Evaluation of the Multivariate Accommodation Performance of the Grid Method Kihyo Jung a, Ochae Kwon b, and Heecheon You c,* a The Harold and Inge Marcus Department of Industrial and Manufacturing Engineering, The Pennsylvania State University, University Park, PA 16802, USA b Samsung Electronics Co., LTD. 10F, Samsung Electronics Bldg., Seocho 2-dong, Seochogu, Seoul 137-857, South Korea c Department of Industrial and Management Engineering, Pohang University of Science and Technology, Pohang, Kyungbuk 790-784, South Korea * Corresponding author. Tel.: +82-54-279-2210. Fax: +82-54-279-2870. E-mail address: [email protected] Evaluation of the Multivariate Accommodation Performance of the Grid Method Abstract The present study examined the multivariate accommodation performance (MAP) of the grid method, a distributed representative human models (RHM) generation method, in the context of men’s pants sizing system design. Using the 1988 US Army male anthropometric data and ±2.5 cm of fitting tolerance, the grid method selected two key dimensions (waist girth and crotch height) out of 12 anthropometric dimensions and identified 25 RHMs to accommodate 95% of the population. The average MAP of the RHMs decreased dramatically as the number of anthropometric dimensions considered increased (99% for single dimension and 14% for 12 dimensions). A standardized regression model was established which explains the effects of two factors (sum of anthropometric dimension ranges; adjusted R2 between key dimensions and other anthropometric dimensions) on the MAP of RHMs. This regression model can be used to prioritize anthropometric dimensions for efficient MAP improvement of men’s pants design. Keyword: Multivariate accommodation performance; Grid method; Representative human model generation; Anthropometry Introduction In ergonomic design and evaluation, a small group of human models which represents the anthropometric variability of the target population is commonly used. Representative human models (RHMs) are determined by considering the anthropometric characteristics of the population and a designated accommodation percentage (e.g., 90%) (HFES 300, 2004; Jung et al., 2009). For example, You et al. (1997) used three RHMs (5th, 50th, and 95th percentiles) which accommodate 90% of the target population to evaluate an ergonomic design of a bus operator’s workstation. Use of a small group of RHMs provides an efficient way to develop a product design which is fitting for the population. However, some studies use a rather large group of human models (e.g., 6 to 45 manikins) to better reflect the diversity of anthropometric sizes for ergonomic design and evaluation (Bittner, 2000; Case et al., 2001; Case et al., 2009; Jung et al., 2009). Depending on the characteristics of a product being designed, RHMs are determined on a boundary (Figure 1.a) or a set of grids (Figure 1.b) formed on selected anthropometric dimensions to accommodate a designated percentage of the population. In designing a onesize product (one size to accommodate people within a designated percentage of the population) such as a bus operator’s workstation and a helicopter cockpit, RHMs are selected on an accommodation boundary. For example, Bittner (2000) generated 17 RHMs at the centroid and the boundary of a hyper-ellipsoid which encompasses 90% of the population for a workspace design. On the other hand, in designing a multiple-size product (n sizes to fit n groups of people within a designated percentage of the population) such as gloves and shoes, RHMs are chosen over a set of grids formed in the distribution of anthropometric dimensions. For example, Kwon et al. (2009) and Robinette and Annis (1986) constructed grids which accommodated a designated percentage of the population and then defined representative cases at the centroids of the grids. [Figure 1 about here] Of the various RHM generation methods, the grid method determines RHMs by following a three-step procedure: selection of key dimensions, formation of representative grids, and generation of RHMs (Figure 2). First, a small, manageable