# Distinguishing between size of compliers and never-takers in control group

Say we have data on the total number of units assigned to the control group (1200) and their outcome (20%). We are dealing with one-sided non-compliance, and have data on number of never-takers in the treatment group (500), the outcome of never-takers (25%), and the number of compliers in the treatment group (1500) and their outcome (30%).

We can use excludability to estimate the number and outcome of never-takers in the control group. But how can we estimate these for the compliers in the control group? Also, is it possible to find the treatment effect for compliers (relative effect between compliers in treatment to compliers in control)?

• What is "one sided non-compliance"? And what is "excludability"? Commented Nov 2, 2022 at 18:31
• Some ideas here. Commented Jun 21 at 15:53

$$\begin{array}{c|ccc} & \text{Never-took} & \text{Complied} & \text{Total} \\ \hline \text{Treatment} & 500 (25) & 1500 (30) & 2000 (31.3) \\ \text{Control} & & &1200 (20.0) \\ \end{array}$$
• It wasn't clear from your problem description. Anyway, it's a simple arithmetic problem and you don't know all the variables. When $n_{1,2} + n_{2,2} = n_{., 2}$ you can only solve for the third by knowing two other free parameters. Commented Nov 3, 2022 at 13:59