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In searching for constant body ratio benchmarks
International Journal of Industrial Ergonomics 40 (2010) 59–67
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International Journal of Industrial Ergonomics journal homepage: www.elsevier.com/locate/ergon
In searching for constant body ratio benchmarks Eric Min-yang Wang*, Wei-Cheng Chao Department of Industrial Engineering and Engineering Management, National Tsing Hua University, 101, Section 2, Kuang-Fu Road, Hsinchu 30013, Taiwan, ROC
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 October 2008 Received in revised form 27 July 2009 Accepted 4 August 2009 Available online 9 September 2009
Anthropometric data is the foundation of ergonomic design for all products and environments. However, the procedures for collecting anthropometric data are tedious, complicated and costly in terms of labor, time and financial resources. It will be much cheaper if the old anthropometric data can be updated easily without lengthy measurement processes. However, most practitioners do not know how the old anthropometric data can be converted into applicable new data when updated data is unavailable (Wang et al., 1999). Therefore, it is important to develop methods that can easily update old data into new data with minimal error. A last, complete and large-scale anthropometric database (Wang et al., 2002a) was built in Taiwan in the late 1990s and published in 2002. In order to maximize the value of the Taiwanese anthropometric database, this study analyzed the available pairwise body dimension ratios (PBD ratios) in an attempt to find the constant body ratio benchmarks (CBR benchmarks) that are least affected by gender and age. This resulted in the identification of 483 unique CBR benchmarks, which were verified by calculating and processing 35,245 PBD ratios; meanwhile, quasi-CBR benchmarks that are least affected by either gender or age were also identified. This study and CBR benchmarks make it possible to update anthropometric data quickly, accurately, and at low cost. Relevance to industry: Establishing anthropometric data is usually a difficult, costly, time consuming and labor-intensive procedure. This study developed a method that can convert data to updated ones with high rates of accuracy, using a limited number of subjects, time, and measurement equipment. This method can help designers and engineers to obtain updated anthropometric data quickly for their product or environmental designs. Ó 2009 Elsevier B.V. All rights reserved.
Keywords: Anthropometric database Constant body ratio benchmarks Design Anthropometry Taiwan
1. Introduction In recent decades, as many countries have been enjoying the rapid economic growth brought upon by globalization, people begin to ask for products and environments that better suit their own requirements. This trend has led to the emergence of mass customization, in which anthropometric data becomes a basic design requirement. Anthropometric data is the foundation of ergonomic design for all products and environments, such as military facilities, vehicles, hand tools (Okunribido, 2000), furniture (Drury et al., 1998), agricultural machines, clothing (Laing et al., 1999), working environments (Das and Sengupta, 1996; Quintana and Hernandez-Masser, 2003), environments constructed for the disabled (Chumlea et al., 1998; Nowak, 1996), and many other environments specially designed for human use. In addition, anthropometric data and related knowledge have contributed to the ability of forensic
* Corresponding author. E-mail address: [email protected] (E.M. Wang). 0169-8141/$ – see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.ergon.2009.08.003
medicine to identify dead bodies, especially after a major disaster, whether caused by natural disaster, human error or terrorist attacks ¨ zaslan et al., 2003; Ozden et al., 2005). (Mall et al., 2001; O Anthropometric surveys are usually time consuming, labor intensive, and expensive (Wickens et al., 2004). In Taiwan, anthropometry surveys emerged in the late 1970s and were mostly conducted on college and university campuses, e.g. Chiu (1984) and Du and Lee (1984). Those surveys were conducted with limited resources in terms of researchers, equipment, and budgets. As such, a limited set of body dimensions were measured, solely on student subjects, so the applications of these data were also limited. A later survey was conducted in 1985 and 1986, in which 95 body dimensions from 933 subjects from the general populace were measured (Li et al., 1990). The relevant data from this survey was used for designing the carriages and the cabs in Taipei Rapid Transit System. However, the 95 body dimensions were far less enough for design purposes in Taiwan. Therefore, in order to provide applicable anthropometric data for local engineering design and other purposes, a large-scale and more complete anthropometry survey was conducted in Taiwan in the 1990s (Wang et al., 2002b). The complete data set that was collected was published under the title
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Anthropometric data book of Chinese people in Taiwan in 2002 (Wang et al., 2002a). This database has been employed by local and international designers and engineers ever since its publication. Comparing the data of 1986 (Li et al., 1990) with those of the survey by the R.O.C. Joint Commission on Rural Reconstruction (1972), Li et al. (1990) indicated that anthropometric data are not always applicable, since body dimensions may change over time and need to be updated regularly every few years, as argued by Cole (2003). According to the survey by Wang et al. (1999), the data revealed an interesting phenomenon in which people are taller than a decade ago. The average statures were 0.09% and 1.24% taller than those of 1986 for the female and the male workers, respectively. This implies that even if the anthropometric database has been established, some of these data will become outdated in a few years and continuous surveys for updating the data are needed. It has also been shown that most designers and engineers did not know how these data could be used properly, nor how the data could be
updated (Wang et al., 1999). Since it is unlikely that the updated anthropometric data will be available whenever the designers and engineers need it, they are generally using data that is outdated, thus their designs may be in a risk of not anthropometrically fit well. This problem can be solved by developing a convenient and cheap way of updating the data without sacrificing accuracy. One commonly used technique is to obtain specific body dimensions by measuring the stature and multiplying it by the body proportion. However, many of the data calculated with this method appear to be inconsistent for different groups of people (Lin et al., 2004; Park et al., 1999). This fact indicates that stature may not be a good benchmark choice for body proportion. This leads to the further question of whether there is any other body dimension that can serve as a better body ratio benchmark than stature, which is the aim of this study. By ‘‘better benchmarks,’’ it means benchmarks that are more accurate, more consistent, and easier for designers and engineers to use. It is expected that with the new benchmarks,
Categorize data according to gender and three age groups (1) Categorize and calculate PBD ratios
Calculate categorized PBD ratios
(2) Normality test of PBD ratios Do the PBD ratios meet the normality test?
Yes
No
Carry out the 2-way ANOVA (Female; Male)*(18~20; 21~40; 41~60)
Carry out the nonparametric method M-W U test; K-W test (Female; Male)* (18~20; 21~40; 41~60)
(3) Test of central tendency of PBD ratios Are the PBD ratio means for gender equal ? Yes
No Are the PBD ratio means for three age groups equal ?
Are the PBD ratio means for three age groups equal ?
No The PBD ratios are least affected by gender, but they are affected by age. Yes The PBD ratios are least affected by gender and age.
No
The PBD ratios are affected by gender and age. Yes Excluded
The PBD ratios are least affected by age, but they are affected by gender.
(4) Test of variability of PBD ratios Are the CVs of the PBD ratios under 33 ? Are the CVs of the PBD ratios under 33 ? No
Yes Excluded
Yes
No
CBR benchmarks
(5) Evaluate CBR benchmarks
Verify CBR benchmarks
Fig. 1. Flowchart of the statistical methods used in this study.
Quasi-CBR benchmarks
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the body ratios can be calculated more accurately and consistently; thus, it will be easier for designers and engineers to update anthropometric data when needed. 2. Materials and methods 2.1. The anthropometric database The data analyzed in this study were taken from the raw data from the Anthropometric data book of Chinese people in Taiwan (Wang et al., 2002a). Manual measurements were employed in this anthropometric survey and the advanced 3D coordinate measuring probe (accuracy within 0.001 mm), digital calipers (accuracy within 0.01 mm), and digital measuring tapes (accuracy within 0.1 mm) were used by well-trained researchers to ensure the data accuracy. Initially, each body dimension to be measured was precisely defined to guide the training and measurements. The researchers involved in this survey were trained by osteological physicians prior to the survey to familiarize them with the body dimensions and accurately identify the surface landmarks on the human body. In addition, they were given intensive practices and their performances were evaluated to ensure that consistent and quality measuring techniques would be applied. Such measures minimized the intra- and inter-personal errors as well as the operational variations. These data were measured in Taiwan over a period of three years from subjects of 1790 male and 710 female laborers, soldiers and university/college students. The subjects’ ages ranged from 18 to 60 years old. The database covers 266 items of static body dimensions and 42 items of dynamic ranges of motion but in this study only the static body dimensions were considered. 2.2. Statistical method In order to extract information systematically from the complicated anthropometric database and further transform the data into valuable knowledge, the five-stage statistical method was utilized (Fig. 1). The five-stage method started with categorizing and calculating pairwise body dimension ratios (PBD ratios), followed with testing on normality, central tendency, and variability of PBD ratios, and ended with evaluating constant body ratio benchmarks (CBR benchmarks). Fig. 1 and the following paragraphs illustrate and describe each stage in detail.
