Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
We have calculated minimum detectable effects for the outcome of “new lease-up in an opportunity area in the first 12 months after random assignment” at each of the three reporting timepoints for the CMRS versus Control comparison. For existing voucher families, a new lease-up is defined as leasing-up with a voucher in a move to a new unit. For waitlist families, a new lease-up is defined as a lease-up with a voucher. The sample sizes for this 12-month outcome allow for a minimum of 6 months of follow-up after random assignment. For families with less than one year of observation since RA, the observation window will be the maximum time observed (6 to 11 months).
With no adjustment for multiple comparisons, for the Rapid Cycle Evaluation Report, the minimum detectable effect for all families (CMRS n=842; Control n=828) is expected to be 4.3 percentage points. For existing voucher families (CMRS n=797; Control n=797), the minimum detectable effect is expected to be 4.4 percentage points. For waitlist families (CMRS n=45; Control n=31), the minimum detectable effect is expected to be 20.9 percentage points.
With no adjustment for multiple comparisons, for the Phase 1 Impact Evaluation Report, the minimum detectable effect for all families (CMRS n=3,366; Control n=3,312) is expected to be 2.2 percentage points. For existing voucher families (CMRS n=3,186; Control n=3,186), the minimum detectable effect is expected to be 2.2 percentage points. For waitlist families (CMRS n=180; Control n=126), the minimum detectable effect is expected to be 10.3 percentage points.
With no adjustment for multiple comparisons, for the Phase 2 Impact Evaluation Report, the minimum detectable effect for all families (CMRS n=6,444; Control n=6,354) is expected to be 1.6 percentage points.
All of these minimum detectable effect calculations assume 80% power for a two-tailed test significant at the 10% level and that 15 percent of the control group will lease-up in opportunity areas, as was the case in CMTO (Bergman et al. 2020). If the control proportion is lower than 15 percent, the minimum detectable effect will be smaller.