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Physical exercise and aggressive behavior in rural left-behind children: the mediating roles of psychological capital and self-control

Abstract

Objective

Since children left behind in rural areas are more prone to aggressive behavior due to incomplete families or inappropriate parenting styles, it is essential to identify influencing factors and potential mechanisms to mitigate their aggression. This study aims to examine the relationship between physical exercise and aggressive behavior among rural left-behind children in China and the mediating effects of psychological capital and self‑control.

Methods

Participants consisted of 453 rural left-behind children (Mage = 12.58, SD = 1.41; boys = 231, girls = 222) from two rural primary schools and two rural junior high schools in a city in central China. These rural left-behind children completed a questionnaire measuring physical exercise, psychological capital, self-control, and aggressive behavior. Descriptive analysis, correlation analysis, and mediation analysis were conducted using SPSS software and the Process plug-in.

Results

The results showed that (1) physical exercise, psychological capital, and self-control were all significantly positively correlated with each other, and they were all significantly negatively correlated with aggressive behavior. (2) psychological capital and self-control partially serve as both independent and chain mediators between physical exercise and aggressive behavior.

Conclusion

This study provides further insight into the underlying mechanisms linking physical exercise and aggressive behavior in rural left-behind children. Physical exercise not only has a direct negative effect on aggressive behavior but also indirectly predicts aggressive behavior through its impact on psychological capital and self-control. This mediating effect model provided a valuable insight for improving their physical exercise and preventing aggressive behavior.

Peer Review reports

Introduction

Since the 1980s, with the deepening of China’s economic reform and the rapid acceleration of urbanization, many young laborers have migrated from rural areas to cities for work. Due to financial constraints and the restrictions imposed by the household registration system, many migrant parents are compelled to leave their children with other family members. This has led to the emergence of a group known as “left-behind children”. Left-behind children are minors under the age of 16 whose parents both work away from home, or one parent work away from home and the other is unable to supervise them [1]. According to a 2020 survey, there are 66.93 million left-behind children in China, with 41.77 million of whom live in rural areas [2]. Adolescence is a high-risk period for the development of problematic behaviors in individuals [3]. Adverse childhood experiences such as separation and financial strain increased the risk of externalizing and internalizing behaviors [4]. The psychological adjustment problems of children left behind in rural areas are pronounced due to incomplete family structures or inappropriate parenting styles. They are more susceptible to psychological problems such as anxiety [5], and loneliness [6]. Under certain conditions, these intrinsic problem behaviors may be converted into extrinsic problem behaviors, such as aggression. Aggressive behavior (AB) refers to actions intended to cause physically or psychologically harm to another person [7]. Such behavior not only affects the physical and mental well-being of both the aggressor and the victim, but also has broader social consequences. The rural left-behind children are more likely to choose aggressive behavior as a conflict resolution strategy than non-left-behind children [8]. A survey involving 20,747 rural primary and secondary school students in five regions of China showed that the detection rate of aggressive behavior was 27.8% for left-behind children compared to 24.6% for non-left-behind children. The detection rate of aggressive behavior was significantly higher for left-behind children than for non-left-behind children [9]. Moreover, the development of aggressive behavior tends to be continuous; aggressive behavior in early childhood may predict violent crime in adulthood [10]. Therefore, identifying protective factors to mitigate aggressive behavior in rural left-behind children is crucial for promoting their healthy growth and development.

Physical exercise and aggressive behavior

Physical exercise (PE) is a subset of physical activity that is planned, structured, and repeated with the ultimate or intermediate objective of the improving or maintaining physical fitness [11]. Regular physical exercise is associated with numerous health benefits, including reduced risk of chronic diseases [12], and improved mental health [13]. In addition, physical exercise is an effective means of preventing and reducing aggressive behaviors in adolescents [14]. The frustration-aggression theory suggests that individuals who experience frustrating events are more likely to develop negative emotions and aggressive behaviors [15]. The challenging living conditions of rural left-behind children often lead to personal frustration, and as these risk factors accumulate, the likelihood of triggering aggressive emotions increases. However, physical exercise can enhance individuals’ resilience to frustration, contributing to more stable emotional development. Based on the catharsis theory, physical exercise allows adolescents to express and release internal emotional pressure, thereby reducing aggressive behavior through exercise [16]. Two studies of college students found a significant negative association between physical exercise and aggressive behavior [17, 18]. Systematic reviews and meta-analyses have found that physical exercise interventions are effective in reduced aggressive behavior in children and adolescents [19, 20]. However, there is relatively little research has focused on rural left-behind children. As a non-pharmacological intervention, physical exercise serves as a low-cost means to regulate physiological stress responses and emotions in rural left-behind children. Team sports compensates for the attachment deficits of left-behind children and reduces hostile attribution bias by providing a sense of peer belonging and positive feedback [21]. The present study further explored the relationship between physical exercise and aggression behavior in rural left-behind children, it was proposed in this study that H1: Physical exercise in rural left-behind children significantly and negatively associated with aggression behavior.

