Article European Physical Education Review 2021, Vol. 27(3) 574–594 Principals’ involvement ª The Author(s) 2020 Article reuse guidelines: in comprehensive school sagepub.com/journals-permissionsDOI: 10.1177/1356336X20976687 journals.sagepub.com/home/epe physical activity programmes: A social-ecological perspective Karie Orendorff Panayiotis Doutis Montana State University, USA University of South Carolina, USA Collin A Webster Brian Dauenhauer University of South Carolina, USA University of Northern Colorado, USA Diana Mı̂ndrilă David F Stodden University of West Georgia, USA University of South Carolina, USA Kathleen MW Cunningham University of South Carolina, USA Abstract To support school physical education, United States (US) national organizations in medicine, health, and education recommend that schools adopt comprehensive school physical activity programmes (CSPAPs). An important factor in successful CSPAP implementation is the involvement of the school principal. The purpose of this study was to examine relationships between principals’ self-reported CSPAP involvement and their social-ecological-based perceptions about CSPAPs. We analysed survey responses from a national sample of principals in the US who indicated their school had a CSPAP (n ¼ 198). Exploratory structural equation modelling supported a single-factor solution for CSPAP involvement (12 items) and three social-ecological factors, which we labelled ‘intrapersonal’ (nine items mainly focused on expected outcomes of CSPAPs), ‘interpersonal’ (five items focused on par- ents’ and teachers’ supportof the CSPAP), and ‘environmental’ (12 items focused on the support of the overall school environment, the community surrounding the school, and public policy for the CSPAP). Path analysis showed involvement factor scores are predicted by intrapersonal factor scores, which, in turn, are predicted by interpersonal and environmental factor scores. The results of this study are helpful in identifying targets for future research and practice related to CSPAP implementation and can inform efforts to prepare and support principals with respect to their CSPAP involvement. Corresponding author: Collin A Webster, Blatt Physical Education Center, 1300 Wheat Street, University of South Carolina, Columbia, SC 29208, USA. Email: websterc@mailbox.sc.edu Orendorff et al. 575 Keywords Head teacher, school leader, administrator, whole-of-school approach, child, adolescent, survey, exploratory structural equation modelling, path analysis Introduction In the United States (US), the Physical Activity (PA) Guidelines for Americans (US Department of Health and Human Services (USDHHS), 2018) recommend that children and adolescents ages 6– 17 should accumulate at least 60 minutes of mostly moderate-to-vigorous PA each day, as this can lead to health benefits such as healthy bones and muscles, improved muscular strength and endurance, reduced development of chronic disease risk factors, improved self-esteem, and reduced stress and anxiety (Physical Activity Guidelines Advisory Committee, 2018). Unfortu- nately, approximately three quarters of children and adolescents in the US are not meeting this benchmark for daily PA participation (National Physical Activity Plan Alliance, 2018). Moreover, children spend 80–93% of their waking hours in sedentary time (Turner et al., 2014) and it is estimated that the majority of school-aged youth are not meeting national content standards in physical education (Hastie, 2017). National organizations (e.g. Centers for Disease Control and Prevention (CDC), 2011; Institute of Medicine (IOM), 2013 (now named the National Academy of Medicine); Society of Health and Physical Educators (SHAPE) America, 2015) suggest that schools should be a key focus of intervention efforts when attempting to increase and promote youth PA engagement. Schools have access to nearly all youth in the US and school-based PA not only can improve students’ health but also enhance their academic performance (IOM, 2013). Furthermore, education settings can play a major role in public health initiatives related to PA, given that schools directly reach approximately 25% of the US population (National Physical Activity Plan Alliance, 2016). Comprehensive school physical activity programmes In 2008, the National Association for Sport and Physical Education (NASPE) (formerly an association of the American Alliance for Health, Physical Education, Recreation and Dance (AAHPERD), and now encompassed within SHAPE America) published a position statement (NASPE, 2008), which was updated in 2015 (SHAPE America, 2015) called ‘Comprehensive School Physical Activity Programs’ (CSPAPs). A CSPAP is described as a multicomponent approach to enhancing physical education and promoting increased PA among school commu- nities. The components of a CSPAP can include (a) physical education, (b) PA before and after school, (c) PA during school, (d) staff involvement, and (e) family and community engagement (SHAPE America, 2015). However, given limited descriptive research on CSPAPs, recent liter- ature reflects a broader conceptualization of a CSPAP, which focuses less on the total number of programme components and more on whether a school, through multiple possible approaches, provides all students with sufficient opportunities to meet the programme goals (Webster et al., 2020b, 2020c, 2020d). Implementing a CSPAP is intended to provide children and adolescents with PA support and opportunities before, during, and after school as a means to ‘[developing] physically educated students who are physically active for the nationally recommended 60-plus minutes each day and who develop the knowledge, skills and confidence to be physically active for a lifetime’ (SHAPE America, 2015: 3). 576 European Physical Education Review 27(3 ) A survey conducted by AAHPERD in 2011 found that CSPAPs existed in only 16% of elementary schools, 13% of middle schools, and 6% of high schools. In 2013, the IOM endorsed a multi- component, or ‘whole-of-school’, approach to youth PA promotion (IOM, 2013: 30) and the CDC partnered with SHAPE America to develop a step-by-step guide for implementing a CSPAP (CDC, 2013). However, based on a recent survey by the CDC (Brener et al., 2017), a mere 3% of secondary schools have implemented a CSPAP. Thus, while CSPAPs are recommended to increase students’ daily PA and support the educational goals of physical education (SHAPE America, 2015), and the CDC has adopted the CSPAP framework as the national framework for physical education and PA in the US (CDC, 2019), the apparent continued low prevalence of CSPAPs in the US underscores the need to investigate the factors that are associated with programme implementation. Principals’ involvement in CSPAPs One factor that has consistently been cited as critical in school reform efforts and in creating and maintaining an effective school is the principal (also referred to as the head teacher, headmaster/ headmistress, school director, and other titles in various contexts) and their involvement (Dow and Oakley, 1992; Fullan, 2016). As a figurehead of school leadership, the principal is a key driver in the school’s mission, vision, and culture (Bryk et al., 2010; Leithwood and Jantzi, 1999). A principal’s involvement in a school programme, for example by actively assisting in its development and taking part in its promotion, can lead to teachers feeling they are supported and showing increased commitment to the programme (Leithwood and Jantzi, 1999). The principal is the main reason programmes are or are not successful in schools; they hold the most influence for implementation of programmes and policies (Datnow and Castellano, 2001). Carson et al. (2014) proposed that support from administrators, such as the principal, is necessary to the successful implementation of a CSPAP. However, the concept of ‘support’ may not fully encompass the range of ways in which a principal might be involved with a CSPAP. According to Webster et al. (2020e: 130), ‘Staff involvement with promoting PA can be broadly conceptualized in terms of the direct and indirect actions staff members take to increase the concomitant or future amount of PA in which youth engage’. A recent scoping review (Webster et al., 2020a) identified three themes in the published recommendations for school administrators’ involvement in school- based health promotion. These themes included collaboration (e.g. using a distributive leadership style, being involved with defining