Normalization of Ground Reaction Forces

The appropriateness of normalizing data, as one method to reduce the effects of a covariate on a dependent variable, should be evaluated. Using ratio, 0.67-nonlinear, and fitted normalizations, the aim of this study was to investigate the relationship between ground reaction force variables and body mass (BM). Ground reaction forces were recorded for 40 female subjects running at 3.7 ± 0.18 m·s–1 (mass = 58 ± 6 kg). The explained variance for mass to forces (peak-impact-vertical = 70%; propulsive-vertical = 27%; braking = 40%) was reduced to < 0.1% for mass to ratio normalized forces (i.e., forces/BM1) with statistically significantly different power exponents (p < 0.05). The smaller covariate effect of mass on loading rate variables of 2–16% was better removed through fitted normalization (e.g., vertical-instantaneous-loading-rate/BM0.69±0.93; ±95% CI) with nonlinear power exponents ranging from 0.51 to 1.13. Generally, these were similar to 0.67 as predicted through dimensionality theory, but, owing to the large confidence intervals, these power exponents were not statistically significantly different from absolute or ratio normalized data (p > 0.05). Further work is warranted to identify the appropriate method to normalize loading rates either to mass or to another covariate. Ratio normalization of forces to mass, as predicted through Newtonian mechanics, is recommended for comparing subjects of different masses.

Letters to the Editor

The following is the abstract of the article discussed in the subsequent letter: Batterham, Alan M., Keith Tolfrey, and Keith P. George. Nevill’s explanation of Kleiber’s 0.75 mass exponent: an artifact of collinearity problems in least squares models? J. Appl. Physiol. 82(2): 693–697, 1997.—Intraspecific allometric modeling (Y = a ⋅ mass b , where Y is the physiological dependent variable and ais the proportionality coefficient) of peak oxygen uptake (V˙o 2peak) has frequently revealed a mass exponent ( b) greater than that predicted from dimensionality theory, approximating Kleiber’s 3/4 exponent for basal metabolic rate. Nevill ( J. Appl. Physiol. 77: 2870–2873, 1994) proposed an explanation and a method that restores the inflated exponent to the anticipated 2/3. In human subjects, the method involves the addition of “stature” as a continuous predictor variable in a multiple log-linear regression model: ln Y = ln a + c ⋅ ln stature + b ⋅ ln mass + ln ε, where c is the general body size exponent and ε is the error term. It is likely that serious collinearity confounds may adversely affect the reliability and validity of the model. The aim of this study was to critically examine Nevill’s method in modelingV˙o 2peak in prepubertal, teenage, and adult men. A mean exponent of 0.81 (95% confidence interval, 0.65–0.97) was found when scaling by mass alone. Nevill’s method reduced the mean mass exponent to 0.67 (95% confidence interval, 0.44–0.9). However, variance inflation factors and tolerance for the log-transformed stature and mass variables exceeded published criteria for severe collinearity. Principal components analysis also diagnosed severe collinearity in two principal components, with condition indexes >30 and variance decomposition proportions exceeding 50% for two regression coefficients. The derived exponents may thus be numerically inaccurate and unstable. In conclusion, the restoration of the mean mass exponent to the anticipated 2/3 may be a fortuitous statistical artifact.

Nevill's explanation of Kleiber's 0.75 mass exponent: an artifact of collinearity problems in least squares models?

Batterham, Alan M., Keith Tolfrey, and Keith P. George.Nevill’s explanation of Kleiber’s 0.75 mass exponent: an artifact of collinearity problems in least squares models? J. Appl. Physiol. 82(2): 693–697, 1997.—Intraspecific allometric modeling ( Y = a ⋅ mass b , where Y is the physiological dependent variable and a is the proportionality coefficient) of peak oxygen uptake (V˙o 2 peak) has frequently revealed a mass exponent ( b) greater than that predicted from dimensionality theory, approximating Kleiber’s 3/4 exponent for basal metabolic rate. Nevill ( J. Appl. Physiol. 77: 2870–2873, 1994) proposed an explanation and a method that restores the inflated exponent to the anticipated 2/3. In human subjects, the method involves the addition of “stature” as a continuous predictor variable in a multiple log-linear regression model: ln Y = ln a + c ⋅ ln stature + b ⋅ ln mass + ln ε, where c is the general body size exponent and ε is the error term. It is likely that serious collinearity confounds may adversely affect the reliability and validity of the model. The aim of this study was to critically examine Nevill’s method in modelingV˙o 2 peak in prepubertal, teenage, and adult men. A mean exponent of 0.81 (95% confidence interval, 0.65–0.97) was found when scaling by mass alone. Nevill’s method reduced the mean mass exponent to 0.67 (95% confidence interval, 0.44–0.9). However, variance inflation factors and tolerance for the log-transformed stature and mass variables exceeded published criteria for severe collinearity. Principal components analysis also diagnosed severe collinearity in two principal components, with condition indexes >30 and variance decomposition proportions exceeding 50% for two regression coefficients. The derived exponents may thus be numerically inaccurate and unstable. In conclusion, the restoration of the mean mass exponent to the anticipated 2/3 may be a fortuitous statistical artifact.