A global public health concern is the rise in childhood physical inactivity and reduced physical fitness. Numerous cross-sectional studies have shown a positive correlation between physical fitness (cardiorespiratory, muscular, and motor) and academic performance (grade points or standardized test scores). Longitudinal studies, including observational studies and RCTs, have supported this, suggesting a causal link between fitness improvements and better academic performance. However, some large-scale cluster RCTs have found no such effect, raising questions about the relationship's causality. Discrepancies may arise from participant characteristics (sex) and the type/duration of physical activity. This study focused on intra-individual variability in grade points to explore potential moderators of the fitness-academic performance association. Previous research showed inconsistent associations between cardiorespiratory fitness and specific subjects (mathematics vs. reading). This inconsistency might stem from baseline student performance; studies suggest that those with lower baseline cognitive performance or math scores benefit more from physical activity interventions. This study hypothesized that improvements in physical fitness would positively impact a student's worst grades but have minimal or no impact on their best grades. The study controlled for confounding variables, including out-of-school learning time and socioeconomic status (SES).

Existing research reveals a mixed relationship between physical fitness and academic performance. While cross-sectional studies largely demonstrate a positive correlation, longitudinal studies show contradictory results, possibly due to variations in subject matter or baseline performance. Some studies highlight a stronger association between cardiorespiratory fitness and mathematics than reading, while others show the opposite. Moreover, longitudinal studies have yielded inconsistent findings concerning academic subject-specific changes. To address this, some researchers have re-analyzed data from RCTs to understand if baseline performance moderates the effect of physical activity interventions on executive function, a cognitive process strongly linked to academic achievement. Results suggest that individuals with lower baseline cognitive performance show greater improvement in executive function after interventions. This implies that inter-individual differences in baseline performance might moderate the effects of physical activity on academic performance. Alternatively, intra-individual variability in grades might play a crucial role. Previous work suggests that a student's weakest subjects are more responsive to the benefits of improved physical fitness. These studies also indicated that increased physical activity does not negatively affect the best grades. Recent studies have controlled for confounders like SES, but often overlooked out-of-school learning activities, a significant factor influencing academic achievement. Therefore, this study addresses these gaps by re-analyzing longitudinal data to examine the differential effects of improved cardiorespiratory fitness on a student's best and worst grades, controlling for out-of-school learning time and SES.

This study reanalyzed data from a previous two-year longitudinal study involving 469 Japanese junior high school students (214 girls, 255 boys). Data was collected at the end of the seventh and ninth grades. Academic performance was measured using grade points (GPs) from five subjects (Japanese, mathematics, social studies, science, and English). The lowest and highest GPs for each student were analyzed. Cardiorespiratory fitness was assessed using a standardized test (20-m shuttle run or endurance run), converted to a 1-10 score. Out-of-school learning time was assessed via a self-reported questionnaire, summing weekday and weekend scores. Socioeconomic status (SES) was assessed at baseline using a questionnaire on household income and maternal education. Body mass index (BMI) was also calculated. Pearson's correlation analyses examined the association between changes in cardiorespiratory fitness and out-of-school learning time with the lowest and highest GPs. Multiple regression analyses, using full-information maximum likelihood estimation, predicted the lowest and highest GPs, controlling for household income, maternal education, sex, BMI change, and learning time change. Statistical analyses were conducted with α = 0.05 using R Studio. Post-hoc power analyses were performed using G*Power 3.1.2.

Pearson's correlation analyses (Table 1) revealed no association between changes in cardiorespiratory fitness and learning time. However, changes in learning time were positively associated with changes in both lowest and highest GPs. Importantly, changes in cardiorespiratory fitness were positively associated only with changes in the lowest GP (Figure 1), indicating that improvements in fitness were associated with better grades in the student's weakest subject. No such association was found for the highest GP. Multiple regression analyses (Table 2) confirmed these findings, showing that the associations between changes in cardiorespiratory fitness and changes in the lowest and highest GPs remained significant even after controlling for household income, maternal education, sex, change in BMI, and change in learning time. The effect size for the association between changes in cardiorespiratory fitness and changes in the lowest GP was small (Cohen's *f* = 0.02), while the effect size for the association between changes in cardiorespiratory fitness and changes in the highest GP was even smaller (Cohen's *f* = 0.003).

The findings support the hypothesis that improvements in physical fitness are associated with better grades in a student's worst subjects, but not necessarily their best subjects. This aligns with previous research showing that individuals with lower baseline performance benefit more from physical activity interventions. This study extends this by demonstrating that the association between fitness improvements and academic performance is moderated by intra-individual variability in grades. The null effect of some physical activity interventions on overall academic performance could be explained by the difficulty of the academic tests; benefits might be undetectable when overall scores are high. The lack of association between fitness changes and highest GP supports the idea that increased physical activity doesn't negatively impact academic performance. The positive association between increased out-of-school learning time and both lowest and highest GPs was expected. Importantly, the association between fitness changes and the lowest GP remained independent of out-of-school learning time, suggesting that the improvement in the lowest GP may result from changes in classroom behavior. Improved fitness might enhance concentration and motivation, leading to better grades in weaker subjects. This contrasts with the best subjects, where students are likely already highly motivated.

This longitudinal study demonstrates a strong positive association between improvements in physical fitness and academic performance specifically in a student's weakest subjects. The results support the notion that increased physical activity does not negatively impact academic performance. Future research should investigate the long-term effects of physical activity on classroom behaviors, explore the impact of different types of physical activity and fitness components, and examine the role of neuropsychological factors and potential confounding variables.

This observational study cannot rule out the effects of catch-up growth. It used cardiorespiratory fitness as a proxy for regular physical activity, without distinguishing between fitness improvements due to development or activity. The study focused only on cardiorespiratory fitness, and the GP system may vary across countries, limiting generalizability. The lack of data on mental health, learning disabilities, or neurological disorders is also a limitation. Selection bias may have occurred due to the consent rate being only 74%.