health issues, identifying solutions, and monitoring progress), advocacy (e.g. knowing about and valuing health promotion, and educating policymakers about the importance of school health promotion), and support (e.g. providing resources for teachers, visiting teachers’ classrooms, and offering feedback). Yet, a descriptive research base to inform the specific actions school principals might take to be involved with a CSPAP is lacking. A social-ecological perspective of principals’ CSPAP involvement In addition to the limited research available to operationally define principals’ CSPAP involve- ment, little is known about variables that may influence principals’ involvement with CSPAPs. Van den Berg et al. (2017) found that principals perceived PA to have academic, physical, and social-emotional benefits but also perceived barriers to implementing PA that were related to time limitations, school priorities, space constraints, and financial challenges. A gap that remains in the literature, however, is research on principals’ perceptions specifically pertaining to CSPAPs. It is important to investigate these perceptions, particularly to understand how they may be related to Orendorff et al. 577 principals’ CSPAP involvement. In the present study, we adopted a social-ecological perspective to investigate principals’ perceptions of CSPAPs and how these perceptions relate to principals’ CSPAP involvement. Based on the work of Bronfenbrenner (1976, 1977), a social-ecological perspective of human behaviour considers the influence of a wide range of variables on targeted behaviours of interest. Social-ecological models are used to organize these variables into multiple levels of influence and illustrate relationships among individuals, groups, and their environments (Golden et al., 2015; McLeroy et al., 1988; Sallis et al., 2006, 2008; Stokols, 1996). Numerous examples of social- ecological models exist in theory and research specific to school-based PA promotion (e.g. Carson et al., 2014; Langille and Rodgers, 2010; Webster and Suzuki, 2014; Webster et al., 2013). In general, these models encompass five levels of influence: (a) intrapersonal, (b) interpersonal, (c) organizational, (d) community, and (e) public policy. Intrapersonal variables may include beliefs (e.g. self-efficacy in implementing an educational programme, expected outcomes of imple- menting the programme), attitudes, and other psychological attributes (e.g. motivation to imple- ment a new programme) of the individual whose behaviour is being targeted (e.g. school principal). Variables at the interpersonal level tend to focus on relationships between the individual and others with whom the individual interacts (e.g. other administrators, teachers, students, par- ents, community stakeholders). The organizational level of influence is usually comprised of variables that reflect institutional resources (e.g. school facilities, available educational materials), norms (e.g. cultural customs commonly followed by students and staff, a school honour code), practices (e.g. allocated curriculum time for different school subjects, instructional approaches used by teachers), and policies (e.g. expectations for student conduct, whether or not teachers are allowed to withhold recess as a punishment). At the community level, variables often centre on factors, such as the support of other organizations (e.g. a facility joint-use agreement between the school and a local YMCA), which surround the individual’s own organization. Public policy variables may include the presence of any local, state, or federal policies that are pertinent to the targeted behaviour (e.g. a state policy that requires schools to provide students with a certain number of minutes of PA each week). In the context of a CSPAP, a social-ecological perspective can help to identify key variables that should be the focus of interventions and professional learning directed towards influencing the PA promotion efforts of programme implementors. Previous social-ecological research in the area of school-based PA promotion has not con- ceptualized or investigated the intrapersonal, interpersonal, organizational, community, or public policy variables that may influence school principals’ CSPAP involvement. Purpose of the study Overall, although considerable research exists on the staff involvement component of the CSPAP framework, particularly in regard to classroom teachers and afterschool programme staff, there is currently an absence of research on principals’ involvement in CSPAPs (Webster et al., 2020e). The purpose of this study was to examine relationships between principals’ CSPAP involvement and their perceptions about CSPAPs from a social-ecological perspective. In accordance with social-ecological theory and research related to school PA promotion (Carson et al., 2014; Langille and Rodgers, 2010; Webster et al., 2013; Webster and Suzuki, 2014), we hypothesized that intrapersonal variables would have the strongest and most direct association with the targeted behaviour (i.e. principals’ CSPAP involvement), while variables at each subsequent level (inter- personal, organizational, community, and public policy, respectively) would have an indirect and 578 European Physical Education Review 27(3 ) increasingly weaker association. The results of this study will help to advance research focused on the role of principals in CSPAP implementation and may inform future directions in CSPAP planning and professional development for school administrators. Methods Instrumentation We developed an online survey to investigate principals’ involvement in CSPAPs. The survey encompassed a range of variables hypothesized to be associated with principals’ CSPAP invol- vement from two distinct theoretical perspectives (social ecology theory and social learning theory). The present investigation, which focuses on social-ecological variables and their relationship to principals’ CSPAP involvement, is the first study using data from the survey. The final version of the survey, specifically the parts of the survey used in the present study and as administered to the main study sample, is described in this section. The development of the survey is described in the Procedures section that follows. All phases of survey development and administration were facilitated via Survey Monkey. The survey was organized into seven sections: (a) informed consent, (b) introduction, (c) CSPAP implementation, (d) CSPAP involvement, (e) social-ecological factors, (f) professional/ context biography, and (g) participant demographics. The first page of the survey was an informed consent form. Subsequently, in the introduction section, participants were provided with an overview of the CSPAP framework and the purpose of the survey. The CSPAP implementation section of the survey listed possible CSPAP components (e.g. physical education, PA during school, PA before and after school) with examples and included a single dichotomous response question (‘yes/no’) asking participants if their school has a CSPAP. A CSPAP was conceptualized as follows, based on the recent work by Webster et al. (2020a, 2020b, 2020c): [your school provides] OPPORTUNITIES, through any combination or variety of CSPAP components – for all students at your school to: (a) receive standards-based physical education experiences designed to prepare individuals for a lifetime of participation in physical activity, and (b) meet the national guideline for school-aged youth to accumulate at least 60 minutes of mostly moderate-to-vigorous physical activity each day (including lunch time activities, and before and after school activities). A logic mechanism was built into the survey so that ‘yes’ respondents proceeded to the subsequent two sections (involvement and social-ecological factors) with items written in the past/present tense (e.g. ‘I am involved with supporting my school staff in their efforts to promote physical activity’). ‘No’ respondents proceeded to two identical sections except that items were written in the future tense (e.g. ‘I would be involved with supporting my school staff in their efforts to promote physical activity’). The final two sections on professional context/biography and participant demographics focused on the PA promotion strategies, within each CSPAP component, currently used at participants’ schools, as well as participants’ school context (e.g. geographic location, total student enrolment), educational background (e.g. highest