements. In over 95% of the cases, the absolute difference for each observer and between observers was less than 1 mm or 0.5%. In a few cases where the bone on the left side was damaged or was affected by trauma, data were collected from the right side. Both femur and humerus data were used to assess any differences between the upper and lower limb. Data for this research were collected from the Terry Collection because it is one of the few identified skeletal collections with reliable, documented stature for a large number of individuals [17]. Stature data were collected by Robert Terry and his assistants using a standardized protocol for positioning, measuring and photographing the cadaver in a ‘‘standing’’ position that closely approximated living stature [1,34]. For some cases it was not always possible to accurately reproduce living stature from the cadavers. Those cases were easily excluded from our sample using Terry’s detailed notes and photographs of cadavers. The humerus and the femur data for our sample of 19th Century White males were entered into Fordisc and stature was estimated using 22 different equation options for a total of 616 trials: 19th and 20th Century Black males, 19th and 20th Century Black females, 19th and 20th Century White females, 19th and 20th Century White males, 19th and 20th Century Any, and 20th Century Hispanic males. There is no 19th Century Hispanic option. The ‘‘Any’’ option is better described as ‘‘all’’ because it includes all
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racial groups and both sexes in a century-specific equation. The 90% confidence interval was used for this analysis. If the race, century and sex assumptions are true, then the 19th Century White male equation should consistently provide the best predictions of stature for the test sample of 28 White males who were born and had their entire growth and development period in the 19th century. The latest version of Fordsic was used: Version 3.1, build 307, released October 16, 2015. The accuracy and utility of the equations were assessed several ways. First, we assessed the equations using a simple count to determine the utility of the equations for providing useful information in a forensic investigation. We counted the number of times the actual stature was bracketed by the predicted range calculated using the 90% confidence interval, which provides the narrowest estimated range. We calculated the mean difference (MD) and mean absolute deviation (MAD). The MD is the average of the difference of the estimated stature minus the documented stature. One limitation of the MD is that some positive and negative errors may cancel each other out. One clear benefit of the MD is that it can be used to identify a tendency or bias to overestimate or underestimate stature using a specific equation. When calculated as the estimated stature minus the documented stature as in this research, a positive MD suggests a tendency to overestimate documented stature and a negative MD suggests a tendency to underestimate documented stature. The MAD is the mean of the absolute value of the documented stature minus predicted stature. In contrast to the MD, which is always equal to or lower than the MAD, the MAD is a better measure of overall error because it is the mean of the absolute difference, and positive and negative errors do not cancel each other out. Together the MAD and MD provide a good measure of precision (how close the estimate is to the documented stature), and bias (trend towards overestimation or underestimation), respectively. Both the MDs and MADs for each equation were tested using a one-sample t-test to assess whether they are significantly different than zero. The MADs for each equation were also tested for significant differences from each other using 1way ANOVA. Finally, the estimated mean for each equation was tested for significant differences from the mean of the documented statures using 1-way ANOVA and Tukey HSD post hoc to group means into homogeneous subsets.
3. Results The MAD and MD are listed for each equation for the humerus and the femur in Table 1. The equations are listed from best to
Table 1 Mean difference (MD) and mean absolute difference (MAD) for equations using the humerus and femur ranked by overall utility. The 19th Century White male equations calculated by Fordsic 3.1 do not provide the best results when tested on a sample (n = 28) of 19th Century White males from the Terry Collection. Humerus No 20th 20th 20th 20th 20th 20th 19th 19th 19th 19th 19th * & ^ # **
Century Century Century Century Century Century Century Century Century Century Century
Black Male Black Female White Female Any (All) White Male Hispanic Male Any (All) White Male Black Male White Female Black Female
0 0 0 0 1 1 1 2 2 2 8
Yes 28 28 28 28 27 27 27 26 26 26 20
Femur % 100 100 100 100 96.4 96.4 96.4 92.9 92.9 92.9 71.4
MAD* 3.58 3.73 3.66 3.68 3.89 3.58 3.95 3.64 3.83 3.84 4.84
All MADs are significantly different from zero at p < 0.0001 level. Significantly different from zero at p < 0.05 level. Significantly different from zero at the p < 0.01 level. Significantly different from zero at p < 0.001 level. Significantly different from zero at the p < 0.0001 level.
