Sample size (or number of clusters) by treatment arms
Treatment is not binary. See the intervention for an explanation. For example, for a participant who identifies as a Democrat or Republican, the message they are shown will match their partisan affiliation with a 50% probability. Similarly, in terms of age, the probability of the message being matched is 33% (considering that the categories are young, middle-aged, old). Since the message is randomly drawn from all possible messages, all of the covariates being matched is rare: 50% (ideology with Liberal/Conservative) * 50% (political partisanship with Democrat/Republican) * 20% (race with Black, White, Hispanic, Asian, Native American) * 50% (gender with male/female) * 33% (financial status with poor, middle-class, upper-class) * 33% (age with young, middle-aged, old) = 0.28%. For categorical variables, note that, in practice, some participants will likely be part of a category not considered in our prompts (e.g., those whose partisanship is "Independent"). Accordingly, the share of those with a match for the categorical variables is, in expectation, slightly lower than what the calculation above suggests. For the continuous variables, we will follow our implementation partner's mapping into categories and evaluate its robustness to other cutoffs.