Estimating indicator weights for the motor health of pre-school-aged children: an integrated-methods approach

Introduction Motor health and long-term development of pre-school children is a pressing issue that requires urgent attention. While motor health is critically important for the early growth stage of pre-school children, establishing a multi-dimensional health evaluation indicator weighting system using an integrated subjective-objective weighting method remains a cutting-edge challenge in current research. Methods WPS Office 6.4 and IBM ® SPSS ® Statistics 26.0 were used to analyze the data, with the significance threshold set at P -value < 0.05. The integrated subjective-objective weighting method mainly consists of four steps: (i) the Delphi subjective weighting method, including A i , A s , A a , W i , W i ′ ω; (ii) the entropy objective weighting method, including X ij , P ij , E j , d j , and W j ; (iii) the comprehensive weighting method, including relevant parameters W j * , among others; (iv) IBM ® SPSS ® Amos (TM) 24.0 was used to conduct further data analysis. Results The total combined weight of the six primary indicators is 1.0, with individual weights ranging from 0.109 to 0.213. The corresponding weights of the 26 secondary indicators range from 0.014 to 0.215. Regarding the weighting of first-level indicators, no significant correlation was found between the comprehensive weighting method and the Delphi method ( r = 0.771, P = 0.072), nor between the comprehensive weighting method and the entropy weight method ( r = 0.600, P = 0.208). Similarly, no significant correlation was observed between the Delphi method and the entropy weight method ( r = 0.143, P = 0.787). In contrast, for second-level indicators, the comprehensive weighting method demonstrated a strong correlation with both the Delphi method ( r = 0.917, P < 0.001) and the entropy weight method ( r = 0.558, P = 0.003). However, no significant correlation was detected between the Delphi method and the entropy weight method ( r = 0.268, P = 0.185). Conclusion By adopting an integrated subjective-objective weighting method, this study establishes evaluation indicator weights based on two foundations: the intrinsic patterns within the data and expert experience. The weights derived through this dual-foundation approach therefore exhibit improved rationality and credibility, providing important reference value for the comprehensive assessment of pre-school children's motor health.