Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Power is assessed by Monte Carlo simulation calibrated to preliminary data: the baseline (no-photo control) effective-response probability is about 0.56, and 66.5 percent of geolocated preliminary listings fall in right-leaning neighborhoods, the share over which the primary estimand is identified. Because the sample is bounded by the rental market, we fix the sample size and report minimum detectable effects at 80 percent power and a 5 percent two-sided test, at the expected sample of about 3,000 listings and at 4,000 and 5,000 should the market allow a larger sample.
At the expected 3,000 listings, the minimum detectable effect is 6.7 percentage points for the average left penalty and 7.9 percentage points for the primary quantity, the left-signal penalty in right-leaning neighborhoods. At 4,000 and 5,000 listings the primary minimum detectable effect falls to 7.0 and 5.9 percentage points (6.0 and 5.3 for the average penalty). The interaction—whether the left penalty in right-leaning neighborhoods differs from the one in left-leaning neighborhoods—has a minimum detectable effect of about 14 percentage points at 3,000 listings, falling to about 10 at 5,000.