number of anthropometric dimensions (e.g., one to five dimensions) are selected as key dimensions by analyzing the statistical relationships between anthropometric dimensions under consideration (Gordon and Freill, 1994; Hidson, 1991; Resonblad-Wallin, 1987; Zheng et al., 2007). Second, representative grids with a fitting tolerance are formed over the distribution of the key dimensions to accommodate a designated percentage of the population. The value of fitting tolerance is specified by the product designer by considering various practical aspects including production economy and material properties (Kwon et al., 2009). Lastly, the values of the centroid of each representative grid are used for the key dimensions of an RHM and then regression equations having the key dimensions as regressors are applied to estimate the other anthropometric dimensions of the RHM (Robinette and Annis, 1986). [Figure 2 about here] Research which evaluates the accommodation performance of the grid method in a comprehensive manner is lacking. Most studies such as Chung et al. (2007) and McCulloch et al. (1998) using the grid method have considered the multivariate accommodation performance (MAP) of the grid method only for key dimensions, but not for non-key anthropometric dimensions. Since some non-key anthropometric dimensions have low correlations with key dimensions but still affect the fit of product to the population, the MAP of the grid method needs to be analyzed for all anthropometric dimensions considered in the design. The present study examined the MAP of the grid method in a comprehensive manner and the effects of two factors (sum of anthropometric dimension ranges; adjusted R2 between key dimensions and other anthropometric dimensions) on MAP. The measure MAP was quantified by calculating the proportion of the population belonging to grids formed to accommodate a designated percentage of the population. The two MAP factors were identified from our empirical observation as possible attributes affecting the MAP of the grid method. Lastly, standardized multiple regression analysis was conducted to examine the relative effects of the two factors on MAP. Methods Selection of anthropometric dimensions Referring to Chung et al. (2007) and Hsu and Wang (2005), the present study selected 12 anthropometric dimensions (Table 1) for the design of a men’s pants sizing system. The 1988 US Army anthropometric data of 1774 men (Gordon et al., 1988) was used to generate RHMs. The anthropometric data was randomly divided into (1) a learning data set of 1,000 cases for generation of RHMs and (2) a testing data set of 774 cases for cross-evaluation of the accommodation performance of the generated RHMs. [Table 1 about here] Determination of key dimensions To determine the number of key dimensions for a men’s pants sizing system, maximum average adjusted R2 was analyzed for different numbers of key dimension candidates as displayed in Figure 3. The 12 anthropometric dimensions were used to form sets of key dimension candidates consisting of 1 to 11 anthropometric dimensions. Then, multiple regression analysis was conducted using each set of key dimension candidates as regressors and non-key anthropometric dimensions as dependent variables. Finally, for each number of key dimension candidates, the maximum of average adjusted R2 values were identified. Table 2 illustrates the identification process of the maximum of average adjusted R2 values for single key dimension candidate cases: for each individual key dimension candidate from AD1 to AD12, adjusted R2 values of regression equations were obtained for the other anthropometric dimensions and their average adjusted R2 value was calculated, and then the maximum of the adjusted R2 values was found 0.43 at AD1. Figure 3 shows that the increase rate of maximum average adjusted R2 becomes significantly small (< 0.1) after two; thus, this study determined that two anthropometric dimensions would be selected for key dimensions of a men’s pants sizing system. [Figure 3 about here] [Table 2 about here] Based on the maximum average adjusted