Two Important Cautions in the Use of Allometric Scaling: The Common Exponent and Group Difference Principles

Abstract

Allometric scaling (AS), used to model relations between physiological traits and body size, has proved useful for both individual and group comparisons. Several recent studies, however, have violated key measurement principles of AS, contributing to erroneous conclusions. The objective of this article is to demonstrate the correct use and interpretation of two of these principles, the common exponent (CE) and group difference (GD) principles. Multivariate AS was applied to a data set of 60 and 51 college-age men and women, respectively, to model the relation between body mass (BM), gender (G), and maximal total work done on a cycle ergometer in 10 min (TW10) as TW10 α BM^-b middot; G^-c. Results indicate that the men's and women's BM exponents were not statistically significantly different, so the CE principle was not violated. This allowed group comparison which, when done according to the GD principle, indicated that TW10 · BM^-.67 is the proper scaled index of BM-adjusted TW10 for men and women. Failure to comply with this principle would have resulted in a spurious index of TW10· BM^-1.17, an index that would have led to different results in both individual and group differences.