Development and Cross-Validation of LMS-Based Normative Reference Standards and Health Benefits Zones for Muscular Strength among Adolescents by Age and Sex

Yang Yang¹Syed Ghufran Hadier^2,3*Liu Long¹Syed Danish Hamdani^4,5*Dr. Syed Muhammad Zeeshan Haider Hamdani^3,6*

• ¹School of Physical Education, Suzhou University, Suzhou, Anhui, 234000, China
• ²School of Physical Education, Shanxi University, Taiyuan, China
• ³Department of Sports Sciences, Bahauddin Zakariya University, Multan, Punjab, Pakistan
• ⁴Division of Olympic Sports, China Swimming College, Beijing Sport University, Beijing, China
• ⁵School Education Department, Government of Punjab,, Multan, Punjab, Pakistan
• ⁶School of Exercise and Health, Shanghai University of Sport, Shanghai, China

Objective: This study aims to develop and validate age- and sex-specific normative reference standards for muscular strength (MS) using the LMS (Lambda–Mu–Sigma) method and to establish Health Benefit Zones (HBZs) for Pakistani adolescents aged 12–16 years. Methods: A cross-sectional study was conducted with 2,970 adolescents (49.7% boys, 50.3% girls) selected through stratified random sampling from 60 public high schools across three divisions of South Punjab. Anthropometric indicators and muscular strength were measured following standardized protocols. Using the LMS , age and sex specific normative reference values and smoothed percentile curves (3rd, 10th, 35th, 50th, 65th, and 90th) were developed. Five Health Benefit Zones (Very Poor, Poor, Medium, Good, and Excellent) were derived from these percentile ranges to classify strength levels. The robustness of the generated standards was examined through internal cross validation using a back generation procedure to confirm high predictive accuracy. Results: Boys demonstrated significantly higher muscular strength than girls across all ages (p < 0.001), with strength increasing progressively with age in both sexes. At age 16, median MS reached 35.47 kg for boys and 20.18 kg for girls. LMS-derived percentile reference values and percentile curves illustrated consistent age- and sex-related growth trends. Approximately 40% of participants fell within the “poor” or “very poor” HBZs. MAPE values remained below ±0.05, indicating excellent model fit. Compared to international benchmarks, adolescents from South Punjab exhibited lower MS values across corresponding age groups. Conclusion: This study provides the first LMS based, age and sex specific normative reference standards and HBZs for muscular strength among Pakistani adolescents. These standards offer a population relevant tool for fitness assessment, enable early identification of youth at risk of low muscular strength, and support targeted interventions to enhance strength development and overall physical health in school aged populations.