### INTRODUCTION

### MATERIALS AND METHODS

### Design

### Participants

### Measures

### Statistical analysis

*post hoc*analysis was performed with Bonferroni’s multiple comparison test. To determine the age range at which significant progression of isometric strength could be observed in girls and boys (second secondary objective), the narrowest age range of strength was identified by significant differences (

*P*<0.05) observed between the lowest and highest age of the interval selected. Eta-squared (

*η*

^{2}) for ANOVA was used to examine the effect size. A

*η*

^{2}less than 0.06 was classified as “small,” 0.07–0.14 as “moderate,” and greater than 0.14 as “large.” In addition, Cohen

*d*for paired samples was used as an indicator of the effect size. A Cohen

*d*less than 0.2 was classified as “trivial,” 0.2–0.5 as “small,” 0.5–0.8 as “moderate”, and greater than 0.8 as “large” (Cohen, 1992).

*r*) from 0–0.4 was considered as weak, 0.41–0.7 as moderate, and 0.71–1.0 as strong. A stepwise multiple linear regression analysis was then performed. The dependent variable was the total upper limb strength, and the independent variables were the maximum isometric strength of each muscle group, adjusted for sex, height, and age. For this method, the independent variable that showed the strongest, simple, significant correlation with the total upper limb strength was initially selected for the analysis. The remaining variables that showed simple significant correlations (from highest to lowest correlation) were consecutively added to this model. The goodness of fit was determined by means of the

*R*

^{2}coefficient and its percentage of change. In addition, collinearity diagnoses were verified through values less than 0.10 tolerance and the identification of the variance inflation factor (VIF), opting to eliminate the variables that showed collinearity with a VIF >10, in order to define the definitive multiple linear regression model.

### RESULTS

*df*]=8,

*F*=2.056,

*P*=0.0412,

*η*

^{2}=0.05, small effect), wrist flexors (

*df*=8,

*F*=2.483,

*P*=0.0134,

*η*

^{2}=0.07, small effect) and extrinsic and intrinsic hand muscles (

*df*=8,

*F*=2.067,

*P*= 0.0400,

*η*

^{2}=0.05, small effect). Multiple comparisons showed significant differences in age and sex. As depicted in Table 3, for the boys, the narrowest age range in the progression of maximum isometric strength were: 10–12 years for wrist flexors (mean difference=−0.38,

*P*=0.0392,

*d*=1.09, large effect), 11–13 years for elbow flexors (mean difference=−0.71,

*P*=0.0074,

*d*=1.23, large effect), and 13–15 years for extrinsic and intrinsic hand muscles (mean difference=−0.16,

*P*=0.0012,

*d*=1.60, large effect). In the girls, no significant differences were observed between those aged 7–15 years in the maximum isometric strength of any muscle group.

*P*=0.0143,

*d*=0.95, large effect). These differences in maximum isometric strength between the sexes were consolidated at 15 years of age, with the observation of three muscle groups with higher values in boys: elbow flexors (

*P*=0.0268,

*d*=1.70, large effect), wrist flexors (

*P*=0.0250,

*d*=1.69, large effect), and extrinsic and intrinsic hand muscles (

*P*=0.0001,

*d*=2.75, large effect). In this sense, boys showed greater total upper limb strength compared to girls only at 15 years of age (

*P*=0.0269,

*d*=1.97, large effect); Fig 2 shows graphically these differences between sex only at 15 years.

*r*=0.62–0.86,

*P*=0.001). Conversely, total upper limb strength did not show significant correlation with age (

*r*=0.12,

*P*=0.058) or height (

*r*=0.01,

*P*= 0.919). The stepwise multiple linear regression model (Table 4) revealed that the shoulder flexors, shoulder abductors, shoulder medial rotators, and wrist flexors explained the highest percentage of variance (

*R*

^{2}=0.933,

*P*<0.001) in total upper limb strength. Of these, the shoulder flexor group (β=1.12; standard error=0.06; 95% confidence interval, 1.00–1.24) was the main factor that explained the performance of the total upper limb strength (

*R*

^{2}= 0.742;

*P*<0.001). The remaining muscle groups explained a change in

*R*

^{2}between 0.004–0.030 points (

*P*<0.001). The sum of age (

*P*=0.288), sex (

*P*=0.236), and height (

*P*=0.356) did not improve the prediction of total upper limb strength.

### DISCUSSION

*R*

^{2}=0.933). Of these, the shoulder flexors were the muscle group that contributed the greatest proportion (change in

*R*

^{2}=0.742) to the prediction model of total upper limb strength; therefore, it can be considered as the target muscle group to be prospectively evaluated in the development of the total upper limb strength in girls and boys, in a simple and abbreviated way.