# CIS Primer Question 3.3.3

Here are my solutions to question 3.3.3 of Causal Inference in Statistics: a Primer (CISP). \(\DeclareMathOperator{\do}{do}\)

The drug you have been assigned determines which ward you go to. Whether you get a lollipop is determined by which ward you go to and whether you show signs of depression. Depression is a symptom of certain risk factors. These risk factors, together with the drug you have been assigned, determine your capacity for recovery.

Since `lollipop`

is a collider in this diagram, there are no backdoor paths from `drug`

to `recovery`

. In other words, it is not necessary to condition on any variables to estimate the causal effect of `drug`

on `recovery`

. In this case, \(\mathbb P (Y \mid \do(X)) = \mathbb P(Y \mid X)\).

If the nurse were to give out the lollipops in the day after the study, there would be no difference in the causal diagram.