Body fat and skinfold thicknesses: A dimensional analytic approach

Background: Body fat may be estimated from skinfold thickness measurements (Skfs), but current prediction equations are dimensionally inconsistent and do not properly allow for the influence of body size on fat mass. Aim: To find a dimensionally correct formula relating fat content to Skfs and body size. Subjects and methods: 285 African children aged 9-11 years, with fat content measured by dual-energy X-ray absorptiometry, were studied. Because least-squares regression parameters can be a misleading guide to true functional relationships, the real data were compared with simulated data sets conforming to a dimensionally correct statistical model. Results: The data are consistent with functional relationships such that fat mass is proportional to Skfxheight(2). The mean ratio (fat mass)/(Skfxheight(2)) is 6% higher in the girls than in the boys. Discussion: Appropriately, Skfxheight(2) has the dimensions of fat mass/density. Height(2) has no obvious physical significance and a more meaningful expression might be 'heightxX', where X corresponds to some measure of body width or girth. Conclusion: In formulae for predicting fat mass, multiplying Skfs by height(2) gives better estimates, especially for the tallest and shortest individuals. Fat mass, rather than percentage body fat (%BF), is best taken as the variable initially predicted.