Timmons et al. BMC Public Health 2012, 12:284 http://www.biomedcentral.com/1471-2458/12/284 Motor Skills Motor skills are being developed during the early years [32], and typically developing preschoo- lers with better motor skill proficiency tend to display higher levels of physical activity [33-37], particularly par- ticipation in vigorous physical activity [37]. We measure motor skills using 2 tests. The first test is the Peabody Developmental Motor Scales-2. This is a criterion and norm-referenced scale composed of six subtests that measure interrelated motor abilities that develop early in life. It is designed to assess gross and fine motor skills of children from birth through 5 years of age; we use only subtests for gross motor skill assessment. The second test is the short form of the Bruinitisky-Oserestky Test of Motor Proficiency (BOT-2). The BOT-2 short form is composed of 14 items and provides a total motor composite score across 4 areas: fine manual control, manual coordin- ation, body coordination, and strength and agility. The BOT-2 is designed to identify individuals with mild to moderate coordination deficits [38]. It is validated for use in 4–21 year olds; thus, it is not used at the initial assessment of 3-year-olds. In addition, all children complete two BOT-2 tasks that are not included in the short form: 50 ft shuttle run and standing long-jump. Parents’ Beliefs about Physical Activity for their Pre- schooler Using an approach based on the theory of planned behaviour [39] encompassing parental attitudes regarding their child's physical activity, social normative beliefs, perceived control/self-efficacy, and intentions, we developed a questionnaire to assess parents/caregivers’ beliefs about physical activity for their preschooler. The theory of planned behaviour has been used extensively in prospective and intervention studies of health related behaviours including physical activity [40], with variables in the theory accounting for 29 % of the variance in physical activity behaviour. Following recommendations by Ajzen [41], we gathered pilot data from a sample of parents (n = 26), assessing their behavioural, normative, and control beliefs regarding their preschool children’s participation in moderate-vigorous intensity physical ac- tivities. Content analysis of those data was carried out and results used to develop measures of parents’ atti- tudes (6 items), subjective norms (7 items), perceived be- havioural control (5 items) and behavioural intentions (3 items). We also examine parents' self-efficacy regarding their abilities to provide opportunities for their children to be active. Using guidelines by Bandura [42], a behav- iourally-specific self-efficacy measure (9 items) was con- structed based on pilot data identifying common barriers and scheduling issues relevant to preschoolers’ physical activity. Our decision to focus on parents’ beliefs is con- sistent with their own reporting that their beliefs about physical activity probably influence that of their pre- schooler [43]. Parent physical activity levels are also Page 5 of 7 assessed using the International Physical Activity Ques- tionnaire for 15–69 year olds (Short Form). Data analyses We are not interested in simply describing changes in physical activity over a 3-year period in young children. Rather, the novelty in the HOPP study is in describing how the prevalence and patterns of physical activity in preschoolers are associated with health outcomes, and whether the strength of these associations changes as preschoolers advance through the early years. In addition to performing standard linear regression analyses for each health outcome with physical activity (i.e., cross- sectional analyses), we propose to assess the associations between each key health outcome and physical activity using mixed-effects modeling to conduct longitudinal analyses, thereby taking full advantage of the richness of our data set. In addition to characterizing and testing the average pattern of change in preschoolers of different physical activity levels, the mixed-effects analyses provide for both random- and fixed-effects of the parameters of change that correctly account for the repeated measure- ments within the same child. In effect, individual change curves are predicted for each child and the degree of in- dividual variations are estimated. We can then include other available information about the children to predict or explain variations in both initial status and subsequent change. These predictors may include both important baseline covariates such as gender and ethnicity, but also potentially-modifiable factors (e.g., parents’ beliefs, motor skill proficiency) that are hypothesized to influence the risk of unhealthy trajectories.). Similar analyses can be per- formed for each health outcome plotted as the trajectory of interest. Sample size estimation Based on our pilot studies, the association between daily minutes of physical activity and various health outcomes demonstrated effects size (R2) of at least 0.11, indicating medium effect sizes according to Cohen, as referenced by Green [44]. Thus, for regression analyses to be com- pleted at each year of assessment, based on medium ef- fect sizes, Green [44] recommends a sample size of 50 + 8(m) (where m = number of predictors). With up to 6 predictors in a comprehensive model (e.g., physical ac- tivity variable, sex, parents’ beliefs, motor skills, socio- economic status, and child temperament), a sample size of 100 in each age group would provide at least 80 % power for those statistical tests. Thus, with 3 age groups (3, 4, and 5 years) at baseline, 300 children are needed. Assuming an attrition rate of 10 % per year, our goal is to recruit 400 children. We also wish to ensure the adequacy of this sample with respect to the linear mixed-effects ana- lysis. Sample size calculations for this purpose are complex,