I am doing the evaluation for a program with 200 members (they enrolled in the program at different times in the past year and the program doesn't end). Only 78 completed the pre test survey. Now I have to look for a control group and resources are scant... What is the ideal number of a sample size for the control group? What is the optimal number? I also know it is a big limitation that treatment and control group didn't take the pre test at the same time, how big is that limitation? Thanks! M.
In epidemiological research an optimal ratio is of 4 controls to 1 case (assuming it's an unmatched design). After that, power increases but at a decreasing rate as the ratio of controls/cases increases.
from Woodward, M. Epidemiology Study Design and Analysis. Boca Raton: Chapman and Hall:, 1999, p.265