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APPLIED SCIENCES: Biodynamics

Gender differences in adult foot shape: implications for shoe design

WUNDERLICH, ROSHNA E.; CAVANAGH, PETER R.

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Medicine and Science in Sports and Exercise: April 2001 - Volume 33 - Issue 4 - p 605-611
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Abstract

It is commonly recognized that correct shoe fit is attained by matching shoe shape to foot shape (8). Appreciation of the gender differences in foot shape is therefore essential to the proper design of both men’s and women’s shoes. Traditionally, women’s sport shoes have been made using a small version of a men’s last with all dimensions proportionally scaled according to foot length. However, if women’s feet differ in shape from men’s feet, this is an inappropriate model for a women’s shoe last and could lead to improper shoe fit in women. In 1993, the American Orthopaedic Foot and Ankle Society’s Women’s Shoe Survey (4) reported that 88% of the healthy women surveyed were wearing shoes smaller than their feet (1.2 cm average in length), 80% of the women surveyed reported foot pain while wearing shoes, and 76% had some sort of foot deformity. These statistics argue for greater attention to the shape and fit of women’s shoes. To date, most of the limited attention to women’s footwear has been focused on the design and fit of dress shoes and the detrimental effects of high-heeled shoes (3,4,11,12). However, despite increasing participation of women in sport at both the elite and recreational levels, and increasing awareness of the predisposition of women to particular injuries in sport, surprisingly little attention has been given to foot shape and sport shoe and boot fit in women. Here, we address the first of these elements—gender differences in foot shape—necessary to the proper design of women’s sport shoes and boots.

Previous studies of gender differences in foot shape are limited. Most of these studies have been addressed to an audience of forensic scientists and therefore have focused almost exclusively on absolute dimensions of osteological specimens (10). Studies of external foot shape have been focused on shoe fit and/or ethnic differences, and they are usually limited in the number of dimensions examined and therefore in their ability to fully characterize foot shape. It has been observed that male and female feet differ in size relative to stature as well as in shape, especially in the angle formed by the axis of the metatarsal heads and the dimensions of the arch (5,6). Furthermore, gender differences in foot shape vary across populations and may be influenced by habitual use of inappropriate footwear (1).

When attribution of a given foot to a gender category is the goal (for example, in a forensic setting), discrimination based on absolute measurements is justified. However, for the analysis to be useful in shoe design, the question needs to be posed as follows: given two feet of the same length, do any of the available dimensions allow the attribution of the foot to a gender category? Thus, in the general case, an analysis of all measurements normalized by foot length is warranted.

A number of investigators have reported on absolute foot dimensions in large samples. In the Fort Knox study (2) 27 foot and ankle dimensions together with height, weight, and brief clinical evaluations were collected on 7559 male subjects in the U.S. Army. More recently another U.S. Army study (9) was conducted in which height, weight, and 31 foot and leg measurements were collected on 293 male and 574 female soldiers. The data for men and women were analyzed separately, but no comparisons were made between the two groups. These two studies of soldiers have been influential in the design of boots used by the U.S. Army.

The aims of the present study are as follows: 1) to assess foot shape differences between U.S. men and women in a variety of foot and leg measurements, 2) to determine how well a suite of variables can discriminate between the foot shapes of U.S. men and women, and 3) to assess the relative contribution of each variable to the classification of cases into gender categories.

METHODS

The data set collected at Fort Jackson, SC, by Parham et al. (9) was used in the present study. That report, which is in the public domain, includes anthropometric and demographic data on 293 men and a subset of 491 women from the U.S. Army. The number of women in the sample was reduced to reflect the racial balance of the U.S. Army at the time of the original study. A total of 33 right and left foot and leg measurements as well as stature and weight were taken. Only the 26 measurements on the right foot and leg were used in the present analysis. Details of these measurements are provided in Figure 1 and a description of the landmarks and instrumentation used in the measurements can be found in Parham et al. (9).

FIGURE 1
FIGURE 1:
Diagram and list of 25 measurements included in this study, adapted from Parham et al. (9).

After an initial analysis of absolute foot dimensions was performed, all variables were standardized to foot length. Student’s t-tests were used to test for significant differences between men and women. A standard Bonferroni correction was used to account for the increasing likelihood of rejecting H0 with an increasing number of tests.

Discriminant function analysis was used to test the extent to which the foot shape variables could discriminate between men and women, and to determine the reliability with which one might classify an individual of unknown gender using these variables. Canonical variates analysis was used to assess the contribution of each variable to the discrimination among groups. Both the absolute data set, shown in Figure 1, and a data set using the same variables standardized to foot length were used in the analyses.