degree earned, licensure obtained), professional experience (e.g. years serving as a principal, years serving as a teacher), age, gender, and race/ethnicity. Items focusing on PA promotion strategies within each CSPAP component were based on recommended strategies from SHAPE America (2015) and the CDC (2019). Orendorff et al. 579 In all, 80 items from the final survey were used for this study. This item count is based on having counted equivalent items for ‘yes’ and ‘no’ respondents as single items. One item was included to assess CSPAP implementation; 12 items were included to assess the dependent variable (principal involvement in a CSPAP); 52 items were included to assess social-ecological variables at five levels of influence, including intrapersonal (29 items), interpersonal (five items), organizational (nine items), community (five items), and public policy (four items); 12 items were included to assess professional context/biography; and three items were included to assess participant demographics. Procedures Phase 1: item construction, scale development, and participant instructions. To construct an initial set of items for the survey, we completed a comprehensive literature search to find published records (e.g. peer-reviewed articles, books, doctoral dissertations, public policies) in the areas of CSPAP (e.g. Carson et al., 2014; Rink et al., 2010; SHAPE America, 2015), principals’ perceptions of health-related school programming (e.g. physical education, recess, fitness, wellness) (e.g. Davis, 2012; Greaney et al., 2007; Morrison, 2006; Van den Berg et al., 2017; Weiler et al., 2003), and social-ecological theory and research (e.g. Golden et al., 2015; McLeroy et al., 1988; Sallis et al., 2008; Webster and Suzuki, 2014). We developed a six-point Likert-type response scale (see the Instrumentation section) for the items based on recommendations for scale development (Fink, 2003; Johnson and Morgan, 2016; Krosnick and Fabrigar, 1997) and the treatment of categorical variables (Finney and DiStefano, 2006). Based on recent literature, including research on physical education teachers’ perceptions related to CSPAPs (Webster et al., 2020b, 2020c) and conceptual work intended to advance CSPAP research and practice (Webster et al., 2020d), we incorporated instructions for participants along with a definition and examples of a CSPAP (see Instrumentation section). Phase 2: pilot testing. Before data collection started, we obtained approval from the first author’s university institutional review board (IRB) to conduct the study. There were two rounds of pilot testing. The purpose of the first round of pilot testing was to enhance the content validity of the survey and obtain feedback about the length, formatting, and clarity of the survey. The purpose of the second round of pilot testing was to obtain feedback about the survey from a convenience sample of principals and to conduct a preliminary assessment of the survey’s psychometric properties. For the first round, we emailed the survey to CSPAP authors (n ¼ 41), authors who have published research using social-ecological theory (n ¼ 51), and university faculty in the area of educational leadership (n ¼ 89). We identified CSPAP authors from an edited book about CSPAP research and practice (Carson and Webster, 2020). For each section of the survey, we instructed participants to rate the appropriateness of the items (completely inappropriate, mostly inap- propriate, somewhat inappropriate, mostly appropriate, and completely appropriate) and provide feedback about the content on each page. A total of 24 CSPAP authors (59% response rate) provided responses. Using their ratings and comments, 24 items were removed (15 items intended to measure intrapersonal variables, seven items intended to measure interpersonal variables, and two items intended to measure organizational variables). Additionally, several minor revisions were made: the term ‘CSPAP’ was replaced with ‘physical activity opportunities’ and ‘physical activity programming’ in two of the items on the involvement scale, negatively worded items 580 European Physical Education Review 27(3 ) (e.g. ‘A CSPAP would lead to a chaotic school environment’) were either deleted or revised as positively worded items, and items that included the term ‘parents’ were changed to read ‘parents/ guardians’. To identify authors in the area of social-ecological theory, we located published articles online (e.g. Golden et al., 2015; McLeroy et al., 1988; Sallis et al., 2008). We found email addresses for 51 authors and emailed the authors with instructions to match each of the social-ecological items on the survey to its respective level of influence (intrapersonal, interpersonal, community, orga- nizational, or public policy). We also asked the authors to provide feedback on the quality and appropriateness of specific items and/or the items in general. A total of six authors provided responses (12% response rate). Based on their feedback, items were found to match their intended social-ecological levels, so no changes were made to the survey. We compiled a list of 89 university faculty, representing 58 US institutions, who work in the area of educational leadership and policy. These individuals encompassed all levels of academic rank/seniority from assistant professor to retired professor, and many of the faculty had served as former school- and district-level administrators. For each section of the survey, participants were instructed to rate the appropriateness of the items (completely inappropriate, mostly inappropriate, somewhat inappropriate, mostly appropriate, and completely appropriate), considering the roles and responsibilities of a school principal, and provide feedback about the content on each page. A total of 16 educational leadership faculty provided responses (18% response rate), which informed several changes to the survey. Specifically, two items were removed (‘Others in my school environment notice/would notice the impact of promoting physical activity’ and ‘I have a good relationship with the teachers at my school’). Educational leadership faculty believed the princi- pals would have low efficacy in judging the first item, and felt the second item was ‘leading’ and that principals would not admit to having a bad relationship with their staff. Also, the introduction to the survey was revised to use less academic jargon. After making revisions to the survey based on the first round of pilot testing, we sent the survey to a convenience sample of principals (n ¼ 42) from elementary, middle, and high schools and asked them to complete the survey, as well as to provide general feedback. Twenty-one principals responded (16 indicated they had a CSPAP at their school) for a 50% response rate. Using the data from this second round of pilot testing, we employed Bayesian exploratory factor analysis (EFA) to individually examine each survey scale. This served as a preliminary statistical analysis to identify any additional items for potential removal from the final survey to be used with the main study sample. Previous research showed that EFA can provide accurate results with samples as small as 20 or 10 observations when the data are well conditioned (i.e. high œ, low f, high p) (de Winter et al., 2009; Preacher and MacCallum, 2002). Further, the Bayesian estimation method does not rely on a large-sample theory, and therefore can provide accurate results with small samples, such as our convenience sample of principals (Heerwegh, 2014; Muthén and Asparouhov, 2012). Items with non-significant factor loadings were only removed for subsequent data collection in the main study if the loadings were below 0.320 or if removing the items created convergence problems. In all, five items were removed based on the results of the EFA. Additionally, in accordance with respondents’ feedback about the survey, we revised the CSPAP implementation section of the survey for brevity. We also asked the respondents from the convenience sample to retake the survey one week after their survey closed, to assess test–retest reliability. A one-week time limit was provided for them to retake the survey. There were 13 respondents (11 indicated they had a CSPAP at their school) for a Orendorff et al. 581 62% response rate. Thirteen items were removed from the survey due to having a Kappa value lower than 0.2. Phase 3: main study. The administration of our survey to the main study sample occurred in the spring of 2019. Using information