Humerus and Femur MD 0.78 0.23 1.97& 1.01 2.32# 1.23 2.35^ 1.49 2.10& 1.95& 4.45**
No 0 0 0 0 0 1 1 1 1 3 12
Yes 28 28 28 28 28 27 27 27 27 25 16
% 100 100 100 100 100 96.4 96.4 96.4 96.4 89.3 57.1
MAD* 4.31 4.02 3.56 2.55 2.74 2.66 3.68 2.43 3.24 4.20 5.96
MD **
3.90 3.78** 3.08** 0.93 1.20& 0.39 3.02** 0.54 2.64** 3.95** 5.89**
No
Yes
%
0 0 0 0 1 2 2 3 3 5 20
56 56 56 56 55 54 54 53 53 51 36
100 100 100 100 98.2 96.4 96.4 94.6 94.6 91.0 64.3
J. Albanese et al. / Forensic Science International 261 (2016) 154–158
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worst by overall utility for both bones. For the first four groups (eight equations) estimated range bracketed the documented stature 100% of the time for both the femur and the humerus: 20th Century Black male, 20th Century Black female, 20th Century White female, 20th Century Any. The 19th Century White male equation did not bracket documented stature twice using the humerus and once using the femur, but performed well by bracketing the documented stature 94.6% (53 out of 56). Twenty out of the 22 group-specific equations bracketed the documented stature of the 19th Century White males over 90% of the time. The exceptions to the trend in utility were the 19th Century Black female equations which performed poorly using both the femur and the humerus. The one-sample t-tests indicate that the MADs, which range from 2.43 cm for the 19th Century White male femur equation to 5.96 cm for the 19th Century Black female femur equation, are all significantly different (p < 0.0001) than zero. The 1-way ANOVA of the MADs indicates that (1) although the 19th Century White male femur equation has the lowest MAD, that MAD is not significantly different than any other MAD except for the 19th Century Black female humerus equation and the 19th Century Black female femur equation; and (2) The MAD for the 19th Century White male humerus equation is in the middle of the range of MADs and is not significantly different than any other MAD (Table 2). Six of 11 humerus equations and eight of the 11 femur equations have MDs that are significantly different than zero (significance varies in level from p < 0.05 to p < 0.0001). Statistically, significance of MDs in these cases suggests a bias in error rather than a random distribution of error. With the way MDs were calculated in this study, a positive MD suggests a tendency to overestimate stature and a negative MD suggests a tendency to underestimate stature. Of the 14 MDs that are significantly different from zero, only one has a tendency to overestimate stature: the 20th Century White male humerus equation. For most equations with a significant bias, the MDs are absolutely small and relatively small when compared to the 90% prediction interval generated by Fordisc which ranged from a low of 5.2 cm for 20th Century Hispanic male femur equations to high of 11.4 cm for 19th Century Black female humerus equations.
Table 2 Homogeneous subsets, grouped using Tukey HSD post hoc, of MAD for various equations using the humerus and the femur. Equation
n
1
Femur White Male 19th C Femur Any 20th C Femur Hispanic Male 20th C Femur White Male 20th C Femur Black Male 19th C Femur White Female 20th C Humerus Black Male 20th C Humerus Hispanic Male 20th C Humerus White Male 19th C Humerus White Female 20th C Femur Any 19th C Humerus Any 20th C Humerus Black Female 20th C Humerus Black Male 19th C Humerus White Female 19th C Humerus White Male 20th C Humerus Any 19th C Femur Black Female 20th C Femur White Female 19th C Femur Black Male 20th C Humerus Black Female 19th C Femur Black Female 19th C
28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28
2.43 2.55 2.66 2.74 3.24 3.56 3.58 3.58 3.64 3.66 3.68 3.68 3.73 3.83 3.86 3.89 3.95 4.02 4.20 4.31
Sig.