The mediating role of psychological capital

Psychological capital (PC) refers to the positive psychological energy and resources that an individual expresses during growth and development. It encompasses four dimensions: self-efficacy, hope, optimism, and resilience [22]. Psychological capital plays a critical role in helping rural left-behind children cope with various risks in adverse situations and achieve positive development [23]. Physical exercise can promote positive emotional experiences and increase psychological capital reserves [24]. A study of 797 left-behind children in rural areas indicated that there was a positive correlation between physical exercise and psychological capital [25].

In addition, psychological capital is often viewed as a positive internal resource for individuals [26]. The Conservation of Resources theory suggests that individuals with fewer resources are more likely to engage in maladaptive coping strategies [27]. The General Aggression Model suggests that when individuals have insufficient psychological resources or they are dissatisfied with outcomes, they are more likely to experience aggressive impulses that may subsequently develop into aggressive behavior [7]. A cross-sectional study of Chinese adolescents reported that the development of psychological capital help reduce the occurrence of aggressive behavior [28]. For left-behind children in rural areas, a higher level of psychological capital reduce their loneliness, increase their self-esteem and well-being, thereby reduce the occurrence of problem behaviors [29]. On this basis, it was proposed in this study that H2: Psychological capital mediates the relationship between physical exercise and aggressive behavior.

The mediating role of self-control

Self-control (SC) refers to an individual’s ability to autonomously regulate his behavior in accordance with personal values and social expectations [30]. It is a crucial element in the socialization process of children. According to the strength model of self-control, exerting self-control consumes a finite amount of psychological energy [31]. However, physical exercise can replenish or extend self-control resources by increasing an individual’s overall psychological and physiological resilience. While most research on this topic has focused on the relationship between physical exercise and self-control among college students, studies specifically targeting rural left-behind children are relatively scarce. Empirical evidence suggests that physical exercise reduces aggressive behavior [32], mobile phone dependence [33, 34], and problematic internet use [35] by improving self-control in college students, suggesting a positive relationship between physical exercise and self-control.

The strength model of self-control theory posits that after exerting self-control in an initial task, individuals experience a temporary depletion that impairs their ability to effectively manage subsequent self-control tasks. This weakening of self-control is known as the ego-depletion effect [31]. Ego depletion is a significant factor contributing to increased aggressive behavior in adolescents [36]. Behavioral evidence suggests that individuals with high ego depletion display more aggressive behavior than those with low ego depletion. An event-related potential study further suggests that the level of ego depletion affects both the decision-making phase and the outcome-evaluation phase of aggressive behavior [36]. As children’s self-control ability increases, physical aggression, hostile thoughts, and negative emotions decrease significantly [37]. A study of 2951 Chinese children suggested that self-control partially mediated the relationship between physical exercise and both physical and verbal aggression [38]. Based on this, the present study proposed H3: Self-control mediates the relationship between physical exercise and aggressive behavior in rural left-behind children.

The chain mediation effect of psychological capital and self-control

Individuals with higher levels of psychological capital have more abundant psychological resources, allowing them to expend more resources and exhibit stronger self-control. Conversely, an increase in self-control may reflect the mobilization of internal resources through psychological capital [24]. A study of 1208 junior high school students showed that psychological capital positively predicted the levels of self-control in middle school students [39]. The four dimensions of psychological capital enhance individuals’ positive emotions and cognitive abilities, enabling them to exercise greater self-control in the face of stress and tasks [40]. On this basis, this study proposed H4: Psychological capital and self-control mediate the relationship between physical exercise and aggressive behavior through a chain-mediated effect.