available on a federal website listing all public schools in the US, we applied stratified random sampling to select 60 schools (20 elementary, 20 middle/junior high, and 20 high) from each state (total of 3000 schools). Next, we visited the schools’ websites to find email addresses (where available) for principals and compiled a list of 2941 email addresses. With these addresses, we sent a blanket email briefly describing the study and inviting recipients to complete the survey. The link to the survey was included in the email. Respondents for the main study were 291 principals. For the purposes of this study, we only analysed data from participants who indicated their school has a CSPAP (n ¼ 198). Data analysis for the main study Before conducting statistical analyses, we screened survey variables to examine the prevalence of ‘don’t know’ responses as well as the distribution of missing values. Missing responses represented approximately 1.9% of the data. The ‘don’t know’ response option was included to prevent item non-response, forced responses, or guessing, but was not included in statistical analysis because it indicates insufficient information to provide an informed opinion. To avoid losing data, we recorded ‘don’t know’ responses as missing values. Cases with more than 15% invalid responses were listwise deleted. The resulting proportion of values that were missing or recoded as missing ranged between 0.0% and 2.7% per item and represented approximately 2.3% of the data. Little’s Missing Completely at Random (MCAR) test showed that these values were distributed com- pletely at random (2(1825) ¼ 1800.867, p ¼ .652); therefore, we imputed them using the expectation-maximization algorithm. The resulting sample included 198 respondents. We com- puted the mean and standard deviation for all survey items to examine the distribution of survey responses and identify the items with the highest ratings. Exploratory structural equation modelling. Although social-ecological research exists in the area of school PA promotion (e.g. Langille and Rodgers, 2010; Webster and Suzuki, 2014; Webster et al., 2013), researchers in previous studies have not examined principals’ CSPAP involvement from a social-ecological perspective. Since we developed the survey for our research and had not pre- viously examined the factor structure of the final survey, the initial step of our investigation with the main study sample was to identify the latent variables underlying the data. We used exploratory structural equation modelling (ESEM) for this purpose because it allows the estimation of an exploratory factor model with rotations and estimation of cross-loadings, thus yielding a more realistic representation of the data and reducing estimation bias, while also allowing the compu- tation of goodness-of-fit indices (Marsh et al., 2014; Morin and Maiano, 2011; Morin et al., 2013). A group of 51 observed indicators was used to estimate latent variables. Our study met the recommendation of 3:1–6:1 observations per variable (Cattell, 1978; de Winter et al., 2009). Studies have shown that sample sizes as low as 50 or even 20 may be suitable for factor analysis when the factor loadings are high, the number of factors is low, and the number of observed variables is high (de Winter et al., 2009; MacCallum et al., 2001; Marsh et al., 1998). We used the mean and variance adjusted weighted least squares (WLSMV) estimation method and geomin rotation with the Mplus 8.2 software. This estimation method is recommended for small sample 582 European Physical Education Review 27(3 ) sizes and data that are ordinal or non-normally distributed (Finney and DiStefano, 2006). The geomin rotation is an oblique procedure; oblique rotation methods are employed when factors are expected to correlate (Browne, 2001). The optimal number of factors was determined after examining the scree plot, the number of eigenvalues larger than one, the interpretability of the factor structure, and goodness-of-fit indices. The indices used to assess model fit were: (a) 2 and corresponding p-value, (b) 2/df, (c) the root mean square error of approximation (RMSEA) and 90% confidence interval (CI), (d) the com- parative fit index (CFI), (e) the Tucker–Lewis index (TLI), and (f) the weighted root mean residual (WRMR). We sequentially removed cross-loading items and items with loadings lower than .320 (Costello and Osborne, 2005). When an optimal solution was identified, we estimated the internal consistency of each factor using the Cronbach’s alpha coefficient. Path analysis. Following the identification of the factors underlying the data, we computed factor scores, which show the location of each individual on the identified factors (DiStefano et al., 2009). Relationships between factor scores were then examined using path analysis. Relationships in the path model were based on theoretical considerations and results from previous studies (Langille and Rodgers, 2010; Webster and Suzuki, 2014; Webster et al., 2013), as well as on specified scores on social-ecological factors as predictors of factor scores measuring principals’ CSPAP involvement. The indices used to assess model fit were: (a) 2 and corresponding p-value; (b) 2/df; (c) the RMSEA and 90% CI; (d) the CFI; (e) the TLI; and (f) the standardized root mean square residual (SRMR). Results of the main study Participant demographic and professional context/biographical information The demographic and professional context/biographical information for participants in the main study is presented in Table 1. Table 1 displays participants’ self-reported age band, gender identification, race, education level, years of experience working as a principal, and grade level, as well as participants’ self-reported school context information including total student enrolment, number of students participating in free or reduced cost school lunch (a proxy for socioeconomic status), school setting, and the region of the US where they are located. Overall, the percentages in each of these categories were similar for principals who indicated their school has a CSPAP compared to principals who indicated their school does not have a CSPAP. Table 2 displays the PA promotion strategies, by CSPAP component, that the principals identified as being used at their schools. These data clearly demonstrate that, based on principals’ self-reports, schools with a CSPAP are using more PA promotion strategies across all CSPAP components than schools without a CSPAP. Factor structure Initial exploratory analyses yielded six eigenvalues larger than one, while the scree plot indicated solutions with 3–5 factors as optimal. We estimated models with 3–5 factors. Although the five- factor solution had the best fit to the data, the fifth factor included only three items and all of them were cross-loading. Based on goodness-of-fit indices (2 (557) ¼ 123.452, p < .001, 2/df ¼ 0.221, RMSEA (90% CI) ¼ 0.079 (0.073–0.085), CFI ¼ 0.947, TLI ¼ 0.933, WRMR ¼ 0.950) and the interpretability of the factors, we considered the four-factor solution optimal (Table 3). The 2 test Orendorff et al. 583 Table 1. Participants’ self-reported demographics and school contexts for the main study. Participants who Participants who responded ‘no’ to their responded ‘yes’ to their school having a CSPAP school having a CSPAP (n ¼ 36) (n ¼ 147) Age band 31–35 8% 1% 36–40 25% 12% 41–45 22% 20% 46–50 11% 23% 51–55 11% 14% 56–60 17% 18% 60þ 6% 12% Gender identification Male 56% 58% Female 44% 42% Race Asian 0% 2% African American or Black 8% 12% Hispanic or Latino 6% 3% White 86% 82% No response 0% 1% Education Masters 30% 25% Masters þ30 42% 44% Ed.D. 17% 24% Ph.D. 11% 7% Years of experience 0–5 31% 28% working as a principal 6–10 31% 21% 11–15 8% 28% 16–20 11% 11% Over 20 19% 12% Grade level Elementary 19% 32% Jr. high / middle school 42% 29% High school 19% 26% Grades K–8 6% 5% Grades 7–12 14% 8% Total student enrolment  400 36% 27% 401–600 31% 27% 601–800 19% 24% 801–1000 8% 8% 1001–1200 3% 4%  1201 3% 10% Percentage of students 0–20% 3% 16% participating in free or 20–40% 14% 18% reduced cost lunch 40–60% 36% 24% 60–80% 14% 15% 80–100% 33% 27% School setting Metro urban 28% 17% Suburban 25% 47% (continued) 584 European Physical Education Review 27(3 ) Table 1. (continued) Participants who Participants who responded ‘no’ to their responded ‘yes’ to their school having a CSPAP school having a CSPAP (n ¼ 36) (n ¼ 147) Rural 47% 36% Region of US where Far West 3% 10% employed