.366
2 2.55 2.66 2.74 3.24 3.56 3.58 3.58 3.64 3.66 3.68 3.68 3.73 3.83 3.86 3.89 3.95 4.01 4.20 4.31 4.84
.077
3
3.58 3.58 3.64 3.66 3.68 3.68 3.73 3.83 3.86 3.89 3.95 4.01 4.20 4.31 4.84 5.96 .051
These small but significant biases do not necessarily translate into poorer estimates of stature. For example, the femur MD for the 20th Century Black female equation is negative and significantly different than zero suggesting a bias to underestimate stature, but the estimated range brackets the documented stature 100% of the time. The MD indicates a slight significant bias for the 20th Century Black females, but the MAD is not significantly different from the 19th Century White male MAD. The pattern is the same for all the equations with the best utility and an MD that is significantly different from zero: 20th Century Black male femur, 20th Century White female femur and 20th Century White female humerus. The small but significant bias has no impact on utility. The obvious outliers that do not follow the overall pattern are the 19th Century Black female equations for the humerus and the femur which have the highest MDs that are significantly different from zero. For the humerus, 24 of 28 cases are negative and for the femur 27 of 28 cases are negative. This tendency is evident in how similar the MD is to the MAD for each equation, respectively (last row of Table 1). Furthermore, the 19th Century Black female MADs are the only MADs that are significantly different than the MADs for 19th Century White male femur equations. Both 19th Century Black female equations are excluded from group 1 in Table 2. The 1-way ANOVA results for the mean documented stature and the means of estimated stature for each group-specific equation for both the humerus and the femur are presented in Table 3. The means are listed from lowest to highest and are grouped into statistically significant homogenous subsets. Although there are three statistically significant groups, (1) there is no pattern to the grouping by sex, race, century or bone, and (2) the documented mean clusters with all three subsets, and there is no significant difference between the mean of the document stature and the means of the estimated stature using any of the equations for either bone (Table 2). 4. Discussion Almost all the equations regardless of group specificity would have provided information that would have been useful in a
Table 3 Homogeneous subsets, grouped using Tukey HSD post hoc, of mean documented stature and of mean stature estimates using various humerus and femur equations. None of the means are significantly different than the mean of the documented stature (in bold). Equation
n
1
Femur Black Female 19th C Humerus Black Female 19th C Femur White Female 19th C Femur Black Male 20th C Femur Black Female 20th C Femur White Female 20th C Femur Any 19th C Femur Black Male 19th C Humerus Any 19th C Humerus Black Male 19th C Humerus White Female 20th C Humerus White Female 19th C Humerus White Male 19th C Femur Any 20th C Femur White Male 19th C Documented Stature Humerus Black Female 20th C Femur Hispanic Male 20th C Humerus Black Male 20th C Humerus Any 20th C Femur White Male 20th C Humerus Hispanic Male 20th C Humerus White Male 20th C
28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28 28
164.6 166.0 166.5 166.6 166.7 167.4 167.4 167.8 168.1 168.4 168.5 168.5 169.0 169.5 169.9 170.5
Sig.
2
.051
3
166.0 166.5 166.6 166.7 167.4 167.4 167.8 168.1 168.4 168.5 168.5 169.0 169.5 169.9 170.5 170.7 170.9 171.2 171.5 171.7 171.7
.077
167.4 167.4 167.8 168.1 168.4 168.5 168.5 169.0 169.5 169.9 170.5 170.7 170.9 171.2 171.5 171.7 171.7 172.8 .126
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forensic investigation over 90% of the time, and the ‘‘Any’’ option was not a second best choice for estimating stature. Considering the group-specific equation that is opposite in every parameter for group membership, the 20th Century Black female equations produce results that are not significantly different (MAD, mean stature and humerus MD) than the 19th Century White males, but provide a higher utility by bracketing the documented stature 100% (versus 94.6%). The 19th Century White male equations provide good results but they do not provide any improvement in stature estimates when compared to other group-specific equations with two exceptions. An unexpected result of the uniformity of the results is that the MDs, MADs, 1-way ANOVA, and utility results from this study suggest that the humerus can provide comparable, consistent results if the femur is not available for analysis. The results for the 19th Century Black female equations seem to be the exception to the pattern, but are not necessarily inconsistent with the overall results when the source of the data used by Fordisc is considered. As Komar and Grivas [18] have noted, not enough attention has been paid to the impacts on research of the biased nature of all reference collections. There is some information about the sources of the reference sample used by Fordisc to calculate various equations in the Fordisc Help File (Version 1.35, http://math. mercyhurst.edu/sousley/Fordisc/): generally ‘‘a good number [of American Blacks] come from the Terry Collection’’ (page 4), and specifically with respect to stature, there are 41 Black females in the 19th Century reference sample from the Terry Collection (page 45). Although individuals from the Terry Collection are likely included in all the 19th and 20th Century Black and White groups, the most problematic group is 19th Century Black female. The anomalous results of the 19th Century Black female equations are likely due the nature of this reference sample. Black females from the Terry Collection are the most biased sub-sample in the collection [19]. In the past, this bias has been misinterpreted as ‘‘racial’’ differences in Black females, but is due to physiological stress resulting in compromised