Suppose we accept the model in question 10, but data are collected on Xi and Yi in an observational study, not a controlled experiment. Subjects assign themselves to treatment (Xi = 1) or control (Xi = 0), and we observe the response Yi as well as the covariates wi . One person suggests separating the subjects into several groups with similar wi’s. For each group on its own, we can compare the fraction of successes in treatment to the fraction of successes in control. Another person suggests fitting a probit model: conditional on the X’s and covariates, the probability that Yi = 1 is (Xiα + wiβ). What are the advantages and disadvantages of the two suggestions?