Great Lakes 3% 12% Midsouth 17% 19% Midwest 13% 11% Mountain West 25% 11% New England 3% 9% Northeast 6% 6% Northwest 7% 3% South Central 6% 6% Southeast 17% 13% Note: the sample sizes represented in this table are smaller than the total number of respondents because not all respondents provided demographic/school context information. CSPAP: comprehensive school physical activity programme. is an overall measure of model fit; a non-significant 2 statistic indicates good fit (Barrett, 2007); however, this statistic is sensitive to sample size and model size. Therefore, the 2/df is often used, where values lower than 3 show good model fit (Finney and DiStefano, 2006). For RMSEA, values larger than .10 show poor model fit, values between .08 and .10 indicate acceptable fit, values between .05 and .08 indicate good fit, and values lower than .05 indicate excellent fit (Hu and Bentler, 1999). CFI and TLI values above .95 indicate excellent model fit, while values larger than .90 indicate good fit. WRMR values lower than 1 indicate very good fit (DiStefano et al., 2018; Yu and Muthén, 2002). All items in the four-factor solution had statistically significant loadings, above the cutoff of .320 (Costello and Osborne, 2005). Items with lower loadings and items that were cross-loading were sequentially removed; the final solution retained 39 items. Table 4 lists the items included in each factor along with their means, standard deviations, factor loadings, standard errors, corresponding t statistics and p values. Descriptive analyses showed that most respondents provided high ratings on the majority of the survey items. The item with the highest average response was ‘A CSPAP enhances students’ physical development’ (M ¼ 5.31, SD ¼ .755), followed by the item ‘A CSPAP promotes students’ social development’ (M ¼ 5.24, SD ¼ .748). The item with the lowest average was ‘I am involved with setting performance standards for my school’s CSPAP’ (M ¼ 3.47, SD ¼ 1.316). The strongest factor was labelled F1 (‘Involvement’) and included 13 items referring to CSPAP involvement. Item loadings ranged between .463 and .851, and the item with the highest loading was ‘I am involved with CSPAP planning at my school’. Cronbach’s alpha index of internal consistency for this factor was .900. The second factor, F2 (‘Intrapersonal’), included nine items mostly referring to beliefs about the outcomes of a CSPAP. Item loadings ranged between .578 and .914 and the item with the highest loading was ‘A CSPAP promotes a whole-child learning approach’. Cronbach’s alpha index of internal consistency for this factor was .898. The third factor, F3 (‘Interpersonal’), included five items, which referred to personnel within the school community and their support of a CSPAP. Orendorff et al. 585 Table 2. Physical activity promotion strategies by CSPAP component as perceived by respondents in the main study. Participants who Participants who responded ‘no’ to responded ‘yes’ to their school having their school having a CSPAP (n ¼ 37) a CSPAP (n ¼ 148) Physical education Standards-based instruction 49% 78% Assessment of student learning 30% 55% Opportunities to learn 30% 50% Opportunities for moderate-to-vigorous 38% 60% physical activity Meaningful content 43% 42% None 24% 4% Physical activity Classroom-based physical activity 51% 74% during school Recess 43% 55% Physical activity assemblies 3% 23% Physical activity drop-in opportunities 24% 35% (e.g. keeping the gym open during lunch) None 19% 7% Don’t know 3% 3% Physical activity Active transportation programmes/options 19% 20% before/after Intramurals 16% 38% school Interscholastic sports 57% 49% Physical activity clubs 30% 52% None 24% 11% Don’t know 0% 3% Staff involvement Staff wellness programming (e.g. fitness 46% 62% programmes/events for teachers, health screening for teachers) Staff training for physical activity promotion 5% 18% Administrators involved in promoting physical 19% 36% activity Classroom teachers involved in promoting 24% 57% physical activity None 32% 14% Don’t know 3% 3% Family and Facility joint-use agreements with outside 19% 43% community organizations engagement Physical activity programmes/events for families 8% 27% Parents/guardians involved in physical activity 8% 18% promotion Community members/organizations 8% 37% (e.g. universities, YMCAs, church groups) involved in physical activity promotion Active homework for students 3% 7% None 57% 21% Don’t know 8% 9% Note: the sample sizes represented in this table are smaller than the total number of respondents because not all respondents provided physical activity promotion strategies used at their school. Percentages for each component do not add up to 100% because participants were asked to select all applicable response options. CSPAP: comprehensive school physical activity programme. 586 European Physical Education Review 27(3 ) Table 3. Goodness-of-fit indices for estimated models. Fit index Three-factor model Four-factor model Five-factor model 2 1806 123.452 995.142 df 592 557 523 p-value 0.000 0.000 0.000 2 /df 3.051 0.221 1.903 RMSEA (90% CI) 0.102 (0.096–0.107) 0.079 (0.073–0.085) 0.068 (0.061–0.074) CFI 0.906 0.947 0.963 TLI 0.888 0.933 0.951 WRMR 1.342 0.950 0.772 RMSEA: root mean square error of approximation; CFI: comparative fit index; TLI: Tucker–Lewis index; WRMR: weighted root mean residual. Loadings on this factor ranged between .513 and .869 and the item with the highest loading was ‘Parents/guardians at my school are interested and willing to help our school toward our CSPAP goals’. The internal consistency of this factor was alpha ¼ .842. The fourth factor, F4 (‘Envi- ronmental’), included 12 items referring to organizational, community, and public policy variables that may facilitate CSPAP implementation. Loadings on this factor ranged between .322 and .862, and the item with the highest loading was ‘Policies in my school support physical activity’. The internal consistency of this factor was alpha ¼ .840. As indicated in Table 5, all factor covariances were statistically significant. The strongest relationships were F2–F1 and F2–F4, whereas the weakest relationships were F3–F1 and F4–F1. Path model The estimated path model specified: (a) F4 factor scores as predictors of F3 factor scores; (b) F3 factors scores as predictors of F2 factor scores; and (c) F2 factor scores as predictors of F1 factor scores (Figure 1). This model had an overall good fit to the data (2 (3) ¼ 7.031, p ¼ .071, 2/df ¼ 2.344, RMSEA (90% CI) ¼ 0.082 (0.000–0.164), CFI ¼ 0.982, TLI ¼ 0,964, SRMR ¼ 0.040) and all path coefficients were statistically significant. The strongest relationship in the model was F3–>F2 (estimate ¼ 0.610, S.E. ¼ 0.045, estimate/S.E. ¼ 13.693, p < .001), followed by F2–>F1 (estimate ¼ 0.467, S.E. ¼ 0.056, estimate/S.E. ¼ 8.392, p < .001), and F4–>F3 (estimate ¼ 0.402, S.E. ¼ 0.031, estimate/S.E. ¼ 12.894, p < .001). The indirect effect of F3 and F4 factor scores on F1 factor scores were, therefore, .285 and .114, respectively. Discussion Principals are a key part of the administrative support that is viewed as essential to the successful implementation of CSPAPs (Carson et al., 2014). Using a social-ecological framework, this study’s purpose was to examine relationships between principals’ self-reported CSPAP involve- ment and their perceptions about CSPAPs. As this was the first study to investigate these variables, a discussion of the descriptive data from the survey and the psychometric properties of our measures is warranted before addressing the main results. Orendorff et al. 587 Table 4. Descriptive statistics and factor loadings. Estimate/ Two-tailed Item M SD Estimate S.E. S.E. p-value F1 (Involvement) I am involved with CSPAP planning at my school 4.59 1.215 0.851 0.034 24.744 0.000 I am involved with evaluating my school’s CSPAP 4.60 1.208 0.751 0.043 17.279 0.000 I am involved with providing CSPAP professional 3.86 1.431 0.733 0.048 15.311 0.000 development opportunities at my school I am involved with establishing physical activity 5.00 1.013 0.707 0.043 16.598 0.000 opportunities at my school I am involved with setting performance standards 3.47 1.316 0.705 0.049 14.453 0.000 for my school’s CSPAP I am involved with allocating resources for our 5.04 1.059 0.703 0.042 16.660 0.000 school’s CSPAP I am involved with serving on my school’s CSPAP 3.83 1.581 0.645 0.050 12.846 0.000 committee or other related (e.g. school wellness) board/task force I am involved with building/maintaining