# INTERPRETIVE AND STATISTICAL CONSIDERATIONS FOR RATIOS OF MUSCLE STRENGTH PER UNIT OF MUSCLE SIZE

## Abstract

BACKGROUND: Ratios of muscle strength per unit of muscle size are widely used. Statisticians point out that ratios often lead to spurious findings because they can 1) violate statistical assumptions, and 2) differ systematically across the range of denominator values simply due to mathematical artifact, not physiology. PURPOSE: Evaluate uneven scaling in muscle strength/size ratios via recommended isometry tests. METHODS: To evaluate working with ratios at the population level, 1999-2002 NHANES data including isokinetic knee extensor force and leg lean mass measures (n=2,848) were analyzed. To evaluate decision-making with sample data, we analyzed one-repetition maximum bicep curl (1RM) and bicep ultrasound muscle thickness data (n=151) from one of our previous studies. For each data set, regression lines were fit to numerator (strength) against denominator (size) variables via standardized major axis regression, testing for a non-zero y-intercept (indicates isometry issues). The ratio was then regressed on the denominator, with a non-zero slope indicating uneven scaling due to artifact. Recommended solutions including log transformation and intercept adjustment were also explored. RESULTS: For NHANES data, peak force (kg) regressed on leg lean mass (kg) yielded a line of y=-13.85+6.51x. The zero-intercept test indicated a non-isometric relationship, p<0.001. When the strength/size ratio was regressed on leg lean mass, a systematic difference in the ratio (i.e., significant slope test) was observed across the leg lean mass values, y=5.13-0.06x, R2=0.008, p<0.001. For the smaller sample, 1RM (kg) regressed on muscle thickness (cm) yielded a line of y=-8.28+8.14x. The zero-intercept test indicated a non-isometric relationship, p<0.001. When the strength/size ratio was regressed on muscle thickness, a systematic difference in the ratio was observed across the muscle thickness values, y=3.30+0.58x,R2=0.118,p<0.001. Log transformation did not alleviate scaling issues in either data set, although intercept adjustment may. CONCLUSION: Scaling issues were present in both cases, each in opposite direction. In one case, higher leg lean mass is associated with lower ratio scores, and in the other, greater muscle thickness is associated with greater ratio scores, each likely due to artifact. Ratio data should be evaluated case-by-case before subjected to analysis. Other techniques, i.e., ANCOVA or multiple regression, may better control for muscle size.

## Recommended Citation

Chatlaong, Matthew A.; Bentley, John P.; Loenneke, Jeremy P. FACSM; Dankel, Scott J.; and Jessee, Matthew B.
(2024)
"INTERPRETIVE AND STATISTICAL CONSIDERATIONS FOR RATIOS OF MUSCLE STRENGTH PER UNIT OF MUSCLE SIZE,"
*International Journal of Exercise Science: Conference Proceedings*: Vol. 16:
Iss.
3, Article 333.

Available at:
https://digitalcommons.wku.edu/ijesab/vol16/iss3/333