Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
The primary outcome is any homelessness as measured by HMIS administrative records. We base our power calculations on the homelessness prevention study in Santa Clara County (Phillips and Sullivan, 2025). In this study, 7.2% of those assigned to the control group (i.e., not offered targeted homelessness prevention services) experienced homelessness within 12 months of enrollment. Given a total sample of 20,000 (10,000 people in treatment and 10,000 in control) and a baseline homelessness services entry rate of 7.2%, a two-sided test at the 5% level would have 80% power to detect a 1 percentage point (14%) reduction in homelessness 12 months after random assignment. This power calculation is for a simple difference in means of the outcome across groups. If we estimate the treatment effect in a regression framework that controls for baseline characteristics, we reduce residual variance, yielding an even smaller minimum detectable effect. As a benchmark, one-time financial assistance in Chicago reduced shelter entry by 76% within 6 months of calling for assistance (Evans, Sullivan and Wallskog, 2016) and targeted homelessness prevention in Santa Clara County reduced homelessness by 70% within 12 months of randomization (Phillips and Sullivan, 2025). Given these prior estimates, the present national study is well powered to detect even small changes in homelessness. Repeating this analysis for each site, where each site has a total sample of 2,000 (1,000 people in treatment and 1,000 in control), yields a minimum detectable effect of 3.2 percentage point (44%) in the reduction of homelessness 12 months after random assignment. This means that the study is well powered to detect large but reasonable effects on homelessness at the local level as well.