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smallest body length at birth to the largest stature roughly at the age of 20. This is followed by a stable period when stature changes relatively little from around 21 to 40. Finally, there is a period of decline after around 40, during which stature declines annually until the end of the life. Based on the data to be analyzed, a graph was plotted of how Taiwanese stature proportions change with age, with the result that the two curves in Fig. 2 have similar trends except for the starting and terminal points of the age scale. This is due to the data covered in the database, which ranges from age 18 to 60. In order to better reflect the changing stature trends, the chosen data were divided into three age groups, from the ages of 18–20, 21–40, and 41–60. Considering gender variability and age variability, the chosen data were divided into six categories. The detailed data from the database were saved in the format of a Microsoft Excel 2007 file for processing. Then, all the 35,245 PBD ratios (C266 2 ¼ 35,245 sets) were calculated with Excel. (2) Stage 2: normality test of PBD ratios Statistically, as the sample size increases, the data will approach the real value of the population. In addition, the collected data can be assumed to be a normally distributed population, although some scholars doubted this, and proved that not all anthropometric data meets a normal distribution (Vasu and Mital, 2000). Therefore, it is necessary to make normality tests of all PBD ratios against the gender and age factors. The main task of this stage is to use normality tests to analyze the data for 35,245 PBD ratios, in order to determine whether each PBD ratio meets a normal distribution or not. If the PBD ratio meets a normal distribution, then a parametric statistical technique is used; otherwise, a nonparametric statistical technique is chosen. In statistics, as the p-value of data is greater than the significance level (a ¼ 0.05), the outputs from Statistical Products and Services Solution 12.0 (SPSS 12.0) indicated that the data satisfied the assumption of a normally distributed population (Black, 1997).
(1) Stage 1: categorize and calculate PBD ratios Engineering design may be largely affected by the variability of the anthropometric data. The variability of gender, age, race and growth can be observed from the data on overall body size and the body proportions (Pheasant, 1996), among which the gender and the age are the main contributors to the individual variability in the same race and growing condition. Therefore, in this study, the gender and the age were selected as the bases for data categorization. The data from previous anthropometric surveys (Bridger, 1995; Kroemer et al., 1994; Pulat, 1997; Wickens et al., 2004) have indicated significant differences in various body dimensions between males and females. It is probably because that the stature is the most obvious body dimension that seems in proportion to the other body dimensions, it is generally used as the representative body dimension for describing or comparing the lengths of the other body segments. Kroemer et al. (1994) pointed out that in general, a person’s stature changes with age; these changes are usually measured in terms of the proportion of the largest stature over the subject’s life span. Changes in stature may be divided into three periods (Fig. 2), beginning with the growth period from the
Fig. 2. Changes in the stature proportions of U.S. and Taiwanese citizens with age, with the largest stature as 100% around the age of 20. The change in stature can be divided into three periods: (I) growth period: before 20 years; (II) stable period: 21–40 years; (III) declining period: after 41 years.
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Table 1 Constant body ratio benchmarks (partial). Body parts
Head and neck
Trunk
Upper limbs Lower limbs
Constant body ratio benchmarks
Measures of central tendency
Measures of variability
Mean
SD
CV
Max Min ¼ Range
1.
Sellion to subnasale length ðFig: 5ðeÞÞ ðFig: 6ðcÞÞ Palm length
0.4349
0.046
10.5%
0.617 0.189 ¼ 0.428
2.
Sellion to subnasale length ðFig: 5ðeÞÞ ðFig: 4ðaÞÞ Biauricular breadth
0.2420
0.023
9.8%
0.346 0.107 ¼ 0.239
3.
Subnasale to the end of the nasal septum length ðFig: 5ðgÞÞ Stature ðFig: 4ðf ÞÞ
0.0081
0.001
12.3%
0.013 0.001 ¼ 0.0112
4.
Left gonial angle to anterior point of mentium length ðFig: 5ðhÞÞ Interpupillary breadth ðFig: 4ðbÞÞ
1.1394
0.171
15.0%
2.043 0.570 ¼ 1.473
5.
Left gonial angle to anterior point of mentium length ðFig: 5ðhÞÞ ðFig: 4ðcÞÞ Face breadth ðzygomaticÞ
0.5781
0.082
14.3%
0.899 0.328 ¼ 0.571
6.
Left iliocristale height ðFig: 4ðeÞÞ Right iliocristale height ðFig: 4ðdÞÞ
1.028 0.856 ¼ 0.172
7.
ðFig: 4ðeÞÞ Left iliocristale height Subnasale to the end of the nasal septum length ðFig: 5ðgÞÞ
8. 9.
0.9933
0.007
0.7%
75.2044
18.939
25.4%
Biauricular breadth ðFig: 4ðaÞÞ ðFig: 6ðcÞÞ Palm length
1.8017
0.128
7.1%
2.346 1.426 ¼ 0.920
Buttock to knee length ðFig: 8ðeÞÞ Sitting height ðFig: 8ðdÞÞ
0.6192
0.031
5.1%
0.716 0.446 ¼ 0.270
According to the results of the normality tests, the PBD ratios were classified into two types. For PBD ratios where the p-values of the normality test are greater than the significance level (a ¼ 0.05), a parametric statistical technique (analysis of variance, or ANOVA) for hypothesis testing is utilized. For the other PBD ratios, a nonparametric statistical technique (Mann–Whitney U test, or M–W U test and Kruskal–Wallis test, or K–W test) is utilized.
401.99 46.85 ¼ 355.14
between the population means of each PBD ratio. According to this rule, 35,245 PBD ratios were categorized as four types of PBD ratios: PBD ratios that are least affected by gender, but are affected by age; PBD ratios that are least affected by age, but are affected by gender; PBD ratios that are least affected by gender and age; and PBD ratios that are affected by gender and age (Fig. 1). (4) Stage 4: test of variability of PBD ratios
(3) Stage 3: test of central tendency of PBD ratios At this and next stages, this study determined which PBD ratios are least affected by gender and age. In summarizing and describing the anthropometric measures of a population, measures of central tendency (i.e., mean and percentile) and measures of variability (i.e., coefficient of variation (CV), standard deviation (SD), and range) are important descriptive statistical measures. For this reason, the mean (i.e., measures of central tendency) and the CV value (i.e., measures of variability) were adopted as criteria to examine which PBD ratios are least affected by gender and age. If the assumption of a normally distributed population is satisfied by each PBD ratio in the female and male populations, the twoway ANOVA is used to test whether the population means of each PBD ratio in the two gender groups are equal; otherwise, the M–W U test is used. Similarly, if the assumption of a normally distributed population is satisfied by all three age populations of each PBD ratio, then the same two-way ANOVA is used to test whether the population means of the three age groups of each PBD ratio are equal; otherwise, the K–W test is used. These hypotheses test can be carried out with the p-value method. If this p-value is greater than the significance level (a ¼ 0.05), this could mean that there is no significant difference
Testing measures of central tendency alone is not sufficient to prove that a given PBD ratio is least affected by gender and age, because this study found that some PBD ratios with great variability might have equal means. Statistically, using measures of variability or dispersion in conjunction with measures of central tendency makes a more complete numerical description of the data possible, because measures of central tendency do not yield sufficient information to describe the data set. To avoid selecting improper PBD ratios for which the mean of each distribution is the same but the dispersions vary, this study also examines measures of variability such as the SD, the CV and the range. Nevertheless, there is variation in the PBD ratios. Higher PBD ratios have larger measures of variability; on the other hand, smaller PBD ratios have smaller measures of variability. Therefore, in order to obtain an identical standard measure, this study judges measures of variability using a threshold of a CV value (relative measures of variability) of 33% (Johnson and Welch, 1940; Patel et al., 2001). If a PBD ratio has an equal mean for gender and age, and its CV value is less than 33%, this could mean that this PBD ratio is least affected by gender and age and remain relatively constant among the general populace; thus, this can be listed as CBR benchmarks. Similarly, if the PBD ratio has equal means for either gender or age, and its CV value less
Table 2 Quasi-constant body ratio benchmarks (partial). Affected factors
Quasi-constant body ratio benchmarks
Gender
1.
