Sex-specific allometric modeling and regression-residual normalization for size-adjusted strength assessment

Body mass strongly influences maximal strength, complicating comparisons across individuals of different sizes and sexes. Traditional ratio standards and fixed allometric exponents often fail to adequately reduce body-mass dependence. This study examined whether sex-specific regression-residual normalization derived from log-log allometric models could reduce body-mass dependence to non-significant residual variance across multiple resistance exercises within this sample.

Strength data were obtained from 203 college-aged adults (133 males, 70 females) who performed one-repetition maximum (1RM) tests for the bench press, squat, deadlift, snatch, clean and jerk, and overhead press, along with a 90-s one-arm kettlebell snatch test. Sex-specific allometric models of the form ln(P) = ln(a) + b·ln(M) were fitted for each exercise. Standardized residuals (W-scores) were calculated as size-adjusted performance indices. Normalization effectiveness was evaluated using correlations and regression slopes relating body mass to both raw performance and W-scores.

Raw strength performance was positively associated with body mass across all barbell lifts (males: r = 0.25-0.44; females: r = 0.37-0.50; all p ≤ 0.010; R² ≈ 0.06-0.25). After normalization, associations between body mass and W-scores were reduced to near zero (males: r = - 0.06 to 0.01; females: r = - 0.02 to - 0.01; all p ≥ 0.48). Regression slopes were close to zero, and 95% confidence intervals included zero across all tasks.

Sex-specific regression-residual normalization based on log-log allometric modeling reduced statistical body-mass dependence to negligible levels across diverse strength tasks within this sample. By emphasizing statistical independence of the normalized outcome, this approach provides a statistical framework for generating size-adjusted strength metrics for within-sample comparisons.