Hi  I've a problem at work and looking for some suggestions as to how to progress.

We took a sample of 100 patients.  For each patient we calculated the average number of times they attended the hospital's Emergency Department over a period of time. (These patients were known to be frequent attenders).

Following a project designed to reduce ED attendances we counted the same patient's attendance again over a period of months and calculated the mean average.

Knowing that patients will regress to their means over time, the frequency of attendance naturally decreasing and increasing, what test will show if the campaign was successful and any reduction is not simply regression to the mean (RtM) for each patient.

I was thinking of a binomial test.  If a patient attended 8 times in 10 months, giving an average of 0.8, what is the probability they would attend 4 times in 12 months after.  If the p < 0.05 we can discount RtM.  Unfortunately though some patients have a monthly average of 2 or 3 and it does not work.