partnerships 4.12 1.312 0.619 0.048 12.958 0.000 with community constituents to implement/ sustain our school’s CSPAP I am involved with organizing physical activity 4.39 1.160 0.609 0.052 11.778 0.000 opportunities at my school I am involved with staying up-to-date on best 4.03 1.160 0.602 0.057 10.499 0.000 practices for school physical activity programming I am involved with advocating for our school’s CSPAP 4.76 1.086 0.556 0.044 12.547 0.000 I am involved with being a physically active role 4.56 1.160 0.463 0.054 8.511 0.000 model for others in my school F2 (Intrapersonal) A CSPAP promotes a whole-child learning approach 5.23 .772 0.914 0.021 47.608 0.000 A CSPAP facilitates student learning 5.21 .778 0.912 0.019 52.276 0.000 A CSPAP enhances students’ physical development 5.31 .755 0.874 0.028 31.184 0.000 A CSPAP promotes students’ social development 5.24 .748 0.863 0.039 21.967 0.000 A CSPAP is the ideal programme for our students to 5.21 .769 0.820 0.040 20.636 0.000 pursue a healthy lifestyle A CSPAP improves cognitive performance 5.06 .707 0.815 0.057 14.390 0.000 A CSPAP fosters students’ attention to academics 5.02 .878 0.803 0.037 21.470 0.000 A CSPAP promotes increased school attendance 4.64 .928 0.610 0.064 9.605 0.000 A CSPAP helps our students pursue physically active 5.14 .724 0.578 0.051 11.391 0.000 lifestyles F3 (Interpersonal) Parents/guardians at my school are interested in and 4.08 1.094 0.869 0.032 26.803 0.000 willing to help our school towards our CSPAP goals Classroom teachers at my school are able to 4.32 1.111 0.789 0.032 25.032 0.000 integrate physical activity into academic instruction/learning The majority of teachers at my school are capable of 4.36 1.002 0.711 0.037 19.361 0.000 contributing to developing and implementing a CSPAP (continued) 588 European Physical Education Review 27(3 ) Table 4. (continued) Estimate/ Two-tailed Item M SD Estimate S.E. S.E. p-value Parents/guardians are engaged in helping our school 3.82 1.137 0.686 0.038 18.133 0.000 work towards our CSPAP goals Parents/guardians at my school support our CSPAP 4.71 .863 0.513 0.043 11.876 0.000 F4 (Environmental) Policies in my school support physical activity 5.14 .658 0.862 0.034 25.206 0.000 Policies in my state support school physical activity 5.01 .740 0.843 0.039 21.651 0.000 My school has sufficient funds to support a CSPAP 4.31 1.109 0.747 0.049 15.335 0.000 Adequate CSPAP resources are available for my 4.42 .946 0.706 0.043 16.542 0.000 school faculty/staff Policies in my school support the promotion of 4.56 .974 0.704 0.043 16.297 0.000 students’ physical activity during school hours every school day The facilities at my school are adequate to 4.60 1.149 0.621 0.051 12.074 0.000 implement a CSPAP Our school schedule can accommodate a CSPAP 4.83 .962 0.621 0.047 13.199 0.000 Our district superintendent supports CSPAPs 4.68 .943 0.569 0.053 10.763 0.000 Sufficient professional development for CSPAP is 3.88 1.177 0.510 0.054 9.531 0.000 available for my school staff There are safe routes for active transportation (e.g. 4.08 1.349 0.465 0.061 7.646 0.000 walking, biking) to/from our school Our school’s vision/mission includes the promotion 4.07 1.190 0.324 0.057 5.734 0.000 of physical activity Policies at my school support the promotion of faculty/ 4.56 .974 0.322 0.057 5.649 0.000 staff wellness (e.g. health, fitness, physical activity) CSPAP: comprehensive school physical activity programme. Table 5. Factor covariances. Estimate S.E. Est./S.E. Two-tailed p-value F2–F1 0.491 0.049 10.014 0.000 F2–F4 0.418 0.048 8.633 0.000 F3–F2 0.376 0.048 7.821 0.000 F3–F4 0.313 0.051 6.110 0.000 F4–F1 0.245 0.058 4.232 0.000 F3–F1 0.232 0.054 4.317 0.000 Overall, principals indicated robust agreement concerning the benefits of a CSPAP for students, but they expressed less agreement about certain aspects of their involvement in CSPAPs. Based on these results, we suggest that while principals understand and appreciate the important contribu- tions of a CSPAP to school goals, they may feel their ‘boots on the ground’ involvement with CSPAPs is beyond their call of duty. Since principals’ active involvement in the development and Orendorff et al. 589 Figure 1. Path model illustrating factors associated with principals’ involvement in comprehensive school physical activity programmes (CSPAPs) from a social-ecological perspective. Factor 1 (‘Involvement’) is directly predicted by Factor 2 (‘Intrapersonal’ level of influence), while Factor 2 is directly predicted by Factor 3 (‘Interpersonal’ level of influence) and Factor 3 is directly predicted by Factor 4 (‘Environmental’ level of influence). promotion of school programmes is critical to whether teachers feel they are supported for, and whether teachers are committed to, such programmes (Leithwood and Jantzi, 1999), initiatives to prepare principals for CSPAP implementation should emphasize the importance of their setting performance standards for the programme, serving on a CSPAP committee, and providing CSPAP- related professional development. Principals also agreed less overall that parents/guardians are interested or engaged in supporting CSPAPs. Multicomponent interventions to increase youth PA through school environments have been more effective when they include a focus on family and/or community engagement (Russ et al., 2015). Therefore, strategies to increase family engagement in CSPAPs should be another key focus of principal training. Since we developed new measures to assess principals’ CSPAP involvement and perceptions, we took several steps to increase the rigour of our measures, including an extensive literature search, two rounds of pilot testing, and psychometric analysis. ESEM with data from the main study sample indicated that the most robust and parsimonious model was a four-factor solution containing a total of 38 items. This solution supports a single factor for principals’ CSPAP involvement and three social-ecological factors. The items comprising the involvement factor closely reflect the broad themes identified in published recommendations for administrators’ involvement in school-based health promotion, which include collaboration, advocacy, and sup- port (Webster et al., 2020a). This suggests that many of the ways in which principals become involved with CSPAPs may generalize to conceptualizations of school administrators’ involve- ment in other school-based health initiatives, although additional research is needed to further explore this proposition. The three social-ecological factors each represent distinct levels of influence in relation to such involvement, specifically intrapersonal, interpersonal, and ‘environmental’, which encompasses items focusing on organizational, community, and public policy variables. While proposed social- 590 European Physical Education Review 27(3 ) ecological models often include five levels, it is not uncommon for researchers to collapse levels into groupings that are similar to the factors retained in the present study. Fisher et al. (2018) examined the relationship between the personal, social, and environmental factors regarding PA in community-dwelling older adults, whereas Wilk and colleagues (2018) researched the PA levels of grade 5 children by focusing on individual, interpersonal, and environmental levels of influence. Other examples include studies in which individual, social, and environmental factors were used to investigate young women’s participation in PA at transitional life stages (Craike et al., 2009) and PA participation of adolescents in Spain (Devı́s-Devı́s et al., 2015). Regarding the main focus of our study, we found significant associations between principals’ CSPAP involvement and all social-ecological factors (intrapersonal, interpersonal, and environ- mental) assessed via the survey. Therefore, from a social-ecological perspective, variables across all levels of influence appear to be important in the extent to which principals are involved with CSPAPs. Furthermore, the strength of the relationships between factors and the results of the path analysis support our hypothesis that intrapersonal variables have the strongest and most direct association with principals’ CSPAP involvement, while factors at each subsequent level – inter- personal and environmental (i.e. organizational, community, and public policy, respectively) – have an indirect and increasingly weaker association. These results are consistent with those reported in previous studies of school-based