Discrimination between groups and classification of cases into groups was assessed using the classification matrix. Cross-validation procedures were used to correct for the optimistic apparent error rate that occurs in a discriminant analysis because the data being classified were the same data being used to create the classification function. The cross-validation was performed by omitting each observation one at a time, recalculating the classification function using the remaining data, and then classifying the omitted observation. Both the standard classification and the classification with cross-validation are reported.

As these analyses involved only two groups (comparing men and women only), standardized coefficients were used to assess the relative contribution of each variable to the discriminant function. The standardized coefficients of the discriminant function describe the relative unique contribution of each variable to the discriminant function. It should be noted, however, that standardized coefficients can be deceptive: if two variables contribute in a similar manner to the discriminant function, their standardized coefficients may be small, even though each variable may be highly correlated with the discriminant function (and would probably contribute substantially on its own). Structure coefficients (the correlation between the group centroids and the canonical roots) are the best estimate of the strength of the relationship between a variable and the discriminant function, but between-group structure coefficients cannot be calculated in a discriminant analysis involving only two groups.

Results of Univariate Analysis

Absolute values.

Not surprisingly, men were significantly larger than women for each of the 25 measurements examined (Table 1; critical P-value at 95% confidence level after Bonferroni adjustment = 0.002). Frequency distributions for foot length and ball of foot circumference (as examples) are shown in Figure 2. The foot length of 257 mm (shown as a vertical dashed line on Fig. 2 a) represents a value that is found in both men and women (it is approximately the 20th percentile men’s foot lengths and the 80th percentile women’s foot lengths). This length has been called the “common foot length” and is used later for absolute comparisons of shape differences in men and women with the same size foot.

Table 1
Table 1:
Summary table of variables with male and female means and P-values for absolute and standardized variables.
FIGURE 2
FIGURE 2:
Frequency distributions for a) foot length and b) ball of foot circumference in men and women. The solid lines represent best fit normal distributions. Each vertical bar is referenced to the axis label to its left.

Length and breadth values normalized to stature.

Foot length and diagonal ball of foot breadth, when normalized by stature, were both significantly different between men and women (Table 2). On average, men had longer feet by approximately 0.3% of stature and broader feet by 0.12% of stature. For a man and a woman, both with statures of 170 cm (5 feet 7 inches), the man would have a foot that was approximately 5 mm longer and 2 mm wider than the woman.

Table 2
Table 2:
Foot length and breadth (diagonal ball breadth) normalized by stature and estimates of these values for men and women with a stature of 170 cm; note that men have greater values in both variables for a given stature.

Foot dimensions normalized by foot length.

When the remaining 25 foot variables were normalized according to foot length, only 11 variables were significantly different between men and women (see Table 3). Four of these normalized variables were greater in women (calf height, plantar arch height, ankle circumference, and calf circumference), whereas seven were greater in men (ankle height, medial malleolus height, toe 1 height, instep circumference, ankle length, outside ball of foot length, and bimalleolar breadth). The significant differences ranged from 0.82 to 6.08% (outside ball of foot length and ankle height respectively), and the range of absolute differences at the common foot length was 0.5 mm and 19.0 mm (toe 1 height and calf circumference, respectively).

Table 3
Table 3:
Foot measurements, normalized by foot length, for which there were significant differences between men and women.

Results of Multivariate Analysis

Discrimination by gender using absolute values.

When the absolute values of the data were used to predict gender, classification was correct 95.4% of the time (96.3% of the time for women and 93.8% of the time for men) (Table 4, Fig. 3). When cross-validation procedures were used, these rates of correct classification were reduced to 93.6% total (94.2% for women and 92.7% for men). Because numerous variables were correlated in this analysis due to the influence of size, it is difficult to judge the relative importance of individual variables to the discriminant function. However, instep circumference, ankle height, bimalleolar breadth, calf height, calf circumference, medial malleolus height, and ball of foot breadth had high contributions to the discriminant score (Table 4).

Table 4
Table 4:
Results of the discriminant analysis by gender on the absolute variable set; in the classification matrix, rows are observed classification and columns are predicted classifications.
FIGURE 3
FIGURE 3:
Plot of canonical discriminant scores on a single axis to demonstrate group separation between men and women using absolute variables.

Discrimination by gender using values standardized to foot length.

Although the power of the absolute values to discriminate between women and men was high, the differences between the groups were primarily a function of size. As we were also interested in shape differences between female and male feet, we standardized all the variables to foot length to create a set of foot shape variables.

The discriminant function created from the analysis by gender alone of all standardized (to foot length) variables correctly classified 85.0% of individuals, 85.4% of women, and 84.4% of men. With cross-validation, the percent correct classification values were 81.4%, 80.7%, and 82.5%, respectively. The standardized variables with the highest contributions to the discriminant function were relative instep circumference, relative ankle circumference, relative calf circumference, relative medial malleolus height, relative calf height, and relative ball of foot circumference (Table 5). As redundancy among variables can contribute to lower classification rates (7), another analysis by gender alone was done on only the 10 variables that demonstrated significant differences between men and women in the univariate analyses. Classification was actually lower in that analysis (total 77.9%, women 78.4%, men 77.1%) than in the analysis including all the variables, suggesting that variables beyond this set are indeed contributing to the discrimination among groups.

