Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
We base our power analysis on the between-subject comparison for the salience treatments, using the most conservative restriction of using only the scenario first shown. These comparisons yield the smallest number of observations.
Under these assumptions, we are able to detect a minimum effect size of d = 0.3.
This corresponds to a 1-point difference on our 11-point Likert scale, assuming alpha=0.05, beta=0.8, and, conservatively, an uniform distribution of participants across grid points.