Minimum detectable effect size for main outcomes (accounting for sample
design and clustering)
Using historical data for the same context, we can calculate the power for different horizons of recidivism (the main outcome).
3 months recidivism: Mean 0.18; Std. Dev 0.382
Alpha 0.05, Power 0.80, N 1500: we would be able to detect effects of 5.87 pp.
If alpha was set at 0.10, the MDE is 5.2 pp, and if the power is 0.90 (and alpha 0.05) the MDE is 6.79
6 months recidivism. Mean 0.31; Std. Dev 0.460
Alpha 0.05, Power 0.80, N 1500 --> MDE = of 7.06pp.
Alpha 0.05, Power 0.90, N 1500 --> MDE = of 8.17pp.
Alpha 0.10, Power 0.80, N 1500 --> MDE = of 6.27pp.
The minimum detectable effects of the intervention will be enhanced by utilizing block randomization, considering that the four strata-forming variables are predictors of the outcome (data from a pre-intervention year). Notably, the number of previous offenses, acting as a proxy for the lagged dependent variable, exhibits the strongest correlation.
Moreover, increasing the size of the control group can enhance statistical power (the treatment group size is fixed due to budget constraints). The control group size is estimated as a lower bound, contingent on the unknown flow of released inmates, as previously discussed. A percentage of inmates who will be released in the course of the intervention has not yet committed crimes leading to imprisonment.
A measure of MDE for very short-term recidivism (e.g., 1 week) seems implausible at this point, given a mean of 0.01 (1%) and a standard deviation of 0.108.