In summary, this study aims to examine the impact of physical exercise on aggressive behavior in rural left-behind children and its underlying mechanisms. It will examine the independent mediating roles of psychological capital and self-control, as well as their combined chain mediating effects, in the relationship between physical exercise and aggressive behavior in rural left-behind children. The hypothesized model is depicted in Fig. 1.

Fig. 1
figure 1

Relationships among the concepts of the study

Methods

Participants

This study used a stratified whole cluster random sampling design to examine left-behind children in two rural primary schools and two rural secondary schools in Yichang City, Hubei Province, China. Informed consent was obtained from the caregivers of the participants before administering the questionnaires. Ethical approval for the study was granted by the researcher’s university. 470 questionnaires were distributed, of which 9 were discarded due to parental separation or death, leaving 461 to be returned. However, 4 were excluded due to missing questions, and another 4 were excluded due to variable scores with standardized values greater than ± 3. Finally, 453 valid responses were obtained, with a mean age of 12.58 years, including 231 boys (51.0%) and 222 girls (49.0%). Among the participants, 58 (12.8%) were in fifth grade, 99 (22.9%) in sixth grade, 66 (14.6%) in seventh grade, 103 (22.7%) in eighth grade, and 127 (28.0%) in ninth grade. It is worth noting that the Chinese basic education system consists of six years of primary school, three years of junior high school, and three years of senior high school.

Our results showed that 56.7% of the sample had father working outside the home, 17% had mother working outside the home, and 26.3% had both parents working outside the home. The duration of work ranged from six months to two years or more. Of the parents working outside the home, 74.8% go home once every six months. Of the left-behind children, 45.9% are looked after by their mothers and 44.2% by their grandparents. Detailed information on all participants is shown in Table 1.

Table 1 Overview of all participants’ information

Measures and instruments

Physical exercise

The Physical Activity Rating Scale-3 (PARS-3) was developed by Hashimoto [41] and revised by Liang [42]. This scale assesses physical exercise levels based on three items: intensity, frequency, and duration. Each of these indicators is rated on a 5-point scale (1–5). The physical exercise score is calculated using the formula: Physical exercise Score = Intensity Score × (Duration Score − 1) × Frequency Score. The score range is from 0 to 100 points. The higher score indicates greater physical exercise. In the present study, the Cronbach’s α coefficient for this scale was 0.66.

Psychological capital

Psychological capital was measured using the Positive Psycap Questionnaire (PPQ) developed by Zhang [43]. This scale contains 26 items, including self-efficacy (7 items), optimism (6 items), resilience (7 items), and hope (6 items). Responses are scored on a 7-point Likert scale (1 = strongly disagree to 7 = strongly agree). Scores range from 26 to 182. After reversing the scoring for certain items, all responses are summed to obtain a total score, with higher scores indicating greater psychological capital. In this study, the Cronbach’s α coefficient for the scale was 0.92.

Self-control

Self-control was measured using the Chinese version of the Dual-Mode of Self-Control Scale (DMSC-S) developed by Dvorak and Simons [44] and revised by Xie [45]. This scale contains 21 items, including problem solving (5 items), future time perspective (3 items), impulsivity (6 items), distractibility (3 items), and poor delay of gratification (3 items). Responses are scored on a 5-point Likert scale (1 = strongly disagree to 5 = strongly agree). Scores range from 21 to 105. After reversing the scoring for certain items, all responses are summed to obtain a total score, with higher scores indicating greater self-control. In this study, the Cronbach’s α coefficient for the scale was 0.90.

Aggressive behavior

Aggressive behavior was measured using the Aggression Questionnaire (AQ) developed by Buss and Perry [46] and revised by Li [47]. This scale contains 30 items, including physical aggression (7 items), verbal aggression (5 items), anger (6 items), hostility (7 items), and self-aggression (5 items). Responses are scored on a 5-point Likert scale (1 = strongly disagree to 5 = strongly agree). Scores range from 30 to 150. Higher scores indicate more pronounced aggressive behavior. In the present study, the overall Cronbach’s α coefficient was 0.95.

Analytic strategy

IBM SPSS 26.0 was used to conduct descriptive statistics, reliability tests, and Pearson correlation analysis. After standardizing each research variable, Model 6 of the PROCESS macro [48] was used to test the mediating effects of psychological capital and self-control on the relationship between physical exercise and aggressive behavior, with 5000 bootstrap samples used to estimate the 95% confidence intervals for the mediation effects.

