CIS Primer Question 3.3.2

Here are my solutions to question 3.3.2 of Causal Inference in Statistics: a Primer (CISP).

Part a

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.

A casual diagram for Lord’s paradox
A casual diagram for Lord’s paradox

Part b

Since initial weight \(W_I\) is a confounder of plan and weight gain, the second statistician is correct to condition on initial weight.

Part c

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.