Table 1_Longitudinal associations between structured teaching and attentional functioning in youth badminton: evidence from fixed effects quantile regression.docx

But quantile regression showed significant heterogeneity: on the 10th quantile, the association was small and not significant (β = 0.082, p = 0.221); on the 90th quantile, the association was large and significant (β = 0.506, p < 0.001). The Wald test confirmed a significant difference between the 10th and 90th quantiles (χ²(1) = 22.47, p < 0.001). Non-linear analysis with restricted cubic splines indicated a visually suggestive but statistically unproven non-linear pattern among inattentive students.</p>Conclusions<p>The within-person association between perceived structured instruction and attentional function differed significantly in the conditional distribution of attention.

The positive correlation was significantly stronger in the upper conditional quantile of attentional function and weaker in the lower conditional quantile. This pattern of differences suggests that uniform instructional strategies may risk reinforcing attentional differences. Coaches and educators should consider interventions that are adaptable and matched to individual doses.

Given the observational longitudinal design, no causal conclusions can be drawn; the results reflect intra-individual associations.</p>