Body fat and skinfold thicknesses: A dimensional analytic approach

Abstract

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 Skf×height². The mean ratio (fat mass)/(Skf×height²) is 6% higher in the girls than in the boys.

Discussion: Appropriately, Skf×height² has the dimensions of fat mass/density. Height² has no obvious physical significance and a more meaningful expression might be ‘height×X', where X corresponds to some measure of body width or girth.

Conclusion: In formulae for predicting fat mass, multiplying Skfs by height² 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.

Keywords::

• Skinfold thickness measurements
• body fat
• dimensional analysis

Acknowledgements

The Birth to Twenty birth cohort study receives financial and logistic support from the Urbanization and Health Programme of the Medical Research Council of South Africa; the Anglo-American Chairman's Fund; Child, Youth, and Family Development of the Human Sciences Research Council of South Africa; and the University of the Witwatersrand. The Bone Health study is financially supported by the Wellcome Trust (UK).

Declaration of interest: The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the paper.