Minimum detectable effect size for main outcomes (accounting for sample design and clustering)
Intervention 1: We assume control mean of students completing 12 out of 18 hours of on-line content, with the standard deviation of 2 hours, and ICC of 0.5.
Then MDE is 0.34s.d. (R2=0.2) to 0.38s.d. (R2=0), which is 0.7 to 0.8 hours more content covered.
Intervention 2: for career attitudes, we assume a baseline mean of 0.18, baseline standard deviation of 0.38, and ICC of 0.01.
Then MDE is 0.06s.d., which is a 0.02 change in the Octoskill measure
Intervention 3: for the subject-specific test, we assume a baseline mean of 713, the standard deviation of 119, and autocorrelation of 0.5 (baseline scores will help predict follow-up)
Then MDE is 6 points on the test (0.05 SD).