2.5.1. Sample size justification and power

To account for potential 33% attrition, we plan to over‐sample up to 225 participants (75 per group). Our goal is 50 subjects per group. We are using an intention‐to‐treat analysis by including all randomized participants in our analyses. A sample size of 150 provides at least 80% power for all aims to detect medium effect sizes. Sample size for the study was based primarily on ensuring our ability to detect a clinically meaningful effect for the primary outcome of PA (Aim 1).

For Aim 1, we will have 84.6% power to detect medium effect sizes (effect size of 0.5: a change of 2.5 min/day in PA for pooled SD of 5 min/day) with 50 individuals in each of the three groups. Estimates of the covariance of PA over time (1.2) and effect size (medium) were determined from the pilot study (Dunn et al., 2019). Based on the U.S. Department of Health and Human Services 2018 PA Guidelines Advisory Committee Scientific Report, any increase in PA contributes to the health benefits associated with the accumulated volume of PA. The report provides evidence that for many chronic conditions (including IHD), individuals who become more physically active at any level and duration, relative to their peers with the same condition, have reduced risks of disease progression, development of other chronic diseases, and mortality in addition to improved physical functioning and quality of life (U.S. Department of Health and Human Services, 2018).

For Aim 2 this sample size (50 per group) yields 80% power to detect a correlation of 0.126 between change in PA and change in hopelessness levels. Thus, the estimated correlation of 0.19 from the pilot study will have sufficient power to be detected in the RCT.

For Aim 3, effect sizes of at least 0.5 (as observed in the pilot study) will be detected with at least 84.6% power for the direct impact of treatment groups on social support or motivation after adjustment for mediating variables. Partial correlations of at least 0.126 between social support or motivation and change in PA, after controlling for treatment group, will have at least 80% power. Thus, Aim 3 will have sufficient power to detect moderate to weak mediating effects of social support or motivation on PA.

All power calculations assume a significance level of 0.05 and two‐sided tests.