Age
Male
Female
18–20 Years
21–40 Years
41–60 Years
Sellion to stomion length ðFig: 5ðdÞÞ Hand length ðFig: 6ðbÞÞ
0.3789
0.3807
0.3771 0.3783 0.3859 Average ratio of three age groups ¼ 0.3794
2.
Elbow to elbow breadth ðFig: 7ðaÞÞ Forefinger length ðFig: 6ðdÞÞ
3.7320
3.7215
3.5640 3.7385 3.9250 Average ratio of three age groups ¼ 3.7290
3.
Menton to vertex length ðFig: 5ðcÞÞ Hand length ðFig: 6ðbÞÞ
1.2678 1.2927 Average gender ratio ¼ 1.2747
1.2807
1.2744
1.2677
4.
Sellion to pronasale length ðFig: 5ðfÞÞ Forefinger length ðFig: 6ðdÞÞ
0.3203 0.3127 Average gender ratio ¼ 0.3182
0.3198
0.3182
0.3157
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than 33%, this could mean that this PBD ratio is least affected by either gender or age and remain relatively constant among the general populace; thus, this can be listed as quasi-CBR benchmarks. Other PBD ratios will be excluded except CBR benchmarks and quasi-CBR benchmarks. (5) Stage 5: evaluate CBR benchmarks In order to verify these CBR benchmarks, this study has undertaken an experimental anthropometric sampling. The data were obtained from 15 male and 15 female local subjects whose ages ranged from 18 to 60 years of age. Based on the variability of CBR benchmarks, thirty-two CBR benchmarks which are practically useful and were derived from 30 body dimensions were selected for evaluation. There can be more CBR benchmarks derived from some other meaningful combinations of these 30 body dimensions because some CBR benchmarks could be derived from the same body dimensions. To evaluate the effectiveness of the CBR benchmarks, regardless of their diverse values, the 32 CBR benchmarks selected ranged from the minimum of 0.0081 (i.e., item 3 in Table 1) to the maximum of 75.2044 (i.e., item 7 in Table 1). Further, in considering diverse anthropometric characteristics that may contribute to the CBR benchmarks, the 30 body dimensions were selected in a way that consisted of various sizes, types of dimensions (i.e., length, breadth, depth, thickness, and circumference), and body parts (i.e., head and neck, trunk, upper limbs, and lower limbs). Both the mean absolute deviation (MAD) and the mean squared error (MSE) are measures of estimation errors. The distinctive feature of the mean absolute percentage error (MAPE) is that the error terms are standardized to facilitate comparisons across variables with different scales (Black, 1997). In order to measure and compare the measures of estimation errors between the actual and calculated CBR benchmarks, three error criteria were computed: MAD, MSE, and MAPE. Generally speaking, the MAPE values were less than 0.5, indicating that the estimated values were statistically significant. According to this result, the validity of CBR benchmarks may be determined.
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Table 3 An example of converting the left gonial angle to anterior point of mentium length into the others. Constant body ratio benchmarks
Obtained body dimensions
1.
Interpupillary breadth Left gonial angle to anterior point of mentium length
ðFig: 4ðbÞÞ ¼ 0:8777ðFig: 5ðhÞÞ
2.
Face breadth ðzygomaticÞ Left gonial angle to anterior point of mentium length
ðFig: 4ðcÞÞ ¼ 1:7298ðFig: 5ðhÞÞ
3.
Sellion to wall Left gonial angle to anterior point of mentium length
ðFig: 5ðaÞÞ ¼ 2:4219ðFig: 5ðhÞÞ
Interpupillary breadth Face breadth (zygomatic) Sellion to wall
Each PBD ratio was computed and identified according to the procedure shown in Fig. 1. As a result, 483 CBR benchmarks were identified and verified out of 35,245 PBD ratios. The 483 CBR benchmarks involve 272 head and neck body dimensions, 266 trunk dimensions, 171 upper limb dimensions, and 119 lower limb dimensions. Meanwhile, quasi-CBR benchmarks are illustrated in Table 2. To make it convenient for users to apply this result, the means, maximum values, minimum values, SDs, CVs, and ranges of CBR benchmarks are categorized into four bodily regions (i.e., head and neck, trunk, upper limbs, and lower limbs) as listed in Table 1. Moreover, this study also confirmed the validity of all the CBR benchmarks by examining their means, maximum values, minimum values, ranges, SDs and CVs. Due to limited space, however, only partial CBR benchmarks and quasi-CBR benchmarks discussed in this article are shown in Tables 1 and 2. After an experimental sampling for evaluating CBR benchmarks, the results indicated that the MAPE values of 32 sampled CBR benchmarks were less than 0.3, and most of them were less than 0.2, as shown in Fig. 3. In General, the MAPE values were less than 0.5, indicating that the estimated values were statistically significant. This could mean that the CBR benchmarks are accurate, consistent and feasible for use. The application and significance of CBR benchmarks and quasiCBR benchmarks are illustrated in Tables 1–3 and in the following sections. The relevant body dimensions are presented in Figs. 4–8. These figures indicate the referred anthropometric measurements
3. Results The task of searching and analyzing 35,245 PBD ratios was completed using the five-stage statistical method described above.
Fig. 3. Box plot of MAPE of 32 sampled CBR benchmarks.
Fig. 4. Anthropometric measurements of standing posture used in this study.
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Fig. 5. Anthropometric measurements of the face used in this study.
of standing posture (Figs. 4 and 7), the face (Fig. 5), hands (Fig. 6), and sitting posture (Fig. 8).
3.1. Constant body ratio benchmarks
(2) A specific body dimension may be found as a common element in several CBR benchmarks. In particular, the body dimension of subnasale to the end of the nasal septum length [Fig. 5(g)] has the highest occurrence of 40 times, as shown in Fig. 10. (3) Fifty out of 266 of the body dimensions in the current Taiwanese anthropometric database, such as wrist circumference
Although the means of the 483 identified CBR benchmarks are on different scales, all of them meet the relevant tests for means, and their measures of variability are below the CV threshold of 33%. More specifically, the mean CV values of these CBR benchmarks is 11.52%, and 92% of their CV values are less than 20%, as shown in Fig. 9. This indicated that most of the CBR benchmark values are close to their mean values. The CV value of the CBR benchmark of the left iliocristale height [Fig. 4(e)] to the right iliocristale height [Fig. 4(d)] is even as small as 0.72%. This study made the following findings on CBR benchmarks. (1) CBR benchmarks with at least one easily-measured body dimension such as stature [Fig. 4(f)], hand length [Fig. 6(b)] or palm length [Fig. 6(c)] have a higher potential for application.
Fig. 6. Anthropometric measurements of hands used in this study.
Fig. 7. Elbow to elbow breadth of standing posture used in this study.
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Fig. 8. Anthropometric measurements of sitting posture used in this study.