R2 analysis results and a survey on key dimensions used in the garment industry, crotch height (AD5) and waist girth (AD7) were chosen as key dimensions of a men’s pants sizing system design. The key dimension survey conducted on the internet in the present study identified that AD5 and AD7 are widely used for men’s pants sizing in the US garment industry (Banana Republic, 2009; Polo, 2009; Perry Ellis, 2009). Calculation of multivariate accommodation performance The MAP of a particular set of anthropometric dimensions was quantified by calculating the proportion of anthropometric cases belonging to grids that were formed along generated RHMs. A fitting tolerance of ±2.5 cm was used as the length of a grid for each anthropometric dimension by referring to the garment industry practices for the key dimensions of men’s pants (Banana Republic, 2009; BlueFly, 2009; Polo, 2009; Perry Ellis, 2009). The MAP analysis was conducted for various combinations of anthropometric dimensions from 1 to 12 using a program coded by Matlab 7.0 (MathWorks, Inc., Natick, MA, USA). For example, when the number of anthropometric dimensions was 2, MAPs were calculated for 66 combinations (12C2) of anthropometric dimensions. Results Using the grid method, 25 RHMs (Table 3) were generated for the design of a men’s pants sizing system to accommodate 95% of the population. Square grids with a fitting tolerance of ±2.5 cm were formed which accommodate 95% of the population anthropometric cases (Figure 4) on the distribution of AD5 and AD7. The centroids of the grids were used for the key dimension values of the RHMs, and then the regression equations in Table 4, having the key dimensions as regressors, were applied to determine the values of the other anthropometric dimension values for the RHMs. [Table 3 about here] [Figure 4 about here] [Table 4 about here] The MAP analysis (described in the Methods section) showed that the average MAP of the generated RHMs decreased greatly as the number of anthropometric dimensions increased as displayed in Figure 5. The univariate accommodation percentage of each individual anthropometric dimension was higher (96.6% ~ 99.9%) than the target accommodation percentage (95%); however, the average MAP decreased dramatically as the number of anthropometric dimensions increased and finally dropped to 14% when all 12 dimensions were considered. [Figure 5 about here] During the process of MAP analysis, two factors (sum of anthropometric dimension ranges, SR; average adjusted R2 between key dimensions and other anthropometric dimensions, AR) were presumed as those affecting the MAP of the grid method. It was observed that SR tended to negatively relate to MAP. For example, the MAP of waist-to-knee length (AD3) (range = 21 cm), waist girth (AD7) (range = 47.5 cm), and ankle girth (AD12) (range = 9 cm), of which SR = 77.5 cm, was 94%, while that of crotch length (AD6) (range = 38.1 cm), hip girth (AD8) (range = 43.4 cm), and thigh girth (AD9) (range = 32.9 cm), of which SR = 104.4 cm, was 70% (note that the range data are from Table 1). In contrast, it was observed that AR tended to positively relate to MAP. For example, the MAP of waist height (AD1) (adjusted R2 = 0.89), AD3 (adjusted R2 = 0.70), and outside leg length (AD4) (adjusted R2 = 0.90), of which AR = 0.84, was 95%, while that of waist-ankle length (AD2) (adjusted R2 = 0.88), AD6 (adjusted R2 = 0.64), and AD9 (adjusted R2 = 0.62), of which AR = 0.71, was 64%. The statistical significance and relative influence of the two MAP factors were further examined by multiple regression analysis. A standardized regression equation (F(2, 217) = 95.4, p < 0.001; adjusted R2 = 0.46) was obtained by the stepwise approach (probabilities to enter and to remove = 0.05 and 0.1): MAP (%) = (1.03 - 0.616 × SR + 0.284 × AR) × 100 (Eq. 1) The regression coefficients indicating the directionalities of the factor effects agreed with the aforementioned observations: SR negatively relates to MAP, while AR positively relates to MAP. Also, the standardized regression equation showed that SR is more influential to MAP. Discussion