Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
We base our power calculations based on our outcome for returning to homelessness, using Cohen’s 2024 paper: Housing the Homeless: The Effect of Placing Single Adults Experiencing Homelessness in Housing Programs on Future Homelessness and Socioeconomic Outcomes. The study took place in Los Angeles, and the programs observed have similar dosage, intensity, and timing levels as Make Progress and Fast Track. Cohen draws on administrative records from LA County's HMIS, covering single adults who sought assistance between 2016-2017. The short-term sample comprises 15,990 cases with at least 10 months of post-intake outcomes; the medium-term sample comprises 7,584 cases with at least 20 months.
The population is predominantly Black (~53%) and male (~66%), with an average age of ~46. It is a high-need, high-system-contact group: 70% have a prior homeless history, 80% report a physical or mental disability, 60% are chronically homeless, and 27% have a substance abuse problem. Prior system contact is extensive: 52% had emergency health service receipt, 23% had spent at least one night in jail, and 43% had used emergency or crisis services in the 6-12 months before intake.
We consider this population to be comparable to the population served by Atlanta Mission, with them telling us they anticipate their population might be even more high-risk. We use the control means from the paper for the 10 and 20 month outcomes of returning to homelessness. We also anchor our power calculations to the OLS estimates found by Cohen, anticipating them to be akin to our ITT estimates for this RCT.
We only conduct power calculations for our expected primary comparison, Make Progress to Control.
10-Month Outcome - Control Mean = 0.30. Cohen found 8-9 pp reduction.
Year 1 (N = 472: 283 MP, 189 Control)
Absolute MDE: 12.6 percentage points
Relative MDE: 41.9% reduction relative to baseline of 0.30
Year 2 (N = 944: 566 MP, 378 Control)
Absolute MDE: 8.8 percentage points
Relative MDE: 29.4% reduction relative to baseline of 0.30
Year 3 (N = 1416: 850 MP, 566 Control)
Absolute MDE: 7.2 percentage points
Relative MDE: 23.9% reduction relative to baseline of 0.30
20-Month Outcome - Control Mean = 0.42. Cohen found 5-6 pp reduction.
Year 1 (N = 472: 283 MP, 189 Control)
Absolute MDE: 13.1 percentage points
Relative MDE: 31.2% reduction relative to baseline of 0.42
Year 2 (N = 944: 566 MP, 378 Control)
Absolute MDE: 9.3 percentage points
Relative MDE: 22.1% reduction relative to baseline of 0.42
Year 3 (N = 1416: 850 MP, 566 Control)
Absolute MDE: 7.6 percentage points
Relative MDE: 18.0% reduction relative to baseline of 0.42