CIS Primer Question 3.3.2
Here are my solutions to question 3.3.2 of Causal Inference in Statistics: a Primer (CISP).
The following DAG is a possible casual graph representing the situation. We wish to find the causal effect of the plan on weight gain. The weight gain \(W_g\) is defined as a linear function of the initial and final weights. From the graph we see that the plan chosen by the students is a function of their initial weight.
Since initial weight \(W_I\) is a confounder of plan and weight gain, the second statistician is correct to condition on initial weight.
The causal diagram here is essentially the same as in Simpson’s paradox. The debate is essentially the direction of the arrow between initial weight and plan.