The present study examined the MAP of the grid method for all the combinations of both key and non-key anthropometric dimensions. Previous research has evaluated the MAP of the grid method only for key anthropometric dimensions (Chung et al., 2007; McCulloch et al., 1998), but not for non-key anthropometric dimensions. Although key dimensions mainly determine the fitness of a product and an appropriate size of a product for the user (Kwon et al., 2009), non-key anthropometric dimensions still affect its fitness; thus, an understanding of the accommodation performance of the grid method is necessary for non-key anthropometric dimensions. The MAP analysis results in the present study showed that the grid method can over- and under-accommodate a designated accommodation percentage of the population depending on anthropometric dimensions considered. In addition, relatively large decrease rates (> 10%) or variabilities (> 20%) in accommodation performance were observed in the mid range of the number of anthropometric dimensions (3 to 8) in which the MAPs for all the combinations of the 12 anthropometric dimensions were analyzed in the study. The MAP quantification method used in the present study is applicable to accommodation performance evaluation of any RHM generation methods. Previous research has developed various statistical and optimization methods to generate RHMs over the target population distribution. For example, Eynard et al. (2000) and Laing et al. (1999) used cluster analysis to classify the target population into representative figure types and then generate RHMs for each figure type; McCulloch et al. (1998) applied an optimization algorithm under given constraints (e.g., number of RHMs and fitting tolerance) to generate RHMs. However, comparison between RHM generation methods has not been made in terms of MAP. An indepth MAP analysis is required in the future for existing RHM generation methods. The value of fitting tolerance in MAP analysis is often determined by considering product fitness and production economy (Kwon et al., 2009; McCulloch et al., 1998). A small value of fitting tolerance can increase the level of fit for a product to the users, but requires a large number of size categories which negatively affects production economy; the opposite becomes true for a large value of fitting tolerance. Different values of fitting tolerance can be used in MAP analysis. The present study applied ±2.5 cm as a fitting tolerance uniformly to all the anthropometric dimensions for illustration purposes. However, a value of fitting tolerance for a key or non-key anthropometric dimension would differ depending on specific design conditions such as material properties, production economy considerations, wearing purposes, and design concepts of clothing. Thus, various values of fitting tolerance need to be applied to anthropometric dimensions when applying the proposed MAP analysis procedure by considering the design context. A standardized multiple regression model was established to examine the effects of SR and AR on MAP. The MAP regression model showed that the less the SR, the higher the MAP and that the opposite is held for AR. The MAP regression model can be used to analyze the prioritization of design improvements for better accommodation performance of a product design. For example, material changes or adjustment mechanisms can be examined with a higher priority for design parameters that are related to anthropometric dimensions having a larger SR and/or a smaller AR. To obtain a more comprehensive, optimal solution for design improvement in industry, cost factors would be taken into account in addition to MAP sensitivity results. Acknowledgments This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science, and Technology (2010-0012291). References Banana Republic (2009). Men’s pant sizing system. Retrieved July 10, 2009 from http://www.gap.com/browse/category.do?cid=11889. Bittner, A. C. (2000). A-CADRE: Advanced family of manikins for workstation design. In Proceedings of the IEA 2000/HFES 2000 Congress. San Diego. CA, 774-777. BlueFly (2009). Men’s pant sizing system. Retrieved July 10, 2009 from http://www.bluefly.com/Theory-wheat-khaki-wool-MarloWythetrousers/cat60015/304852501/detail.fly. Case, K., Marshall, R., Hogberg, D., Summerskill, S., Gyi, D., and Sims, R. (2009). HADRIAN: Fitting Trials by Digital Human Modelling. Lecture Notes In Computer Science, 673 – 680. Case, K., Porter, M., Gyi, D., Marshall, R., and Oliver, R. (2001). Virtual fitting trials in design for all. Journal of Materials Processing Technology, 117, 255 - 261. Chung, M., Lin, H., and Wang, M. (2007). The development of sizing systems for Taiwanese elementary- and high-school students. International Journal of Industrial Ergonomics, 37(8), 707-716. Eynard, E., Fubini, E., Masali, M., Cerrone, M., and Tarzia, A. (2000). Generation of virtual man models representative of different body proportion and application to ergonomic design of vehicles. In Proceedings of the IEA2000/HFES2000 Congress. San Diego. CA, 489-492. Gordon, C. C., Bradtmiller, B., Churchill, T., Clauser, C., McConville, J., Tebbetts, I., and Walker, R. (1988). 1988 Anthropometric Survey of US Army Personnel: Methods and Summary Statistics (Technical Report NATICK/TR-89/044), US Army Natick Research Center: Natick, MA. Gordon, C. C., and Friedl, K. E. (1994). Anthropometry in the US armed forces. In Ulijaszek, S. J. (ed.). Anthropometry: The Individual and the Population. Cambridge University Press: Cambridge UK. HFES 300 (2003). Guidelines for Using Anthropometric Data in Product Design. Santa Monica, California: Human Factors and Ergonomics Society. Hidson, D. (1991). Development of a Standard Anthropometric Dimension Set for Use in Computer-Aided Glove Design (DREO Technical Note 91-22). Defense Research Establishment OTTAWA. Hsu, C., and Wang, M. (2005). Using decision tree-based data mining to establish a sizing system for the manufacture of garments. International Journal of Advanced Manufacturing Technology, 26. 669-674. Jung, K., Kwon, O., and You, H. (2009). Development of a digital human model generation method for ergonomic design in virtual environment. International Journal of Industrial Ergonomics. 39 (5), 744-748. Jung, K., You, H., and Kwon, O. (2008). A multivariate evaluation method for representative human model generation methods: Application to grid method. In Proceedings of the Human Factors and Ergonomics Society 52nd Annual Meeting. New York: The Human Factors and Ergonomics Society, 1665-1669. Kwon, O., Jung, K., You, H., and Kim, H. (2009). Determination of key dimensions for a glove sizing system by analyzing the relationships between hand dimensions. Applied Ergonomics, 40 (4), 762-766. Laing, R. M., Holland, E. J., Wilson, C. A., and Niven, B. E. (1999). Development of sizing systems for protective clothing for the adult male. Ergonomics, 42(10), 1249-1257. McCulloch, C. E., Paal, B., and Ashdown, S. P. (1998). An optimization approach to apparel sizing. Journal of the Operational Research Society, 49(5), 492-299. Polo (2009). Men’s pant sizing system. Retrieved July 10, 2009 from http://www.ralphlauren.com/product/index.jsp?productId=3678183&cp=1760781.176081 1&ab=ln_men_cs1_pants&parentPage=family. PerryEllis (2009). Men’s pant sizing system. Retrieved July 10, 2009 from http://www.perryellis.com/Pants/Micro-TwillPant/invt/49mb8308ps&bklist=icat,4,shop,pemen,pedmbott. Robinette, K. M., and Annis, J. F. (1986). A Nine-Size System for Chemical Defense Gloves. Technical Report (AAMRL-TR-86-029) (ADA173 193). Harry G. Armstrong Aerospace Medical Research Laboratory, Wright-Patterson Air Force Base, OH. Rosenblad-Wallin, E. (1987). An anthropometric study as the basis for sizing anatomically designed mittens. Applied Ergonomics, 18(4), 329-333. You, H., Bucciaglia, J., Lowe, B. D., Gilmore, B. J., and Freivalds, A. (1997). An ergonomic design process for a US transit bus operator workstation. Heavy Vehicle Systems, A Series of the International Journal of Vehicle Design, 4(2-4), 91-107. Zheng, R., Yu, W., and Fan, J. (2007). Development of a new Chinese bra sizing system based on breast anthropometric