Harman’s single-factor test was used to assess the potential for common method bias effects. The results revealed a total of seventeen eigenvalues greater than 1 for the common factors, with the first common factor accounting for 27.97% of the variance—below the critical threshold of 40%. This suggests that there is no significant common method bias in the present study.

Results

Differences in demographics for all variables

After importing the dataset into SPSS, independent samples t-tests and one-way ANOVA were used to analyze the demographic differences between several variables. The results from Table 2 showed significant gender differences in physical exercise and psychological capital (p < 0.05), with girls scoring significantly lower than boys on these variables, but both were moderately exercised. However, no significant gender differences were found in self-control and aggressive behavior (p > 0.05). In addition, there were significant differences in physical exercise, psychological capital, and self-control across different grades, except for aggressive behavior (p < 0.05). All variables are not significantly different for the only child, the left-behind types, left-behind types, duration of parental absence, frequency of returning home, and caregiver. Therefore, gender and grade were used as control variables in subsequent analyses to examine the relationships between all variables.

Table 2 Differences in gender and grade for all variables

Descriptive statistics and correlations

Descriptive statistics were performed on the core variables of this study, and the means and standard deviations are presented in Table 3. The results indicated that physical exercise was positively correlated with psychological capital (r = 0.48, p < 0.01) and self-control (r = 0.40, p < 0.01), and negatively correlated with aggressive behavior (r = − 0.25, p < 0.01). Psychological capital was positively correlated with self-control (r = 0.71, p < 0.01) and negatively correlated with aggressive behavior (r = − 0.55, p < 0.01). Self-control was negatively correlated with aggressive behavior (r = − 0.61, p < 0.01).

Table 3 Descriptive statistics and correlation analysis of each variable

** p<0.01.

Chain mediation analysis

This study uses an SPSS macro to examine the mediating effect of psychological capital and self-control between physical exercise and aggressive behavior (Table 4). The analysis showed that physical exercise negatively predicted aggressive behavior (β = −0.27, t = − 5.91, p < 0.001) while controlling for gender and grade. After including psychological capital and self-control together in the regression equation, physical exercise positively predicted psychological capital (β = 0.47, t = 11.15, p < 0.001) and self-control (β = 0.08, t = 2.20, p < 0.05). Psychological capital positively predicted self-control (β = 0.70, t = 19.46, p < 0.001) and negatively predicted aggressive behavior (β = −0.26, t = − 4.78, p < 0.001). Self-control negatively predicted aggressive behavior (β = −0.46, t = − 8.81, p < 0.001).

Table 4 Regression analysis of chain mediation model of psychological capital and self-control

* p < 0.05, *** p < 0.001.

The mediation effects of each mediation path were also examined, and confidence intervals were estimated using the bootstrap method (Table 5; Fig. 2). The analysis showed that the Bootstrap 95% confidence intervals for three indirect effect paths of psychological capital and self-control as mediating variables did not include 0. The indirect effects of the three mediation paths were as follows: (1) Indirect effect 1 was “Physical Exercise → Psychological Capital → Aggressive Behavior”. The effect value was − 0.12 (95%CI: −0.19 ~ − 0.06), accounting for 40% of the total indirect effect value. (2) Indirect effect 2 was “Physical Exercise → Self-Control → Aggressive Behavior”. The effect value was − 0.03 (95%CI: −0.07 ~ − 0.01), accounting for 10% of the total indirect effect value. (3) Indirect effect 3 was “Physical Exercise → Psychological Capital → Self-Control → Aggressive Behavior”. The effect value was − 0.15 (95%CI: −0.21 ~ − 0.11), accounting for 50% of the total indirect effect value.

Table 5 Bootstrap analysis of the mediating effect test
Fig. 2
figure 2

Chain mediating paths between physical exercise and aggressive behavior

Discussion

This study reveals the chain mediating role of psychological capital and self-control in the process by which physical exercise influences aggressive behavior among rural left-behind children. It represents a positive exploration of using physical exercise to prevent aggressive behavior in this group and provides a theoretical foundation for such preventive efforts.

Differences in gender and grade for all variables

The research results indicate that the physical exercise level of the rural left-behind children is in the moderate range, with boys exercising significantly more than girls. Many factors influence the physical exercise of rural left-behind children. Personal factors include individual interests, cognitive level, and emotional communication, while environmental factors include the quality of guardians and physical education teachers, the family sports atmosphere, school sports resources, and family economic conditions [49]. Gender differences in physical exercise levels are also evident among rural left-behind children, consistent with previous research findings [25]. Motivation for physical exercise, social support, and modes of participation may contribute to the differences in sports engagement between boys and girls.