[Fig. 6(e)], elbow to elbow breadth [Fig. 7(a)], and sellion to vertex length [Fig. 5(b)], are not associated with any of the CBR benchmarks. It is further found that CBR benchmarks can be mutually derived by continued multiplication of related CBR benchmarks. For example, items 1 and 8 in Table 1 are the CBR benchmark (i.e., 0.4349) of the sellion to subnasale length [Fig. 5(e)] to the palm length [Fig. 6(c)], and the CBR benchmark (i.e., 1.8017) of the biauricular breadth [Fig. 4(a)] to the palm length [Fig. 6(c)],
Fig. 9. Box plot of the CVs of 483 CBR benchmarks.
respectively. In Table 1, item 1 divided by item 8 leads to the converted value of item 2, which is the PBD ratio (i.e., 0.2414) of the sellion to subnasale length [Fig. 5(e)] to the biauricular breadth [Fig. 4(a)]. The error between the converted value and the actual CBR benchmark of 0.2420 is only 0.25%. In sum, this study demonstrated the possibility of using CBR benchmarks to estimate body dimensions in order to reduce the cost of updating anthropometric data. 3.2. Quasi-constant body ratio benchmarks There are two types of quasi-CBR benchmark ratios, some of which are least affected by gender, and others which are least affected by age. After examining the differences between the means of the gender groups and those of the means of the three age groups, however, they were found to be close, with differences around 1%, as shown in Table 2. Item 2 in Table 2 for example, although statistically the mean ratios of the elbow to elbow breadth [Fig. 7(a)] to forefinger length [Fig. 6(d)] of the gender groups are significantly different, the male mean (3.7320) is close to the female mean (3.7215), with a difference of only 0.28%. Thus, quasi-CBR benchmarks could still be applied to design products intended for users of a particular gender or age. For instance, in designing products for females, certain quasiCBR benchmarks that are least affected by age are still available. Therefore, the mean female PBD ratio could be regarded as a CBR benchmark in this kind of case. In other words, in the case of item 2 in Table 2, the designers and engineers could adopt the quasi-CBR benchmark ratio of the elbow to elbow breadth [Fig. 7(a)] to forefinger length [Fig. 6(d)] for females (i.e., 3.7215) as a CBR benchmark.
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Fig. 10. Top five most frequently occurring body dimensions in CBR benchmarks.
4. Discussions Manual measurements and 3D body scans are two main anthropometric measurement methods commonly used today for building an anthropometric database. Sometime later, it is necessary to update the data, no matter what method the researchers were using in building the database. To make the update process a lot easier and cheaper than measuring all dimensions again, CBR benchmarks and quasi-CBR benchmarks that are recommended in this study can contribute to it by measuring only limited number of dimensions. CBR benchmarks or quasi-CBR benchmarks can play the role of intermediaries between the old and updated anthropometric databases. Using these results, designers and engineers can quickly and easily obtain the necessary anthropometric data needed for their work at lower cost. For example, the three most important body dimensions in the design of eyeglasses are the interpupillary breadth [Fig. 4(b)], face breadth (zygomatic) [Fig. 4(c)] and sellion to wall [Fig. 5(a)]. From Table 3, these dimensions can be derived simply by measuring the dimension of the left gonial angle to the anterior point of mentium length [Fig. 5(h)]. Based on continued multiplication of these CBR benchmarks, it is feasible for designers and engineers to establish formulae to estimate 266 body dimensions with limited body dimensions that can be measured easily. Further, these estimation formulae could be used to save time and money in updating anthropometric data. Consequently, CBR benchmarks extend and maximize the utility of the Taiwanese anthropometric database. With continuous technology development, today 3D body scanners are increasingly used to measure body dimensions and create anthropometric databases (e.g., SizeUSA ([TC]2, 2004) and SizeUK (Sizemic, 2004)). However, comparing with manual measurements, 3D scan technology has a few problems to be solved if it is to use for anthropometric survey. These include the relatively expensive investment in the hardware and the software of a scanner, missing data because of shading (e.g., the arm-pits and crotch areas are often shaded), and occurrence of errors owing to movement artifacts (Daanen and Jeroen, 1998). Additionally, some of the body protrusions are hard to identify on whole body scan images (Daanen and Jeroen, 1998; Ozsoy et al., 2009), thus the measurements related to those locations will be impossible or be biased. In such a case, this study recommends that those dimensions can be derived from their associated CBR benchmarks that involve other easily-identified and measured body dimensions.
From the economic point of view, it can be very expensive for developing countries to use 3D scan technology for anthropometric survey. In considering the needs of building anthropometric database and the costs for updating anthropometric data in developing countries, manual measurements and the method developed in this study should be very helpful and affordable to them. 5. Conclusions and future work This research analyzed Taiwanese anthropometric data and identified 483 useful CBR benchmarks and quasi-CBR benchmarks. Using these CBR benchmarks and quasi-CBR benchmarks, it may be possible to avoid the need for a large-scale anthropometric survey to update the data, thus saving significant time and money. This study has developed an effective, efficient, and low cost method of updating anthropometric data. The remarkable outcomes suggest a new direction for research that will make updating anthropometric data simple and less costly. Further studies are needed to ensure the maturity and completeness of this method because this study only considered gender variability and age variability. In the long run, more factors, such as different times, geographic areas and nutritional conditions, etc., which may affect anthropometric dimensions, should be taken into consideration in order to enhance the reliability of the CBR benchmarks. Furthermore, the accuracy of the CBR benchmarks can be verified later by small-scale anthropometric measurements. It is necessary for CBR benchmarks to be periodically tuned up as new actual anthropometric data become available. Due to the expansion of globalization, designers and engineers may need to consider multinational anthropometric data in their work. Therefore, racial differences (Lin et al., 2004) should be taken into account in the development of international CBR benchmarks and common estimation formulae for body dimensions across national borders. References Black, K., 1997. Business Statistics: Contemporary Decision Making, second ed. West Publishing Company, New York. Bridger, R.S., 1995. Introduction to Ergonomics. International ed.. McGraw-Hill, Inc., New York. Chiu, W.C., 1984. The Research on the Standard of Young Women’s Dress and Difference of External Physical Appearance (in Chinese, Project # NSC73-0415E020-01) (available from National Science Council, Taipei, Taiwan, ROC). Chumlea, C., Guo, S., Wholihan, K., Cockram, D., Kuczmarski, R.J., Clifford, L.J., 1998. Stature prediction equations for elderly non-Hispanic white, non-Hispanic
E.M. Wang, W.-C. Chao / International Journal of Industrial Ergonomics 40 (2010) 59–67 black, and Mexican-American persons developed from NHANES III data. Journal of the American Dietetic Association 98 (2), 137–142. Cole, T.J., 2003. The secular trend in human physical growth: a biological view. Economics and Human Biology 1 (2), 161–168. Daanen, H.A.M., Jeroen, G., 1998. Whole body scanners. Displays 19 (3), 111–120. Das, B., Sengupta, A.K., 1996. Industrial workstation design: a systematic ergonomics approach. Applied Ergonomics 27 (3), 157–163. Drury, C.G., Czaja, S.J., Prabhu, G.V., Mayne, R.W., Noland, S., 1998. Furniture tipping accidents: redesign for prevention. Accident Analysis and Prevention 30 (5), 625–639. Du, J., Lee, Y.L., 1984. A Study on the anthropometric investigation of young adults in Taiwan (in Chinese, Project # NSC73-0415-E027-01) (available from National Science Council, Taipei, Taiwan, ROC). Johnson, N.L., Welch, B.L., 1940. Applications of the non-central t-distribution. Biometrika 31 (3/4), 362–389. Kroemer, K.H.E., Kroemer, H.B., Kroemer, K.E., 1994. Ergonomics: How to Design for Ease & Efficiency, second ed. Prentice Hall Inc., New Jersey. Laing, R.M., Holland, E.J., Wilson, C.A., Niven, B.E., 1999. Development of sizing systems for protective clothing for the adult male. Ergonomics 42 (10), 1249–1257. Li, C.C., Hwang, S.L., Wang, M.Y., 1990. Static anthropometry of civilian Chinese in Taiwan using computer-analyzed photography. Human Factors 32 (3), 359–370. Lin, Y.C., Wang, M.J., Wang, E.M., 2004. The comparisons of anthropometric characteristics among four peoples in East Asia. Applied Ergonomics 35, 173–178. Mall, G., Hubig, M., Buttner, A., Kuznik, J., Penning, R., Graw, M., 2001. Sex determination and estimation of stature from the longbones of the arm. Forensic Science International 117, 23–30. Nowak, E., 1996. The role of anthropometry in design of work and life environments of the disabled population. International Journal of Industrial Ergonomics 17, 113–121. Okunribido, O.O., 2000. A survey of hand anthropometry of female rural farm workers in Ibadan, Western Nigeria. Ergonomics 43 (2), 282–292. _ ¸ can, M.Y., O _ Tug˘cu, H., Koç, S., 2003. Estimation of stature ¨ zaslan, A., Is ¨ zaslan, I., O from body part. Forensic Science International 132, 40–45.