measurements. International Journal of Industrial Ergonomics, 37(8), 697-705. List of Figures Figure 1. Determination of representative cases (small dots: population cases; large dots: representative cases) Figure 2. Representative human model (RHM) generation process of the grid method (AD: anthropometric dimension; K: key dimension) Figure 3. The trend of maximum adjusted R2 by the number of key dimensions Figure 4. Formation of representative grids (fitting tolerance = ±2.5 cm) accommodating 95% of the 1988 US Army male population (small dots: population cases; large dots: representative cases) Figure 5. Average and range (min and max) of accommodation percentage by the number of anthropometric dimensions List of Tables Table 1. Anthropometric dimensions selected for design of men’s pants sizing system Table 2. Analysis of average adjusted R2 for single key dimension candidates Table 3. Representative human models generated by the grid method to accommodate 95% of the 1988 US Army male population Table 4. Regression equations using crotch height (AD5) and waist girth (AD7) as regressors (a) Boundary method (b) Grid method Figure 1. Determination of representative cases (small dots: population cases; large dots: representative cases) (illustrated) Step 1: Selection of key dimensions Step 3: Generation of representative human models Step 2: Formation of representative grids Frequency analysis AD1 = f1 ( K1 , K 2 ) AD1 AD2 . . . ADn Reducing variables K1 K2 RHM1 RHM2 RHM3 . . . K2 AD2 = f 2 ( K1 , K 2 ) . . . ADn = f n ( K1 , K 2 ) Tolerance K1 Correlation analysis Factor analysis Frequency analysis Regression analysis Figure 2. Representative human model (RHM) generation process of the grid method (AD: anthropometric dimension; K: key dimension) 2 with other dimensions Maximum adjusted AverageR of adjusted R2 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1 2 3 4 5 6 7 8 9 10 11 Number of key dimensions Figure 3. The trend of maximum adjusted R2 by the number of key dimensions Figure 4. Formation of representative grids (fitting tolerance = ±2.5 cm) accommodating 95% of the 1988 US Army male population (small dots: representative cases) (illustrated) population cases; large dots: 100 Accommodation (%) 99 80 93 82 69 60 57 40 46 37 30 20 24 20 16 14 11 12 0 1 2 3 4 5 6 7 8 9 10 Number of anthropometric dimensions Figure 5. Average and range (min and max) of accommodation percentage by the number of anthropometric dimensions Table 1. Anthropometric dimensions selected for design of men’s pants sizing system Dimensional type Length and height Girth a Code Selected dimensions AD1 AD2 AD3 AD4 AD5 AD6 AD7 AD8 AD9 AD10 AD11 AD12 Waist height Waist-to-ankle lengtha Waist-to-knee lengtha Outside leg length Crotch height Crotch length Waist girth Hip girth Thigh girth Knee girth Calf girth Ankle girth Hsu and Chung et al. Wang (2005) (2007) { { { { { { { { { { { { { { { { Descriptive statisticsb Mean SD Range 112.7 5.2 43.1 106.0 5.0 40.3 56.8 2.7 21.0 108.2 5.1 41.0 83.7 4.6 39.2 76.7 5.6 38.1 84.0 7.4 47.5 98.4 6.2 43.4 59.7 4.9 32.9 38.6 2.2 14.7 37.8 2.5 16.6 22.2 1.3 9.0 Waist-to-ankle length and waist-to-knee length were estimated by subtracting ankle height and knee height from waist height, respectively, because of their unavailability in the 1988 US Army anthropometric data. b Source: The 1988 US Army anthropometric data of males (n = 1774) (Gordon et al., 1988) Table 2. Analysis of average adjusted R2 for single key dimension candidates (illustrated) Key dimension candidate AD1 AD2 M AD12 Anthropometric dimensions AD2 AD3 AD4 AD5 AD6 AD7 AD8 AD9 AD10 AD11 AD12 AD1 AD3 Adjusted R2 M M AD12 0.13 M M AD1 AD2 0.15 0.13 M M AD11 0.64 0.99 0.89 0.88 0.83 0.20 0.10 0.18 0.12 0.23 0.12 0.15 0.99 0.89 Average adjusted R2 0.43 0.42 M 0.28 Table 3. Representative human models generated by the grid method to accommodate 95% of the 1988 US Army male populationa Non-key anthropometric dimensionb Key dimensions No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Crotch height (AD5) 73.8 (2) 73.8 (2) 73.8 (2) 78.8 (15) 78.8 (15) 78.8 (15) 78.8 (15) 78.8 (15) 78.8 (15) 