growth during the post-civil war segregationist period in the USA. Furthermore, the bias was magnified by how the Terry Collection was amassed. When compared to other groups, there is a disproportionate number of younger Black females which resulted in a significant mortality bias in a group originally described as ‘‘Negro’’ females by Robert Terry and Mildred Trotter. The uniformity of results from the current study is not entirely unexpected. Several studies have concluded that race-specificity is not required and in fact could be a liability for estimating stature [14,30–33]. Feldesman and Fountain [14] found that ‘‘races’’ formed statistical groups but with limited group cohesion, and while there may be a statistical benefit to using a group-specific approach, the cost of selecting the wrong group-specific equation outweighs the benefit of the consistency in estimates that were provided by a generic equation. As Feldesman and Fountain [14] note, there are problems with how they combined data in their meta-analysis since it is possible that the statistically significant differences they found are an artifact of group construction. On a practical level, it may be possible to estimate sex with some certainty even if no method is 100% accurate, but determining race or ancestry can be particularly problematic (see [19] for a critical review of race/ancestry determination methods). Although sex is part of identification in most jurisdictions and race/ancestry is part of identification in some jurisdiction, the results from the current study demonstrate that race- and sex-specific methods are more difficult to apply because the unknown must be allocated to a given group, but this group-specific approach does not provide better results when estimating stature. In fact, the group-specific approach provides results that are worse than expected. Both the 19th and 20th Century ‘‘Any’’ option which include all groups
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in large century-specific reference samples provide results that are as good or better than sex- and race-specific groups. The current study which used the latest build of Fordisc 3.1 is also consistent with previous results that found there was no statistically significant benefit of using century-specific equations when estimating stature using Fordisc 3.0 [20]. An update to the software which includes some changes the 20th Century reference samples has not resulted in any difference in results. Although there may be clear secular trends in stature throughout the 19th and 20th Centuries in much of North America and other parts of the world [21,22–26], there is no clear threshold effect at the start of the 20th century or at any other arbitrary year. Furthermore, secular changes represent population trends while a forensic anthropologist must consider an unknown individual lacking population context. At any given point in a secular trend, there will always be taller and shorter individuals. As with sex and race, the need to choose between centuries in Fordisc complicates stature estimation without providing any improvement in stature estimates. The approach in Fordisc follows the research of [1–3] where the general practice has been to develop group-specific equations. This approach is not unique to Fordisc. Many other methods have developed group-specific methods where the parameters for group membership are based on various combinations of sex, race/ ancestry, continental origin, nationality, year of birth and other criteria (for example, [4–13,27,28]). The basic assumption of all these methods is that group-specific methods should be more accurate because they account or control for variation in body proportions. The results from this study are not consistent with this group-specific methodology for developing stature estimation equations. Twenty out of 22 group-specific equations tested provided very good results regardless of sex, race or century of birth. The fundamental problem is likely the problematic approach to defining the parameters of group membership. For every parameter – sex, race, century – continuous and overlapping human variation is forced into arbitrary categories. Group-specific equations are more difficult to apply because the unknown has to be allocated to a specific group, but these methods do not provide any increase in accuracy or precision.
5. Conclusion The 19th Century White male equation provided good results for estimating stature for 19th Century White males, but it did not provide the best results. Other group-specific equations including 20th Century Black male, 20th Century Black female and 20th Century White female equations provided better results. The results from this study demonstrate that however a group is defined, group-specific equations do not provide better estimates of stature. Two female-specific equations outperformed the malespecific equation which should have worked best on the test sample. Additionally, race-specific equations do not provide any increase in accuracy and precision. Two equations, for Black males and Black females, outperformed the equations for White males when tested on White males. Regardless of the reader’s position on the race concept or the inclusion of race or ancestry as part of identification in some jurisdictions, on a practical level there is no benefit to attempting to determine ‘‘race’’ or ancestry before estimating stature. Race-specific stature estimation methods are at best unnecessary, or at worst a liability because they are more difficult to apply. Lastly, while there are clear secular changes in stature and long bone lengths, century-specific equations provide no benefit when estimating stature. Overall, the results from this study demonstrate that group-specific methods do not provide the best results when estimating stature, and that alternative
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