Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
The full estimation sample will include about 660 people, 300 in treatment and 360 in control. In a pilot conducted in 2023, 150 people applied, 70 were assigned to control and 80 to treatment, of which 66 attended Camp Hope. Though it was not required to apply, 94% of applicants consented to participate in research. Both demand and capacity at Camp Hope have increased over time, so we project that the study will complete enrolling 660 applicants by spring 2026. We assume 40% coverage in administrative records and a 60% survey response rate, decreasing the sample with outcomes to 264 in school data and 502 when combining school and survey data. Based on the pilot experience, we assume an 85% camp take-up rate. In the data on past referrals to camp, the average care-giver has two children, and some baseline controls (particularly gender) have explanatory power. Based on that data we assume 2 cases per cluster, an intra-cluster correlation coefficient of 0.07, and controls that shrink the MDE by 20%. We conduct all calculations for an 0.05 level test with 80% power.
Our primary near-term outcome will be any school behavior incident. We assume a cumulative suspension rate in the control group of 31%, based on the rate in the NLSY for children with an incarcerated parent. Given the assumptions above, in the RCT using a combined sample of administrative and survey records (N=502) we can detect a TOT effect of 11 percentage points, or 36% of the mean. Our long-term outcome will be any incarceration between the ages of 18-25. In past referral data, the control group probability of incarceration in jail or prison in Georgia by age 25 is equal to 9.6 percentage points (pp). Given the other assumptions above, we can detect effects of attending camp on children’s future incarceration greater than or equal to 6.3 pp, or 67% of this control group mean.