Average p-values (black dots) for comparing cosmic times (left) or mass ratios (right) of mergers with CDM to mergers with SIDM-1. We indicate the 95th percentile with an X. The red line indicates the significance threshold of 0.05. For differentiating between CDM and SIDM-1, we wish to have the 95th percentile below the significance threshold. We find that ∼70 mergers are sufficient to attain this when comparing cosmic times, or ∼160 mergers when comparing mass ratios.