Allometric modeling does not determine a dimensionless power function ratio for maximal muscular function

Abstract

Batterham, Alan M., and Keith P. George. Allometric modeling does not determine a dimensionless power function ratio for maximal muscular function. J. Appl. Physiol. 83(6): 2158–2166, 1997.—In the exercise sciences, simple allometry ( y = axb ) is rapidly becoming the method of choice for scaling physiological and human performance data for differences in body size. The purpose of this study is to detail the specific regression diagnostics required to validate such models. The sum (T, in kg) of the “snatch” and “clean-and-jerk” lifts of the medalists from the 1995 Men’s and Women’s World Weightlifting Championships was modeled as a function of body mass (M, in kg). A log-linearized allometric model (ln T = ln a + bln M) yielded a common mass exponent ( b) of 0.47 (95% confidence interval = 0.43–0.51, P < 0.01). However, size-related patterned deviations in the residuals were evident, indicating that the allometric model was poorly specified and that the mass exponent was not size independent. Model respecification revealed that second-order polynomials provided the best fit, supporting previous modeling of weightlifting data (R. G. Sinclair. Can. J. Appl. Sport Sci. 10: 94–98, 1985). The model parameters (means ± SE) were T = (21.48 ± 16.55) + (6.119 ± 0.359)M − (0.022 ± 0.002)M2( R 2 = 0.97) for men and T = (−20.73 ± 24.14) + (5.662 ± 0.722)M − (0.031 ± 0.005)M2( R 2 = 0.92) for women. We conclude that allometric scaling should be applied only when all underlying model assumptions have been rigorously evaluated.