Top panel: flux boosting factor versus observed S/N for simulated data (open circle) and real detections (red filled circle). Central panel: completeness as a function of the injected line flux I_in over the measured flux uncertainty ΔI_CO. The I_in for real detections are line fluxes that have been corrected for flux boosting factors in the top panel. The blue curve shows the best fit to the simulated data (see Eq. (3)). The completeness decreases with decreasing integrated flux normalized by noise, indicating that sources are more difficult to detect at low S/N. This analysis allows us to correct CO luminosity functions for the completeness of our search algorithm. Bottom panel: false positive rate versus S/N for CO detections in this study.