In addition, boys have stronger psychological capital than girls, which may be due to boys’ innate independence and adventurous spirit, which allows them to be more confidence and resilient in the face of challenges. Another factor may be the higher expectations placed on boys in some rural areas, giving them greater access to interpersonal resources, family support, and opportunities for growth [25].

Considering different grade levels, the seventh-grade rural left-behind children show the highest levels of physical exercise, psychological capital, and self-control. This may be because seventh grade is a unique period. On the one hand, students enter early adolescence with higher energy levels and curiosity, making them more likely to engage in physical exercise, while also beginning to develop a more mature self-awareness and social cognition, which helps to improve self-control. On the other hand, external support from schools and families increases students’ psychological capital and self-control.

The relationship between physical exercise and aggressive behavior

The results showed that physical exercise significantly and negatively predicted aggressive behavior in rural left-behind children, which verified hypothesis H1. This finding is consistent with previous research [17]. Left-behind children are more likely to develop problem behaviors such as aggression, withdrawal, and rule-breaking due to inadequate guidance and management of their behavior and mental health by their carers [50]. According to the catharsis theory, physical exercise helps to release negative emotions, thereby reducing aggressive behavior [16]. Additionally, during physical exercise, adolescents can build harmonious interpersonal relationships and develop a healthy psychological mindset, further reducing aggressive behavior. The biological theory of aggression suggests that the primary causes of aggressive behavior include genetic, neurological, and biochemical factors [51]. Exercise may influence adolescent aggression through genetic polymorphisms or by improving cognitive processes such as inhibitory control [52].

The mediating role of psychological capital

This study found that the negative effects of physical exercise on aggressive behavior can be mediated by increasing the psychological capital of rural left-behind children, supporting hypothesis H2. Most researchers define psychological capital as a psychological state that includes an individual’s beliefs, attitudes, and perceptions about self, work, ethics, and life [53]. Due to the disadvantages in their family environment, rural left-behind children tend to have lower psychological capital. However, long-term physical exercise can promote determination foster and resilience in these children, and through various successful experiences, it can effectively enhance their confidence and self-efficacy, leading to higher levels of psychological capital. Previous studies have shown that physical exercise has a significant positive predictive effect on the psychological capital in middle school students [54]. An experimental study has also suggested that moderate-intensity physical exercise promotes psychological capital in college students [55]. Additionally, psychological capital may negatively predict aggressive behavior. Research suggests that students with higher self-efficacy and resilience can regulate their aggressive tendencies by using strategies such as cognitive reappraisal, suppression, and emotional expression [56]. Thus, psychological capital serves as an independent mediator between physical exercise and aggressive behavior in rural left-behind children.

The mediating role of self-control

The present study also found that the negative predictive effect of physical exercise on aggression can be mediated by self-control, supporting hypothesis H3. This is consistent with previous research showing that physical exercise can directly reduce aggressive behavior in college freshmen and indirectly reduce aggressive behavior by increasing self-control [32]. Additionally, participation in physical activities by older elementary school students directly reduces physical/verbal aggression, and hyperactivity, and has an indirect positive effect through increased self-control [38]. Regular physical exercise encourages individuals to consciously regulate their behavior, which in turn strengthens self-control. Empirical studies have found that five weeks of aerobic exercise can effectively improve self-control in college students [57], and moderate-intensity physical exercise can significantly improve self-control in participants [58]. According to the strength model of self-control, a lack of self-control resources is a key factor in aggressive behavior. Individuals in a depleted state exhibit stronger aggression during subsequent self-control tasks compared to those who are not depleted [59]. Moreover, individuals with low trait self-control are more likely to engage in aggressive behavior when in a depleted state [60]. This suggests that self-control plays a mediating role in the relationship between physical exercise and aggressive behavior.