Table 5
Table 5:
Results of the discriminant analysis by gender on the standardized variable set.

DISCUSSION

The results of this study demonstrate that external foot and leg dimensions can be used to reliably distinguish between men and women when either absolute or relative values are employed. This finding has implications for shoe design.

Gender can be predicted using the discriminant function with absolute measures presented in Table 4 with a certainty of at least 93%. This value compares with those of 86–94% when using osteological specimens of metatarsals and phalanges (10). We have also examined foot shape differences among races and by race and gender together, as this information is useful to forensic scientists, and this data will be presented elsewhere (Wunderlich and Cavanagh, in preparation). In general, the external foot measurements from the Army data set were able to correctly classify by race alone with 81% certainty and by race and gender combined with a certainty of 71.8%. Smith’s (10) study of metatarsals and phalanges was able to classify race alone with 79–96% certainty, depending on the bone used, whereas race and gender together were correctly classified 70–84% of the time.

The practical implementation of discrimination by gender using the present approach is achieved by multiplying the individual raw coefficients for each variable in Table 4 by the measured value in a given specimen. If this were done for the mean values of the Army data set, for example, the result would be scores of −1.975 for the male value and 1.168 for the female. As shown in Figure 3, individual male and female values may be greater or less than these means.

We confirmed in U.S. subjects the results of the study of Asian men and women. When foot length and breadth were normalized according to stature, men of the same stature had longer and wider feet than women (1).

The results of our analyses of foot measurements normalized by foot length have shown that there are significant differences in shape between the feet and legs of men and women. These findings indicate that women’s shoes should not be simply scaled-down versions of men’s shoes if optimal fit is to be obtained. Six of the 11 significant differences were at or above the malleoli and are not necessarily relevant to shoe design but are relevant to boot design, such as in ski boots or snowboard boots. At comparable foot lengths, women have larger calf and ankle circumferences, a higher point of maximum calf circumference, and lower ankle and medial malleolus heights. The remaining five measurements indicate that at the same foot length a woman’s foot has a higher arch, a shallower first toe, a shorter ankle length, a shorter length of the outside ball of foot, and a smaller instep circumference than a man’s foot. The last on which a women’s shoe is built should reflect these differences. For example, the lateral side of a woman’s shoe should expand for the fifth metatarsal head at a more proximal location than in a men’s shoe of the same length to accommodate the shorter outside ball of foot length in women’s feet. Ideally, once these modifications were made one should be able to take two shoe lasts and, from external measurements on the last, discriminate whether or not the last was designed for a man or a woman. Although the power to discriminate between the shape of male and female feet is high, it should be noted that the absolute differences in some of the measurements are small. For example, it remains to be seen whether a shoe designed for women that incorporates the many small differences suggested here would be perceived subjectively as being a better fit and therefore more comfortable.

It is interesting to note that some differences anecdotally believed to differ between men’s and women’s feet, such as heel width, were not found to differ significantly between men and women in this study. One limitation of the present study is that the variables used may not fully represent the entire set of three dimensional shape differences that exist between men and women. In some cases, measurements such as heel width may have been more effectively taken at slightly different sites (e.g., more superiorly for the heel) in order to more closely represent the site of functional interaction with the shoe. Future studies should expand the set of measurements, focusing on areas identified as functionally important in this and other studies, perhaps exploiting modern technology enabling the three dimensional characterization of foot shape to avoid reliance on linear measurements made between landmarks that are often difficult to locate reliably.

Shoe fit should be considered as more than an issue that affects comfort. It is likely that injury prevention is associated with appropriate fit, although this association remains to be quantitatively established.

We are grateful to Dr. Carolyn Bensel and her colleagues at U.S. Army Natick RD and E Center for their generosity in assisting us with access to their database. Joe Shinsky assisted with initial analysis of the data, and Dr. William Jungers and Dr. Tony Falsetti provided valuable statistical advice. This research was supported by a gift from Ryka Inc.

Current address for Roshna E. Wunderlich: Department of Biology, MSC 7801, James Madison University, Harrisonburg, VA 22807.

Address for correspondence: Peter R. Cavanagh, The Center for Locomotion Studies, 29 Recreation Building, Penn State University, University Park, PA 16802-5702; E-mail: [email protected]

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Keywords:

FOOT DIMENSIONS,; FOOTWEAR,; ANTHROPOMETRY, GENDER DIFFERENCES

© 2001 Lippincott Williams & Wilkins, Inc.