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Ozden, H., Balci, Y., Demiru¨stu¨, C., Turgut, A., Ertugrul, M., 2005. Stature and sex estimate using foot and shoe dimensions. Forensic Science International 147, 181–184. Ozsoy, U., Demirel, B.M., Yildirim, F.B., Tosun, O., Sarikcioglu, L., 2009. Method selection in craniofacial measurements: advantages and disadvantages of 3D digitization method. Journal of Cranio-Maxillofacial Surgery 37, 285–290. Park, S.J., Park, S.C., Kim, J.H., Kim, C.B., 1999. Biomechanical parameters on body segments of Korean adults. International Journal of Industrial Ergonomics 23, 23–31. Patel, J.K., Patel, N.M., Shiyani, R.L., 2001. Coefficient of variation in field experiments and yardstick thereof – an empirical study. Current Science 81 (9), 1163–1164. Pheasant, S., 1996. Bodyspace: Anthropometry, Ergonomics and Design of Work. Taylor & Francis, New York. Pulat, B.M., 1997. Fundamentals of Industrial Ergonomics, second ed. Waveland Press, Inc., Illinois. Quintana, R., Hernandez-Masser, V., 2003. Research note: limiting design criteria framework for manual electronics assembly. Human Factors and Ergonomics in Manufacturing 13 (2), 165–179. R.O.C. Joint Commission on Rural Reconstruction, 1972. Body Height and Weight Measurements of the People in Taiwan, the Republic of China (in Chinese). Author, Taipei, Taiwan, ROC. Sizemic, 2004. UK National Sizing Survey (SizeUK Project): http://www.sizeuk.org. [TC]2, 2004. US Nation Sizing survey: http://www.tc2.com/what/sizeusa/index.html. Vasu, M., Mital, A., 2000. Evaluation of the validity of anthropometric design assumptions. International Journal of Industrial Ergonomics 26, 19–37. Wang, E.M., Wang, M.J., Yeh, W.Y., Shih, Y.C., 1999. Development of anthropometric work environment for Taiwanese workers. International Journal of Industrial Ergonomics 23, 3–8. Wang, M.J., Wang, E.M., Lin, Y.C., 2002a. Anthropometric Data Book of Chinese People in Taiwan (in Chinese). Ergonomics Society of Taiwan, Republic of China. Wang, M.J., Wang, E.M., Lin, Y.C., 2002b. The anthropometric database for children and young adults in Taiwan. Applied Ergonomics 33, 583–585. Wickens, C.D., Lee, J.D., Liu, Y., Becker, S.E.G., 2004. An Introduction to Human Factors Engineering, second ed. Prentice Hall Inc., New Jersey.
Contents lists available at ScienceDirect
International Journal of Industrial Ergonomics journal homepage: www.elsevier.com/locate/ergon
In searching for constant body ratio benchmarks Eric Min-yang Wang*, Wei-Cheng Chao Department of Industrial Engineering and Engineering Management, National Tsing Hua University, 101, Section 2, Kuang-Fu Road, Hsinchu 30013, Taiwan, ROC
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 October 2008 Received in revised form 27 July 2009 Accepted 4 August 2009 Available online 9 September 2009
Anthropometric data is the foundation of ergonomic design for all products and environments. However, the procedures for collecting anthropometric data are tedious, complicated and costly in terms of labor, time and financial resources. It will be much cheaper if the old anthropometric data can be updated easily without lengthy measurement processes. However, most practitioners do not know how the old anthropometric data can be converted into applicable new data when updated data is unavailable (Wang et al., 1999). Therefore, it is important to develop methods that can easily update old data into new data with minimal error. A last, complete and large-scale anthropometric database (Wang et al., 2002a) was built in Taiwan in the late 1990s and published in 2002. In order to maximize the value of the Taiwanese anthropometric database, this study analyzed the available pairwise body dimension ratios (PBD ratios) in an attempt to find the constant body ratio benchmarks (CBR benchmarks) that are least affected by gender and age. This resulted in the identification of 483 unique CBR benchmarks, which were verified by calculating and processing 35,245 PBD ratios; meanwhile, quasi-CBR benchmarks that are least affected by either gender or age were also identified. This study and CBR benchmarks make it possible to update anthropometric data quickly, accurately, and at low cost. Relevance to industry: Establishing anthropometric data is usually a difficult, costly, time consuming and labor-intensive procedure. This study developed a method that can convert data to updated ones with high rates of accuracy, using a limited number of subjects, time, and measurement equipment. This method can help designers and engineers to obtain updated anthropometric data quickly for their product or environmental designs. Ó 2009 Elsevier B.V. All rights reserved.
Keywords: Anthropometric database Constant body ratio benchmarks Design Anthropometry Taiwan
1. Introduction In recent decades, as many countries have been enjoying the rapid economic growth brought upon by globalization, people begin to ask for products and environments that better suit their own requirements. This trend has led to the emergence of mass customization, in which anthropometric data becomes a basic design requirement. Anthropometric data is the foundation of ergonomic design for all products and environments, such as military facilities, vehicles, hand tools (Okunribido, 2000), furniture (Drury et al., 1998), agricultural machines, clothing (Laing et al., 1999), working environments (Das and Sengupta, 1996; Quintana and Hernandez-Masser, 2003), environments constructed for the disabled (Chumlea et al., 1998; Nowak, 1996), and many other environments specially designed for human use. In addition, anthropometric data and related knowledge have contributed to the ability of forensic
* Corresponding author. E-mail address: [email protected] (E.M. Wang). 0169-8141/$ – see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.ergon.2009.08.003
medicine to identify dead bodies, especially after a major disaster, whether caused by natural disaster, human error or terrorist attacks ¨ zaslan et al., 2003; Ozden et al., 2005). (Mall et al., 2001; O Anthropometric surveys are usually time consuming, labor intensive, and expensive (Wickens et al., 2004). In Taiwan, anthropometry surveys emerged in the late 1970s and were mostly conducted on college and university campuses, e.g. Chiu (1984) and Du and Lee (1984). Those surveys were conducted with limited resources in terms of researchers, equipment, and budgets. As such, a limited set of body dimensions were measured, solely on student subjects, so the applications of these data were also limited. A later survey was conducted in 1985 and 1986, in which 95 body dimensions from 933 subjects from the general populace were measured (Li et al., 1990). The relevant data from this survey was used for designing the carriages and the cabs in Taipei Rapid Transit System. However, the 95 body dimensions were far less enough for design purposes in Taiwan. Therefore, in order to provide applicable anthropometric data for local engineering design and other purposes, a large-scale and more complete anthropometry survey was conducted in Taiwan in the 1990s (Wang et al., 2002b). The complete data set that was collected was published under the title
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Anthropometric data book of Chinese people in Taiwan in 2002 (Wang et al., 2002a). This database has been employed by local and international designers and engineers ever since its publication. Comparing the data of 1986 (Li et al., 1990) with those of the survey by the R.O.C. Joint Commission on Rural Reconstruction (1972), Li et al. (1990) indicated that anthropometric data are not always applicable, since body dimensions may change over time and need to be updated regularly every few years, as argued by Cole (2003). According to the survey by Wang et al. (1999), the data revealed an interesting phenomenon in which people are taller than a decade ago. The average statures were 0.09% and 1.24% taller than those of 1986 for the female and the male workers, respectively. This implies that even if the anthropometric database has been established, some of these data will become outdated in a few years and continuous surveys for updating the data are needed. It has also been shown that most designers and engineers did not know how these data could be used properly, nor how the data could be
updated (Wang et al., 1999). Since it is unlikely that the updated anthropometric data will be available whenever the designers and engineers need it, they are generally using data that is outdated, thus their designs may be in a risk of not anthropometrically fit well. This problem can be solved by developing a convenient and cheap way of updating the data without sacrificing accuracy. One commonly used technique is to obtain specific body dimensions by measuring the stature and multiplying it by the body proportion. However, many of the data calculated with this method appear to be inconsistent for different groups of people (Lin et al., 2004; Park et al., 1999). This fact indicates that stature may not be a good benchmark choice for body proportion. This leads to the further question of whether there is any other body dimension that can serve as a better body ratio benchmark than stature, which is the aim of this study. By ‘‘better benchmarks,’’ it means benchmarks that are more accurate, more consistent, and easier for designers and engineers to use. It is expected that with the new benchmarks,
Categorize data according to gender and three age groups (1) Categorize and calculate PBD ratios
Calculate categorized PBD ratios
(2) Normality test of PBD ratios Do the PBD ratios meet the normality test?
