Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Power calculations were conducted for the primary outcome: the change in the factual belief accuracy index from pre- to post-treatment. The index ranges from 0 to 4 and is based on four factual belief items. The unit of analysis is the individual respondent. The primary estimand is the difference in average pre-post change between treatment and control respondents.
The study uses individual-level random assignment, with no planned clustering. The expected final sample size is between 100 and 150 respondents, with approximately equal assignment to treatment and control. Using a two-sided significance level of α = .05 and target power of 80%, the minimum detectable effect ranges from approximately 0.57 points with 100 respondents to 0.46 points with 150 respondents, assuming a standard deviation of 1.00 for the change score. Sensitivity analyses using alternative standard deviations suggest that the minimum detectable effect ranges from 0.42 to 0.71 points with 100 respondents, and from 0.35 to 0.58 points with 150 respondents.
The expected treatment effect is approximately 0.60 points on the factual belief accuracy index. This is based on anticipated improvements of 5 percentage points for the CO₂ item, 5 percentage points for the reactor-explosion item, 25 percentage points for the cooling-tower item, and 25 percentage points for the radioactive-waste item. Under these assumptions, a sample size between 100 and 150 respondents may be sufficient to detect the expected primary effect, although the study may be underpowered to detect smaller effects. Therefore, statistically insignificant findings will be interpreted cautiously and will not necessarily be taken as evidence of no treatment effect. Secondary outcomes and subgroup analyses will be interpreted as exploratory.