All in the Family: Promoting Family Function Through Physical Activity

The primary objective of this study is to test the efficacy of three family physical activity (PA) interventions on a key family functioning outcome-family cohesion-through increased PA in children and parent-child co-PA. Our study tests three intervention conditions: 1) identity (ID; promotion of a PA parenting identities + self-regulation skills + education), 2) self-regulation (SR; promotion of PA parenting self-regulation skills + education) and 3) education (ED; an education about PA control condition). It is hypothesised that (H1): The ID condition will show significantly larger changes in family cohesion compared to the two other conditions after six-months (primary end-point) and (H2): The SR condition will show significantly larger changes in family cohesion compared to the ED control condition after six-months.

There are three secondary objectives for this study. First, this study aims to assess the impact of the three interventions on the remaining family-functioning dimensions-flexibility and organisation-and on behavioural outcomes (child MVPA and parent-child co-PA) at the 6-month end-point. The ID condition is hypothesized to lead to significantly greater increases in family flexibility, family organization, child MVPA and parent-child co-PA compared to the SR and ED conditions after six months (H3), with the SR condition also expected to outperform the ED condition in these PA outcomes (H4).

Second, this study will also investigate whether group differences in child and parent PA and family functioning outcomes can be explained through a mediation model based on the Multi-Process Action Control (M-PAC) framework. It is hypothesized that changes in child MVPA and parent-child co-PA will mediate the relationship between the intervention groups and family functioning outcomes. These changes in PA behaviors are expected to be predicted by alterations in family social identity and parental PA support identity, which will, in turn, be influenced by parental attitudes, perceptions of control (reflective processes), and behavioral self-regulation (regulatory processes) regarding child PA (H5).

Third, the present study will explore the potential moderating effects of seasonal variation, child sex, dual/single-parent status, parent sex and gender, child age, intervention adherence, and the type and format of PA on the primary outcomes across the three intervention conditions. While no specific hypotheses are pre-set for these factors, it is anticipated that participation in PA may decrease during winter due to weather conditions, and single-parent families might face more barriers to parent-child co-PA, leading to lower participation levels. Additionally, the composition and frequency patterns of child MVPA may influence family functioning outcomes differently across the intervention conditions.

• Family functioning outcomes (i.e., family organisation and flexibility) [Time frame: Baseline, 6 weeks, 3 months, and 6 months]
• Children's moderate to vigorous physical activity (MVPA) [Time frame: Baseline, 6 weeks, 3 months, and 6 months]
• Parent-child intergenerational activity measured via parent self-report [Time frame: Baseline, 6 weeks, 3 months, and 6 months]
• Parental support and M-PAC Constructs [Time frame: Baseline, 6 weeks, 3 months, and 6 months]