Yes
No
Carry out the 2-way ANOVA (Female; Male)*(18~20; 21~40; 41~60)
Carry out the nonparametric method M-W U test; K-W test (Female; Male)* (18~20; 21~40; 41~60)
(3) Test of central tendency of PBD ratios Are the PBD ratio means for gender equal ? Yes
No Are the PBD ratio means for three age groups equal ?
Are the PBD ratio means for three age groups equal ?
No The PBD ratios are least affected by gender, but they are affected by age. Yes The PBD ratios are least affected by gender and age.
No
The PBD ratios are affected by gender and age. Yes Excluded
The PBD ratios are least affected by age, but they are affected by gender.
(4) Test of variability of PBD ratios Are the CVs of the PBD ratios under 33 ? Are the CVs of the PBD ratios under 33 ? No
Yes Excluded
Yes
No
CBR benchmarks
(5) Evaluate CBR benchmarks
Verify CBR benchmarks
Fig. 1. Flowchart of the statistical methods used in this study.
Quasi-CBR benchmarks
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the body ratios can be calculated more accurately and consistently; thus, it will be easier for designers and engineers to update anthropometric data when needed. 2. Materials and methods 2.1. The anthropometric database The data analyzed in this study were taken from the raw data from the Anthropometric data book of Chinese people in Taiwan (Wang et al., 2002a). Manual measurements were employed in this anthropometric survey and the advanced 3D coordinate measuring probe (accuracy within 0.001 mm), digital calipers (accuracy within 0.01 mm), and digital measuring tapes (accuracy within 0.1 mm) were used by well-trained researchers to ensure the data accuracy. Initially, each body dimension to be measured was precisely defined to guide the training and measurements. The researchers involved in this survey were trained by osteological physicians prior to the survey to familiarize them with the body dimensions and accurately identify the surface landmarks on the human body. In addition, they were given intensive practices and their performances were evaluated to ensure that consistent and quality measuring techniques would be applied. Such measures minimized the intra- and inter-personal errors as well as the operational variations. These data were measured in Taiwan over a period of three years from subjects of 1790 male and 710 female laborers, soldiers and university/college students. The subjects’ ages ranged from 18 to 60 years old. The database covers 266 items of static body dimensions and 42 items of dynamic ranges of motion but in this study only the static body dimensions were considered. 2.2. Statistical method In order to extract information systematically from the complicated anthropometric database and further transform the data into valuable knowledge, the five-stage statistical method was utilized (Fig. 1). The five-stage method started with categorizing and calculating pairwise body dimension ratios (PBD ratios), followed with testing on normality, central tendency, and variability of PBD ratios, and ended with evaluating constant body ratio benchmarks (CBR benchmarks). Fig. 1 and the following paragraphs illustrate and describe each stage in detail.
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smallest body length at birth to the largest stature roughly at the age of 20. This is followed by a stable period when stature changes relatively little from around 21 to 40. Finally, there is a period of decline after around 40, during which stature declines annually until the end of the life. Based on the data to be analyzed, a graph was plotted of how Taiwanese stature proportions change with age, with the result that the two curves in Fig. 2 have similar trends except for the starting and terminal points of the age scale. This is due to the data covered in the database, which ranges from age 18 to 60. In order to better reflect the changing stature trends, the chosen data were divided into three age groups, from the ages of 18–20, 21–40, and 41–60. Considering gender variability and age variability, the chosen data were divided into six categories. The detailed data from the database were saved in the format of a Microsoft Excel 2007 file for processing. Then, all the 35,245 PBD ratios (C266 2 ¼ 35,245 sets) were calculated with Excel. (2) Stage 2: normality test of PBD ratios Statistically, as the sample size increases, the data will approach the real value of the population. In addition, the collected data can be assumed to be a normally distributed population, although some scholars doubted this, and proved that not all anthropometric data meets a normal distribution (Vasu and Mital, 2000). Therefore, it is necessary to make normality tests of all PBD ratios against the gender and age factors. The main task of this stage is to use normality tests to analyze the data for 35,245 PBD ratios, in order to determine whether each PBD ratio meets a normal distribution or not. If the PBD ratio meets a normal distribution, then a parametric statistical technique is used; otherwise, a nonparametric statistical technique is chosen. In statistics, as the p-value of data is greater than the significance level (a ¼ 0.05), the outputs from Statistical Products and Services Solution 12.0 (SPSS 12.0) indicated that the data satisfied the assumption of a normally distributed population (Black, 1997).
(1) Stage 1: categorize and calculate PBD ratios Engineering design may be largely affected by the variability of the anthropometric data. The variability of gender, age, race and growth can be observed from the data on overall body size and the body proportions (Pheasant, 1996), among which the gender and the age are the main contributors to the individual variability in the same race and growing condition. Therefore, in this study, the gender and the age were selected as the bases for data categorization. The data from previous anthropometric surveys (Bridger, 1995; Kroemer et al., 1994; Pulat, 1997; Wickens et al., 2004) have indicated significant differences in various body dimensions between males and females. It is probably because that the stature is the most obvious body dimension that seems in proportion to the other body dimensions, it is generally used as the representative body dimension for describing or comparing the lengths of the other body segments. Kroemer et al. (1994) pointed out that in general, a person’s stature changes with age; these changes are usually measured in terms of the proportion of the largest stature over the subject’s life span. Changes in stature may be divided into three periods (Fig. 2), beginning with the growth period from the
Fig. 2. Changes in the stature proportions of U.S. and Taiwanese citizens with age, with the largest stature as 100% around the age of 20. The change in stature can be divided into three periods: (I) growth period: before 20 years; (II) stable period: 21–40 years; (III) declining period: after 41 years.
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Table 1 Constant body ratio benchmarks (partial). Body parts
Head and neck
Trunk
Upper limbs Lower limbs
Constant body ratio benchmarks
Measures of central tendency
Measures of variability
Mean
SD
CV
Max Min ¼ Range
1.
Sellion to subnasale length ðFig: 5ðeÞÞ ðFig: 6ðcÞÞ Palm length
0.4349
0.046
10.5%
0.617 0.189 ¼ 0.428
2.
Sellion to subnasale length ðFig: 5ðeÞÞ ðFig: 4ðaÞÞ Biauricular breadth
0.2420
0.023
9.8%
0.346 0.107 ¼ 0.239
3.
Subnasale to the end of the nasal septum length ðFig: 5ðgÞÞ Stature ðFig: 4ðf ÞÞ
0.0081
0.001
12.3%
0.013 0.001 ¼ 0.0112
4.
Left gonial angle to anterior point of mentium length ðFig: 5ðhÞÞ Interpupillary breadth ðFig: 4ðbÞÞ
1.1394
0.171
15.0%
2.043 0.570 ¼ 1.473
5.
Left gonial angle to anterior point of mentium length ðFig: 5ðhÞÞ ðFig: 4ðcÞÞ Face breadth ðzygomaticÞ
0.5781
0.082
14.3%
0.899 0.328 ¼ 0.571
6.
Left iliocristale height ðFig: 4ðeÞÞ Right iliocristale height ðFig: 4ðdÞÞ
1.028 0.856 ¼ 0.172
7.
ðFig: 4ðeÞÞ Left iliocristale height Subnasale to the end of the nasal septum length ðFig: 5ðgÞÞ
8. 9.
0.9933
0.007
0.7%
75.2044
18.939
25.4%
Biauricular breadth ðFig: 4ðaÞÞ ðFig: 6ðcÞÞ Palm length
1.8017
0.128
7.1%
2.346 1.426 ¼ 0.920
Buttock to knee length ðFig: 8ðeÞÞ Sitting height ðFig: 8ðdÞÞ
0.6192
0.031
5.1%
0.716 0.446 ¼ 0.270
According to the results of the normality tests, the PBD ratios were classified into two types. For PBD ratios where the p-values of the normality test are greater than the significance level (a ¼ 0.05), a parametric statistical technique (analysis of variance, or ANOVA) for hypothesis testing is utilized. For the other PBD ratios, a nonparametric statistical technique (Mann–Whitney U test, or M–W U test and Kruskal–Wallis test, or K–W test) is utilized.
