Control Sample, Association and Causality

We introduce the control sample in survey sampling as a tool for measuring the association between a possible cause X and a particular effect Y. The elements of the target population are divided in two groups according to whether X is present or not, the absence of X identifies the control group. A random sample is selected from each group with the aim of measuring the association between X and Y. We propose an unbiased estimator of the associational risk difference between groups and then generalize our approach to the problem of estimating the causal risk difference