For that comparison, I’d require both staff who can cover the training period and funds approved to hire them in the relevant budget year. I’d record those conditions separately so services with hireable staff but no approved funding remain identifiable. Comparing their participation with overall service participation would show whether average reach conceals a gap for that group, without attributing the gap to funding alone.
I can't tell when those characteristics were measured. My proposed comparison needs values describing services before invitation; records retrieved later could still serve that purpose if they document that earlier period.
Using the eligible-service denominator already suggested, compare participation among services with and without replacement staff available. Lower reach in the latter group would flag a capacity-related gap that overall uptake could hide, though it wouldn't establish why those services didn't participate.
The supplied information does not establish whether nonparticipating eligible services were characterized. That assessment needs characteristics for all eligible services, including those never invited and those invited but not enrolled. Comparing service size, staffing capacity, prior implementation activity, and relevant socioeconomic indicators across those groups could show whether readiness affected entry. The analysis should also report how much of each characteristic is missing, since sparse data on nonparticipants can make the comparison falsely reassuring. Uptake among invited services answers a recruitment question, while uptake among all eligible services better represents system reach. If the latter denominator produces substantially lower adoption, favorable uptake among participants should not be presented as broad implementation success.