401.99 46.85 ¼ 355.14
between the population means of each PBD ratio. According to this rule, 35,245 PBD ratios were categorized as four types of PBD ratios: PBD ratios that are least affected by gender, but are affected by age; PBD ratios that are least affected by age, but are affected by gender; PBD ratios that are least affected by gender and age; and PBD ratios that are affected by gender and age (Fig. 1). (4) Stage 4: test of variability of PBD ratios
(3) Stage 3: test of central tendency of PBD ratios At this and next stages, this study determined which PBD ratios are least affected by gender and age. In summarizing and describing the anthropometric measures of a population, measures of central tendency (i.e., mean and percentile) and measures of variability (i.e., coefficient of variation (CV), standard deviation (SD), and range) are important descriptive statistical measures. For this reason, the mean (i.e., measures of central tendency) and the CV value (i.e., measures of variability) were adopted as criteria to examine which PBD ratios are least affected by gender and age. If the assumption of a normally distributed population is satisfied by each PBD ratio in the female and male populations, the twoway ANOVA is used to test whether the population means of each PBD ratio in the two gender groups are equal; otherwise, the M–W U test is used. Similarly, if the assumption of a normally distributed population is satisfied by all three age populations of each PBD ratio, then the same two-way ANOVA is used to test whether the population means of the three age groups of each PBD ratio are equal; otherwise, the K–W test is used. These hypotheses test can be carried out with the p-value method. If this p-value is greater than the significance level (a ¼ 0.05), this could mean that there is no significant difference
Testing measures of central tendency alone is not sufficient to prove that a given PBD ratio is least affected by gender and age, because this study found that some PBD ratios with great variability might have equal means. Statistically, using measures of variability or dispersion in conjunction with measures of central tendency makes a more complete numerical description of the data possible, because measures of central tendency do not yield sufficient information to describe the data set. To avoid selecting improper PBD ratios for which the mean of each distribution is the same but the dispersions vary, this study also examines measures of variability such as the SD, the CV and the range. Nevertheless, there is variation in the PBD ratios. Higher PBD ratios have larger measures of variability; on the other hand, smaller PBD ratios have smaller measures of variability. Therefore, in order to obtain an identical standard measure, this study judges measures of variability using a threshold of a CV value (relative measures of variability) of 33% (Johnson and Welch, 1940; Patel et al., 2001). If a PBD ratio has an equal mean for gender and age, and its CV value is less than 33%, this could mean that this PBD ratio is least affected by gender and age and remain relatively constant among the general populace; thus, this can be listed as CBR benchmarks. Similarly, if the PBD ratio has equal means for either gender or age, and its CV value less
Table 2 Quasi-constant body ratio benchmarks (partial). Affected factors
Quasi-constant body ratio benchmarks
Gender
1.
Age
Male
Female
18–20 Years
21–40 Years
41–60 Years
Sellion to stomion length ðFig: 5ðdÞÞ Hand length ðFig: 6ðbÞÞ
0.3789
0.3807
0.3771 0.3783 0.3859 Average ratio of three age groups ¼ 0.3794
2.
Elbow to elbow breadth ðFig: 7ðaÞÞ Forefinger length ðFig: 6ðdÞÞ
3.7320
3.7215
3.5640 3.7385 3.9250 Average ratio of three age groups ¼ 3.7290
3.
Menton to vertex length ðFig: 5ðcÞÞ Hand length ðFig: 6ðbÞÞ
1.2678 1.2927 Average gender ratio ¼ 1.2747
1.2807
1.2744
1.2677
4.
Sellion to pronasale length ðFig: 5ðfÞÞ Forefinger length ðFig: 6ðdÞÞ
0.3203 0.3127 Average gender ratio ¼ 0.3182
0.3198
0.3182
0.3157
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than 33%, this could mean that this PBD ratio is least affected by either gender or age and remain relatively constant among the general populace; thus, this can be listed as quasi-CBR benchmarks. Other PBD ratios will be excluded except CBR benchmarks and quasi-CBR benchmarks. (5) Stage 5: evaluate CBR benchmarks In order to verify these CBR benchmarks, this study has undertaken an experimental anthropometric sampling. The data were obtained from 15 male and 15 female local subjects whose ages ranged from 18 to 60 years of age. Based on the variability of CBR benchmarks, thirty-two CBR benchmarks which are practically useful and were derived from 30 body dimensions were selected for evaluation. There can be more CBR benchmarks derived from some other meaningful combinations of these 30 body dimensions because some CBR benchmarks could be derived from the same body dimensions. To evaluate the effectiveness of the CBR benchmarks, regardless of their diverse values, the 32 CBR benchmarks selected ranged from the minimum of 0.0081 (i.e., item 3 in Table 1) to the maximum of 75.2044 (i.e., item 7 in Table 1). Further, in considering diverse anthropometric characteristics that may contribute to the CBR benchmarks, the 30 body dimensions were selected in a way that consisted of various sizes, types of dimensions (i.e., length, breadth, depth, thickness, and circumference), and body parts (i.e., head and neck, trunk, upper limbs, and lower limbs). Both the mean absolute deviation (MAD) and the mean squared error (MSE) are measures of estimation errors. The distinctive feature of the mean absolute percentage error (MAPE) is that the error terms are standardized to facilitate comparisons across variables with different scales (Black, 1997). In order to measure and compare the measures of estimation errors between the actual and calculated CBR benchmarks, three error criteria were computed: MAD, MSE, and MAPE. Generally speaking, the MAPE values were less than 0.5, indicating that the estimated values were statistically significant. According to this result, the validity of CBR benchmarks may be determined.
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Table 3 An example of converting the left gonial angle to anterior point of mentium length into the others. Constant body ratio benchmarks
Obtained body dimensions
1.
Interpupillary breadth Left gonial angle to anterior point of mentium length
ðFig: 4ðbÞÞ ¼ 0:8777ðFig: 5ðhÞÞ
2.
Face breadth ðzygomaticÞ Left gonial angle to anterior point of mentium length
ðFig: 4ðcÞÞ ¼ 1:7298ðFig: 5ðhÞÞ
3.
Sellion to wall Left gonial angle to anterior point of mentium length
ðFig: 5ðaÞÞ ¼ 2:4219ðFig: 5ðhÞÞ
Interpupillary breadth Face breadth (zygomatic) Sellion to wall
Each PBD ratio was computed and identified according to the procedure shown in Fig. 1. As a result, 483 CBR benchmarks were identified and verified out of 35,245 PBD ratios. The 483 CBR benchmarks involve 272 head and neck body dimensions, 266 trunk dimensions, 171 upper limb dimensions, and 119 lower limb dimensions. Meanwhile, quasi-CBR benchmarks are illustrated in Table 2. To make it convenient for users to apply this result, the means, maximum values, minimum values, SDs, CVs, and ranges of CBR benchmarks are categorized into four bodily regions (i.e., head and neck, trunk, upper limbs, and lower limbs) as listed in Table 1. Moreover, this study also confirmed the validity of all the CBR benchmarks by examining their means, maximum values, minimum values, ranges, SDs and CVs. Due to limited space, however, only partial CBR benchmarks and quasi-CBR benchmarks discussed in this article are shown in Tables 1 and 2. After an experimental sampling for evaluating CBR benchmarks, the results indicated that the MAPE values of 32 sampled CBR benchmarks were less than 0.3, and most of them were less than 0.2, as shown in Fig. 3. In General, the MAPE values were less than 0.5, indicating that the estimated values were statistically significant. This could mean that the CBR benchmarks are accurate, consistent and feasible for use. The application and significance of CBR benchmarks and quasiCBR benchmarks are illustrated in Tables 1–3 and in the following sections. The relevant body dimensions are presented in Figs. 4–8. These figures indicate the referred anthropometric measurements
3. Results The task of searching and analyzing 35,245 PBD ratios was completed using the five-stage statistical method described above.