Chain mediation of psychological capital and self-control

This study found that both psychological capital and self-control also jointly act as a chain mediator between physical exercise and aggressive behavior, supporting hypothesis H4. This suggests that rural left-behind children with higher levels of physical exercise tend to have higher levels of psychological capital and self-control, making them less likely to engage in aggressive behavior. Social control theory suggests that the strength of an individual’s connection to society is a key factor in determining whether he or she will engage in criminal or deviant activities. Physical exercise strengthens the connection of rural left-behind children to society, thereby reducing deviant behaviors such as aggression. Additionally, physical exercise helps release negative emotions such as depression and anger [61] while the social support and positive peer relationships gained through physical exercise further enhance psychological capital. This positive mindset increases self-control resources, making these children less likely for these children to resort to aggression when faced with challenges. Thus, psychological capital and self-control serve as chain mediators in the relationship between physical exercise and aggressive behavior among rural left-behind children.

Research implication

Theoretical implications

This study examines the relationship between psychological capital, self-control, and physical exercise in relation to aggressive behavior. It reveals the mechanisms by which physical exercise affects aggressive behavior, contributing to a deeper understanding of how psychosocial factors influence children’s behavioral development. The chain mediation model, constructed from the perspectives of psychological capital and self-control, represents a theoretical innovation that broadens the research perspective on how physical exercise reduces aggressive behavior. It provides important theoretical guidance for understanding and reducing aggressive behavior in left-behind children.

Practical implications

This study draws the attention of society, schools, and communities to the mental and physical well-being of rural left-behind children. It provides a scientific basis for policy makers to formulate supportive policies and measures to promote physical exercise among left-behind children. The study encourages collective efforts by all sectors of society to create a nurturing social environment conductive to the development of left-behind children. It also assists schools and communities in designing and implementing targeted interventions to prevent and reduce aggressive behavior among left-behind children in rural areas.

Limitation

This study has several limitations that should be addressed in future research: (1) Previous research has demonstrated that left-behind children have significantly higher aggressive behaviors than non-left-behind children [8]. It is therefore more meaningful to explore the differences in the effects of physical exercise on aggressive behavior between the two samples and the role of psychological capital and self-control in this. Future research could include a richer sample to validate the results of this study; (2) The type of exercise moderates the relationship between physical exercise and aggressive behavior. Future research could examine which types of exercise are more effective in reducing aggression; (3) This study used cross-sectional data, which makes it difficult to establish causal relationships among the four variables. Additionally, some studies suggest that there are reciprocal mutual influences among these variables. Future research could use a cross-lagged method to further validate these finding; (4) This study treated self-control as a trait, but self-control can also be viewed as a state that varies with mood. There is an interaction between trait self-control and state self-control with aggressive behavior. Future research could examine the role of both types of self-control in the relationship between physical exercise and aggression.

Conclusion

Physical exercise significantly and negatively affects aggressive behavior in rural left-behind children. Physical exercise indirectly influenced the aggressive behavior of rural left-behind children through the independent and chain-mediating effects of psychological capital and self-control. This provides a theoretical basis for reducing aggressive behavior in rural left-behind children.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Abbreviations

AB:

Aggressive behavior

PE:

Physical exercise

PC:

Psychological capital

SC:

Self-control

PARS-3:

Physical Activity Rating Scale-3

PPQ:

Positive Psycap Questionnaire

DMSC-S:

Dual-Mode of Self-Control Scale

AQ:

Aggression Questionnaire

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Acknowledgements

We thank every respondent in the study for their contributions.

Funding

This work was supported by the Cultivation of a Major Project for Seed Fund for Basic Research Operating Expenses of Central Universities under Grant [CCNU23ZZ006].

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Contributions

A.X: Formal analysis, Data Curation, Writing–original draft. X.L: Conceptualization, Writing–review & editing, Supervision. G.Z: Investigation. C.L: Conceptualization, Writing–review & editing, Funding acquisition. All authors reviewed the manuscript.

Corresponding authors

Correspondence to Xiaobing Luo or Changfen Lu.

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The study was approved by the institutional review board of Central China normal University before the initiation of the project (IRB number: CCNU-IRB-202402006b). Informed consent was obtained from the participants and their guardians before the start of the program. We confirm that all the experiment is in accordance with the relevant guidelines and regulations such as the declaration of Helsinki.

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Not applicable.

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The authors declare no competing interests.

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Xu, A., Luo, X., Zhou, G. et al. Physical exercise and aggressive behavior in rural left-behind children: the mediating roles of psychological capital and self-control. BMC Psychol 13, 438 (2025). https://doiorg.publicaciones.saludcastillayleon.es/10.1186/s40359-025-02736-7

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