PA promotion that have used a social-ecological perspective (Langille and Rodgers, 2010; Webster and Suzuki, 2014; Webster et al., 2013). For instance, Webster et al. (2013) found that intrapersonal factors (i.e. domain-specific innovativeness and perceived attributes of PA promotion) directly predicted elementary classroom teachers’ self- reported PA promotion in the classroom setting, and that the organizational level of influence (i.e. perceived school support for PA promotion) and the public policy level of influence (i.e. awareness of a state PA policy for elementary schools) were indirect predictors. Given the extant research and the results of the present investigation, we suggest that initiatives (e.g. professional development, interventions) focused on supporting school-based PA promotion should include strategies that target all levels of influence, but special attention should be given to the intraindividual level of influence. To increase principals’ CSPAP involvement, it is important to ensure principals recognize the many positive outcomes that a CSPAP can help to facilitate, such as increased PA before and after school, decreased off-task behaviours, and increased academic performance (Carson and Webster, 2020). To the authors’ knowledge, this is the first study to examine principals’ CSPAP involvement. Notable strengths of the study are its theoretical grounding within a social-ecological perspective, systematic development of appropriate survey measures with sound psychometric properties, and use of a stratified random national sample. However, this study is limited by the low response rate to the survey, potential response bias, and reliance solely on principals’ perceptions. Future survey studies of principals’ CSPAP involvement should aim to recruit proportionately representative (e.g. by state) samples and use incentives to increase the response rate. It is also worth exploring whether there are times during the year that principals may be more inclined to participate in a survey. For this study, data from the main study sample were collected in the mid-to-late spring, which coincides with end-of-year testing for many schools and may be a more hectic time for principals than the beginning or middle parts of the school year. Finally, examining others’ (e.g. teachers, parents) perceptions of principals’ CSPAP involvement and conducting studies that use different methods (e.g. observation) and designs (e.g. qualitative) will allow for deeper analysis of CSPAP implementation and help to build upon the results of the present study. Orendorff et al. 591 Declaration of conflicting interests The authors have no conflicts of interest to declare. Funding The authors received no financial support for the research, authorship, and/or publication of this article. ORCID iD Collin A Webster https://orcid.org/0000-0003-1680-9149 References American Alliance for Health, Physical Education, Recreation and Dance (2011) Comprehensive School Physical Activity Program (CSPAP) survey report. Report, Reston, VA, Spring. Barrett P (2007) Structural equation modeling: Adjudging model fit. Personality and Individual Differences 42(5): 815–824. Brener ND, Demissie Z, McManus T, et al. (2017) School health profiles 2016: Characteristics of health programs among secondary schools. Report, Centers for Disease Control and Prevention. Bronfenbrenner U (1976) The experimental ecology of education. Educational Researcher 5(9): 5–15. Bronfenbrenner U (1977) Toward an experimental ecology of human development. American Psychologist 32(7): 513–531. Browne MW (2001) An overview of analytic rotation in exploratory factor analysis. Multivariate Behavioral Research 36(1): 111–150. Bryk AS, Sebring PB, Allensworth E, et al. (2010) Organizing Schools for Improvement: Lessons from Chicago. Chicago, IL: University of Chicago Press. Carson RL and Webster CA (2020) Comprehensive school physical activity programs: Putting research into evidence-based practice. Champaign, IL: Human Kinetics. Carson RL, Castelli DM, Beighle A, et al. (2014) School-based physical activity promotion: A conceptual framework for research and practice. Childhood Obesity 10(2): 100–106. Carson RL and Webster CA (eds) (2020) Comprehensive School Physical Activity Programs: Putting Evidence-Based Research into Practice. Champaign, IL: Human Kinetics. Cattell RB (1978) The Scientific Use of Factor Analysis in Behavioral and Life Sciences. New York: Plenum. Centers for Disease Control and Prevention (2011) School health guidelines to promote healthy eating and physical activity. MMWR. Recommendations and reports: Morbidity and mortality weekly report. Rec- ommendations and reports 60(RR-5): 1. Centers for Disease Control and Prevention (2013) Comprehensive school physical activity programs: A guide for schools. Atlanta, GA: US Department of Health and Human Services. Centers for Disease Control and Prevention (2019) Increasing Physical Education and Physical Activity: A Framework for Schools. Centers for Disease Control and Prevention, US Department of Health and Human Services, Atlanta, GA. Costello AB and Osborne JW (2005) Best practices in exploratory factor analysis: Four recommendations for getting the most from your analysis. Practical Assessment, Research & Evaluation 10(7): 1–9. Craike MJ, Symons C and Zimmermann JAM (2009) Why do young women drop out of sport and physical activity? A social ecological approach. Annals of Leisure Research 12(2): 148–172. Datnow A and Castellano ME (2001) Managing and guiding school reform: Leadership in success for all schools. Educational Administration Quarterly 37(2): 219–249. Davis M (2012) Principals’ perceptions of factors associated with the implementation of school wellness policies. Doctoral Dissertation, Mississippi State University, Starkville, MS. Devı́s-Devı́s J, Beltrán-Carrillo VJ and Peiró-Velert C (2015) Exploring socio-ecological factors influencing active and inactive Spanish students in years 12 and 13. Sport, Education and Society 20(3): 361–380. 592 European Physical Education Review 27(3 ) De Winter JD, Dodou D and Wieringa PA (2009) Exploratory factor analysis with small sample sizes. Multivariate Behavioral Research 44(2): 147–181. DiStefano C, Liu J, Jiang N, et al. (2018) Examination of the weighted root mean square residual: Evidence for trustworthiness? Structural Equation Modeling: A Multidisciplinary Journal 25(3): 453–466. DiStefano C, Zhu M and Mı̂ndrilă D (2009) Understanding and using factor scores: Considerations for the applied researcher. Practical Assessment, Research, and Evaluation 14(1): 20. Available at: https://doi. org/10.7275/da8t-4g52. Dow II and Oakley WF (1992) School effectiveness and leadership. Alberta Journal of Educational Research 38(1): 33–47. Fink A (2003) The Survey Handbook. London: SAGE. Finney SJ and DiStefano C (2006) Non-normal and categorical data in structural equation modeling. Struc- tural Equation Modeling: A Second Course 10(6): 269–314. Fisher KL, Harrison EL, Bruner BG, et al. (2018) Predictors of physical activity levels in community- dwelling older adults: A multivariate approach based on a socio-ecological framework. Journal of Aging and Physical Activity 26(1): 114–120. Fullan M (2016) The New Meaning of Educational Change. 