Fig. 3. Box plot of MAPE of 32 sampled CBR benchmarks.
Fig. 4. Anthropometric measurements of standing posture used in this study.
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Fig. 5. Anthropometric measurements of the face used in this study.
of standing posture (Figs. 4 and 7), the face (Fig. 5), hands (Fig. 6), and sitting posture (Fig. 8).
3.1. Constant body ratio benchmarks
(2) A specific body dimension may be found as a common element in several CBR benchmarks. In particular, the body dimension of subnasale to the end of the nasal septum length [Fig. 5(g)] has the highest occurrence of 40 times, as shown in Fig. 10. (3) Fifty out of 266 of the body dimensions in the current Taiwanese anthropometric database, such as wrist circumference
Although the means of the 483 identified CBR benchmarks are on different scales, all of them meet the relevant tests for means, and their measures of variability are below the CV threshold of 33%. More specifically, the mean CV values of these CBR benchmarks is 11.52%, and 92% of their CV values are less than 20%, as shown in Fig. 9. This indicated that most of the CBR benchmark values are close to their mean values. The CV value of the CBR benchmark of the left iliocristale height [Fig. 4(e)] to the right iliocristale height [Fig. 4(d)] is even as small as 0.72%. This study made the following findings on CBR benchmarks. (1) CBR benchmarks with at least one easily-measured body dimension such as stature [Fig. 4(f)], hand length [Fig. 6(b)] or palm length [Fig. 6(c)] have a higher potential for application.
Fig. 6. Anthropometric measurements of hands used in this study.
Fig. 7. Elbow to elbow breadth of standing posture used in this study.
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Fig. 8. Anthropometric measurements of sitting posture used in this study.
[Fig. 6(e)], elbow to elbow breadth [Fig. 7(a)], and sellion to vertex length [Fig. 5(b)], are not associated with any of the CBR benchmarks. It is further found that CBR benchmarks can be mutually derived by continued multiplication of related CBR benchmarks. For example, items 1 and 8 in Table 1 are the CBR benchmark (i.e., 0.4349) of the sellion to subnasale length [Fig. 5(e)] to the palm length [Fig. 6(c)], and the CBR benchmark (i.e., 1.8017) of the biauricular breadth [Fig. 4(a)] to the palm length [Fig. 6(c)],
Fig. 9. Box plot of the CVs of 483 CBR benchmarks.
respectively. In Table 1, item 1 divided by item 8 leads to the converted value of item 2, which is the PBD ratio (i.e., 0.2414) of the sellion to subnasale length [Fig. 5(e)] to the biauricular breadth [Fig. 4(a)]. The error between the converted value and the actual CBR benchmark of 0.2420 is only 0.25%. In sum, this study demonstrated the possibility of using CBR benchmarks to estimate body dimensions in order to reduce the cost of updating anthropometric data. 3.2. Quasi-constant body ratio benchmarks There are two types of quasi-CBR benchmark ratios, some of which are least affected by gender, and others which are least affected by age. After examining the differences between the means of the gender groups and those of the means of the three age groups, however, they were found to be close, with differences around 1%, as shown in Table 2. Item 2 in Table 2 for example, although statistically the mean ratios of the elbow to elbow breadth [Fig. 7(a)] to forefinger length [Fig. 6(d)] of the gender groups are significantly different, the male mean (3.7320) is close to the female mean (3.7215), with a difference of only 0.28%. Thus, quasi-CBR benchmarks could still be applied to design products intended for users of a particular gender or age. For instance, in designing products for females, certain quasiCBR benchmarks that are least affected by age are still available. Therefore, the mean female PBD ratio could be regarded as a CBR benchmark in this kind of case. In other words, in the case of item 2 in Table 2, the designers and engineers could adopt the quasi-CBR benchmark ratio of the elbow to elbow breadth [Fig. 7(a)] to forefinger length [Fig. 6(d)] for females (i.e., 3.7215) as a CBR benchmark.
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Fig. 10. Top five most frequently occurring body dimensions in CBR benchmarks.
4. Discussions Manual measurements and 3D body scans are two main anthropometric measurement methods commonly used today for building an anthropometric database. Sometime later, it is necessary to update the data, no matter what method the researchers were using in building the database. To make the update process a lot easier and cheaper than measuring all dimensions again, CBR benchmarks and quasi-CBR benchmarks that are recommended in this study can contribute to it by measuring only limited number of dimensions. CBR benchmarks or quasi-CBR benchmarks can play the role of intermediaries between the old and updated anthropometric databases. Using these results, designers and engineers can quickly and easily obtain the necessary anthropometric data needed for their work at lower cost. For example, the three most important body dimensions in the design of eyeglasses are the interpupillary breadth [Fig. 4(b)], face breadth (zygomatic) [Fig. 4(c)] and sellion to wall [Fig. 5(a)]. From Table 3, these dimensions can be derived simply by measuring the dimension of the left gonial angle to the anterior point of mentium length [Fig. 5(h)]. Based on continued multiplication of these CBR benchmarks, it is feasible for designers and engineers to establish formulae to estimate 266 body dimensions with limited body dimensions that can be measured easily. Further, these estimation formulae could be used to save time and money in updating anthropometric data. Consequently, CBR benchmarks extend and maximize the utility of the Taiwanese anthropometric database. With continuous technology development, today 3D body scanners are increasingly used to measure body dimensions and create anthropometric databases (e.g., SizeUSA ([TC]2, 2004) and SizeUK (Sizemic, 2004)). However, comparing with manual measurements, 3D scan technology has a few problems to be solved if it is to use for anthropometric survey. These include the relatively expensive investment in the hardware and the software of a scanner, missing data because of shading (e.g., the arm-pits and crotch areas are often shaded), and occurrence of errors owing to movement artifacts (Daanen and Jeroen, 1998). Additionally, some of the body protrusions are hard to identify on whole body scan images (Daanen and Jeroen, 1998; Ozsoy et al., 2009), thus the measurements related to those locations will be impossible or be biased. In such a case, this study recommends that those dimensions can be derived from their associated CBR benchmarks that involve other easily-identified and measured body dimensions.
From the economic point of view, it can be very expensive for developing countries to use 3D scan technology for anthropometric survey. In considering the needs of building anthropometric database and the costs for updating anthropometric data in developing countries, manual measurements and the method developed in this study should be very helpful and affordable to them. 5. Conclusions and future work This research analyzed Taiwanese anthropometric data and identified 483 useful CBR benchmarks and quasi-CBR benchmarks. Using these CBR benchmarks and quasi-CBR benchmarks, it may be possible to avoid the need for a large-scale anthropometric survey to update the data, thus saving significant time and money. This study has developed an effective, efficient, and low cost method of updating anthropometric data. The remarkable outcomes suggest a new direction for research that will make updating anthropometric data simple and less costly. Further studies are needed to ensure the maturity and completeness of this method because this study only considered gender variability and age variability. In the long run, more factors, such as different times, geographic areas and nutritional conditions, etc., which may affect anthropometric dimensions, should be taken into consideration in order to enhance the reliability of the CBR benchmarks. Furthermore, the accuracy of the CBR benchmarks can be verified later by small-scale anthropometric measurements. It is necessary for CBR benchmarks to be periodically tuned up as new actual anthropometric data become available. Due to the expansion of globalization, designers and engineers may need to consider multinational anthropometric data in their work. Therefore, racial differences (Lin et al., 2004) should be taken into account in the development of international CBR benchmarks and common estimation formulae for body dimensions across national borders. References Black, K., 1997. Business Statistics: Contemporary Decision Making, second ed. West Publishing Company, New York. Bridger, R.S., 1995. Introduction to Ergonomics. International ed.. McGraw-Hill, Inc., New York. Chiu, W.C., 1984. The Research on the Standard of Young Women’s Dress and Difference of External Physical Appearance (in Chinese, Project # NSC73-0415E020-01) (available from National Science Council, Taipei, Taiwan, ROC). Chumlea, C., Guo, S., Wholihan, K., Cockram, D., Kuczmarski, R.J., Clifford, L.J., 1998. Stature prediction equations for elderly non-Hispanic white, non-Hispanic
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