83.8 (51) 83.8 (51) 83.8 (51) 83.8 (51) 83.8 (51) 83.8 (51) 83.8 (51) 88.8 (87) 88.8 (87) 88.8 (87) 88.8 (87) 88.8 (87) 88.8 (87) 93.8 (99) 93.8 (99) 93.8 (99) Waist girth (AD7) 74.1 (9) 79.1 (25) 84.1 (50) 69.1 (2) 74.1 (9) 79.1 (25) 84.1 (50) 89.1 (75) 94.1 (91) 69.1 (2) 74.1 (9) 79.1 (25) 84.1 (50) 89.1 (75) 94.1 (91) 99.1 (98) 74.1 (9) 79.1 (25) 84.1 (50) 89.1 (75) 94.1 (91) 99.1 (98) 79.1 (25) 84.1 (50) 89.1 (75) Waist height (AD1) 101.0 (1) 101.9 (2) 102.8 (3) 105.2 (7) 106.0 (10) 106.9 (13) 107.8 (17) 108.7 (22) 109.6 (27) 110.2 (31) 111.1 (38) 112.0 (44) 112.9 (51) 113.7 (58) 114.6 (64) 115.5 (70) 116.1 (74) 117.0 (80) 117.9 (84) 118.8 (88) 119.7 (91) 120.5 (93) 122.0 (96) 122.9 (98) 123.8 (98) Waist-toankle length (AD2) 94.8 (1) 95.6 (2) 96.4 (3) 98.9 (8) 99.7 (10) 100.5 (14) 101.3 (17) 102.1 (22) 102.9 (27) 103.7 (32) 104.5 (38) 105.3 (45) 106.1 (51) 106.9 (57) 107.8 (64) 108.6 (70) 109.4 (75) 110.2 (80) 111.0 (84) 111.8 (88) 112.6 (91) 113.4 (93) 115.0 (96) 115.8 (98) 116.6 (98) Waist-toknee length (AD3) 51.3 (2) 51.8 (3) 52.3 (5) 53.2 (9) 53.7 (12) 54.1 (16) 54.6 (21) 55.0 (26) 55.5 (31) 55.5 (32) 56.0 (38) 56.4 (44) 56.9 (51) 57.4 (58) 57.8 (64) 58.3 (70) 58.3 (70) 58.8 (76) 59.2 (81) 59.7 (85) 60.1 (89) 60.6 (92) 61.1 (94) 61.5 (96) 62.0 (97) Outside leg length (AD4) 96.8 (1) 97.6 (2) 98.4 (3) 100.9 (8) 101.7 (10) 102.6 (13) 103.4 (17) 104.2 (22) 105.1 (27) 105.8 (32) 106.7 (38) 107.5 (45) 108.4 (51) 109.2 (58) 110.0 (64) 110.9 (70) 111.6 (75) 112.5 (80) 113.3 (84) 114.2 (88) 115.0 (91) 115.8 (93) 117.4 (96) 118.3 (98) 119.1 (98) Crotch length (AD6) 69.9 (11) 72.9 (25) 75.8 (44) 67.4 (5) 70.3 (13) 73.3 (27) 76.3 (47) 79.2 (68) 82.2 (84) 67.8 (6) 70.8 (14) 73.7 (30) 76.7 (50) 79.7 (71) 82.6 (86) 85.6 (95) 71.2 (16) 74.2 (33) 77.2 (53) 80.1 (73) 83.1 (88) 86.1 (95) 74.6 (36) 77.6 (57) 80.6 (76) Hip girth (AD8) 89.5 (8) 93.0 (19) 96.4 (38) 87.0 (3) 90.5 (10) 94.0 (24) 97.4 (44) 100.9 (66) 104.4 (83) 88.0 (5) 91.5 (13) 95.0 (29) 98.4 (50) 101.9 (72) 105.4 (87) 108.8 (95) 92.5 (17) 96.0 (35) 99.4 (57) 102.9 (77) 106.4 (90) 109.8 (97) 97.0 (41) 100.5 (63) 103.9 (81) a The values are in cm and corresponding percentile values are presented in parentheses. b Non-key dimensions were estimated by regression equations in Table 4. Thigh girth (AD9) 53.5 (11) 56.1 (24) 58.7 (42) 51.4 (5) 54.0 (13) 56.6 (27) 59.2 (46) 61.8 (67) 64.4 (83) 51.9 (6) 54.5 (15) 57.1 (30) 59.7 (50) 62.3 (70) 64.9 (86) 67.5 (94) 55.0 (17) 57.6 (34) 60.2 (54) 62.8 (74) 65.4 (88) 68.0 (95) 58.1 (38) 60.7 (58) 63.3 (77) Knee girth (AD10) 35.5 (8) 36.5 (17) 37.5 (31) 35.0 (5) 36.0 (12) 37.1 (24) 38.1 (40) 39.1 (59) 40.2 (75) 35.6 (8) 36.6 (18) 37.6 (33) 38.7 (50) 39.7 (68) 40.7 (83) 41.8 (92) 37.2 (25) 38.2 (42) 39.2 (61) 40.3 (77) 41.3 (88) 42.3 (95) 38.8 (53) 39.8 (70) 40.8 (84) Calf girth (AD11) 34.9 (13) 36.0 (24) 37.1 (39) 34.2 (8) 35.3 (16) 36.4 (29) 37.5 (45) 38.6 (62) 39.7 (77) 34.6 (10) 35.6 (20) 36.7 (34) 37.8 (50) 38.9 (67) 40.0 (81) 41.1 (90) 36.0 (24) 37.1 (39) 38.2 (56) 39.3 (72) 40.4 (84) 41.5 (92) 37.5 (45) 38.5 (61) 39.6 (76) Ankle girth (AD12) 20.7 (14) 21.2 (22) 21.6 (34) 20.6 (11) 21.0 (19) 21.5 (29) 21.9 (42) 22.3 (55) 22.8 (68) 20.9 (16) 21.3 (25) 21.7 (37) 22.2 (50) 22.6 (64) 23.1 (75) 23.5 (85) 21.6 (33) 22.0 (46) 22.5 (59) 22.9 (71) 23.3 (82) 23.8 (89) 22.3 (54) 22.7 (67) 23.2 (78) Table 4. Regression equations using crotch height (AD5) and waist girth (AD7) as regressors Anthropometric dimensions Waist height Waist-to-ankle length Waist-to-knee length Outside leg length Crotch length Hip girth Thigh girth Knee girth Calf girth Ankle girth Code AD1 AD2 AD3 AD4 AD6 AD8 AD9 AD10 AD11 AD12 Regression equation AD1 = 13.49 + 1.01°AD5 + 0.18°AD7 AD2 = 11.24 + 0.97°AD5 + 0.16°AD7 AD3 = 10.33 + 0.46°AD5 + 0.09°AD7 AD4 = 11.07 + 0.99°AD5 + 0.17°AD7 AD6 = 19.53 + 0.09°AD5 + 0.59°AD7 AD8 = 23.25 + 0.20°AD5 + 0.69°AD7 AD9 = 7.76 + 0.10°AD5 + 0.52°AD7 AD10 = 11.77 + 0.11°AD5 + 0.21°AD7 AD1 1= 13.47 + 0.07°AD5 + 0.22°AD7 AD12 = 10.04 + 0.06°AD5 + 0.09°AD7 Adjusted R2 0.89 0.88 0.70 0.90 0.64 0.72 0.62 0.55 0.43 0.30
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