5th ed. New York, NY: Teachers College Press. Golden SD, McLeroy KR, Green LW, et al. (2015) Upending the social ecological model to guide health promotion efforts toward policy and environmental change. Health Education & Behavior 42(Suppl 1): 8S–14S. Greaney M, Hardwick CK, Mezgebu S, et al. (2007) Assessing the feasibility of a multi-program school-based intervention to promote physical activity and healthful eating in middle schools prior to wide-scale implementation. American Journal of Health Education 38(5): 250–257. Hastie PA (2017) Revisiting the national physical education content standards: What do we really know about our achievement of the physically educated/literate person? Journal of Teaching in Physical Education 36(1): 3–19. Heerwegh D (2014) Small Sample Bayesian Factor Analysis. Pharmaceutical Users’ Software Exchange annual conference. Available at: www.Lexjansen.Com/phuse/2014/sp/SP03.pdf (accessed 9 March 2020). Hu LT and Bentler PM (1999) Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling 6(1): 1–55. Institute of Medicine (2013) Educating the student body: Taking physical activity and physical education to school. Report. Washington, DC: The National Academies Press. Johnson RL and Morgan GB (2016) Survey Scales: A Guide to Development, Analysis, and Reporting. New York, NY: The Guilford Press. Krosnick JA and Fabrigar LR (1997) Designing rating scales for effective measurement in surveys. In: Lyberg L, Biemer P, Collins M, et al. (eds) Survey Measurement and Process Quality. New York: John Wiley, 141–164. Langille JLD and Rodgers WM (2010) Exploring the influence of a social ecological model on school-based physical activity. Health Education & Behavior 37(6): 879–894. Leithwood K and Jantzi D (1999) Transformational school leadership effects: A replication. School Effec- tiveness and School Improvement 10(4): 451–479. MacCallum RC, Widaman KF, Preacher KJ, et al. (2001) Sample size in factor analysis: The role of model error. Multivariate Behavioral Research 36(4): 611–637. McLeroy KR, Bibeau D, Steckler A, et al. (1988) An ecological perspective on health promotion programs. Health Education Quarterly 15(4): 351–377. Marsh HW, Hau KT, Balla JR, et al. (1998) Is more ever too much? The number of indicators per factor in confirmatory factor analysis. Multivariate Behavioral Research 33(2): 181–220. Marsh HW, Morin AJ, Parker PD, et al. (2014) Exploratory structural equation modeling: An integration of the best features of exploratory and confirmatory factor analysis. Annual Review of Clinical Psychology 10(1): 85–110. Orendorff et al. 593 Morin AJ and Maiano C (2011) Cross-validation of the short form of the physical self-inventory (PSI-S) using exploratory structural equation modeling (ESEM). Psychology of Sport and Exercise 12(5): 540–554. Morin AJS, Marsh HW and Nagengast B (2013) Chapter 10. Exploratory structural equation modeling. In: Hancock GR and Mueller RO (eds) Structural Equation Modeling: A Second Course (2nd ed.). Charlotte, NC: Information Age Publishing, Inc, 395–436. Morrison LE (2006) Principals’ perceptions regarding recess in Georgia elementary schools. Doctoral dissertation, Georgia Southern University, Statesboro, GA. Muthén B and Asparouhov T (2012) Bayesian SEM: A more flexible representation of substantive theory. Psychological Methods 17: 313–335. National Association for Sport and Physical Education (2008) Comprehensive School Physical Activity Programs [position statement]. Available at: https://files.eric.ed.gov/fulltext/ED541610.pdf (accessed 9 March 2020). National Physical Activity Plan Alliance (2016) U.S. National Physical Activity Plan. Available at: https:// physicalactivityplan.org/docs/2016NPAP_Finalforwebsite.pdf (accessed 9 March 2020). National Physical Activity Plan Alliance (2018) The 2018 United States report card on physical activity for children and youth. Report. Washington, DC: National Physical Activity Plan Alliance. Physical Activity Guidelines Advisory Committee (2018) 2018 Physical Activity Guidelines Advisory Com- mittee scientific report. Washington, DC: US Department of Health and Human Services. Preacher KJ and MacCallum RC (2002) Exploratory factor analysis in behavior genetics research: Factor recovery with small sample sizes. Behavior Genetics 32(2): 153–161. Rink J, Hall TJ and Williams LH (2010) Schoolwide Physical Activity: A Comprehensive Guide to Designing and Conducting Programs. Champaign, IL: Human Kinetics. Russ LB, Webster CA, Beets MW, et al. (2015) Systematic review and meta-analysis of multicomponent interventions through schools to increase physical activity. Journal of Physical Activity & Health 12(10): 1436–1446. Sallis JF, Cervero RB, Ascher W, et al. (2006) An ecological approach to creating active living communities. Annual Review of Public Health 27(1): 297–322. Sallis JF, Owen N and Fisher EB (2008) Ecological models of health behavior. In: Glanz K, Rimer BK and Viswanath K (eds), Health Behavior and Health Education: Theory, Research, and Practice. San Fran- cisco, CA: Jossey-Bass, 465–485. Society of Health and Physical Educators (SHAPE) America (2015) Comprehensive school physical activity programs: Helping all students log 60 minutes of physical activity each day [Position statement]. Available at: www.shapeamerica.org/uploads/pdfs/2018/advocacy/position-statements/CSPAP-final.pdf (accessed 9 March 2020). Stokols D (1996) Translating social ecological theory into guidelines for community health promotion. American Journal of Health Promotion 10(4): 282–298. Turner L, Johnson TG, Slater SJ, et al. (2014) Physical activity practices in elementary schools and associa- tions with physical education staffing and training. Research Quarterly for Exercise and Sport 85(4): 488–501. US Department of Health and Human Services (2018) Physical activity guidelines for Americans (2nd ed.). Report. Washington, DC: US Department of Health and Human Services. Van den Berg V, Salimi R, de Groot RH, et al. (2017) “It’s a battle . . .You want to do it, but how will you get it done?”: Teachers’ and principals’ perceptions of implementing additional physical activity in school for academic performance. International Journal of Environmental Research and Public Health 14(10): 1160. Available at: https://doi.org/10.3390/ijerph14101160. Webster CA and Suzuki N (2014) Land of the rising pulse: A social ecological perspective of physical activity opportunities for schoolchildren in Japan. Journal of Teaching in Physical Education 33(3): 304–325. 594 European Physical Education Review 27(3 ) Webster CA, Caputi P, Perreault M, et al. (2013) Elementary classroom teachers’ adoption of physical activity promotion in the context of a statewide policy: An innovation diffusion and socio-ecologic perspective. Journal of Teaching in Physical Education 32(4): 419–440. Webster CA, Glascoe G, Moore C, et al. (2020a) Recommendations for administrators’ involvement in school-based health promotion: A scoping review. International Journal of Environmental Research and Public Health 17(17): 6249. Available at: https://doi.org/10.3390/ijerph17176249 Webster CA, Mı̂ndrilă D, Moore C, et al. (2020b) Exploring the role of physical education teachers’ domain- specific innovativeness, educational background, and perceived school support in CSPAP adoption. Journal of Teaching in Physical Education 39(1): 36–47. Webster CA, Mı̂ndrilă D, Moore C, et al. (2020c) Measuring and comparing physical education teachers’ perceived attributes of CSPAPs: An innovation adoption perspective. Journal of Teaching in Physical Education 39(1): 78–90. Webster CA, Rink JE, Carson RL, et al. (2020d). The comprehensive school physical activity program model: A proposed illustrative supplement to help move the needle on youth physical activity. Kinesiology Review 9(2): 112–121. Webster CA, Weaver RG, Carman M, et al. (2020e). Staff involvement. In: Carson RL and Webster CA (eds) Comprehensive School Physical Activity Programs: Putting Research into Evidence-Based Practice. Champaign, IL: Human Kinetics, 127–142. Weiler RM, Pigg RM and McDermott RJ (2003) Evaluation of the Florida coordinated school health program pilot schools project. Journal of School Health 73(1): 3–8. Wilk P, Clark A., Maltby A, et al. (2018) Examining individual, interpersonal, and environmental influences on children’s physical activity levels. SSM-Population Health 4: 76–85. Yu C and Muthén B (2002) Evaluation of model fit indices for latent variable models with categorical and continuous outcomes. In: Annual meeting of the American Educational Research Association, New Orleans, LA, 1–5 April 2002. Author biographies Karie Orendorff is an assistant professor in the Department of Health and Human Development at Montana State University in Bozeman, Montana, USA. Collin A Webster is a professor in the Department of Physical Education at the University of South Carolina in Columbia, South Carolina, USA. Diana Mı̂ndrilă is an associate professor in the Department of Educational Leadership, Research, and School Improvement at the University of West Georgia in Carrollton, Georgia, USA. Kathleen MW Cunningham is an assistant professor in the Department of Educational Leadership and Policies at the University of South Carolina in Columbia, South Carolina, USA. Panayiotis Doutis is an assistant professor in the Department of Physical Education at the University of South Carolina in Columbia, South Carolina, USA. Brian Dauenhauer is an associate professor in the School of Sport and Exercise Science at the University of Northern Colorado in Greeley, Colorado, USA. David F Stodden is a professor in the Department of Physical Education at the University of South Carolina in Columbia, South Carolina, USA.