Aspirin
and
Potential Outcomes

ICS212

Three slides based on Rubin Basic Concepts of Statistical Inference for Causal Effects in Experiments and Observational Studies

Y(Asp) is how my head feels two hours after taking an aspirin. Y(Not) is how my head feels two hours after not taking an aspirin.

The causal effect is the difference between how I feel two hours after taking an aspirin and two hours after not taking an aspirin.

The outcome is how my head feels two hours after taking an aspirin as compared to how it felt before I took the aspirin.

The causal effect is the difference between the change in my headache after an aspirin and the change in my headache after no aspirin.

Basic Concepts of Statistical Inference for Causal Effects in Experiments and Observational Studies Donald B. Rubin. P 4

The column Asp Not corresponds to you taking an aspirin and me not taking an aspirin.  

The subscripts 1 and 2 refer to your and my, respectively, outcomes - how our heads feel at the end of two hours.  

In the square brackets we have the treatments - you took an aspirin and I did not.

The numbers indicate the "value" of each of our headaches.

Basic Concepts of Statistical Inference for Causal Effects in Experiments and Observational Studies Donald B. Rubin. P 6

The treatment effect for you when I take an aspirin is 

= Y1([Asp,Asp]) - Y1([Not,Asp])
= 0 - 75 = -75

But the treatment effect for you when I do not take an aspirin is

= Y1([Asp,Not]) - Y1([Not,Not])
= 50 - 100 = -50

 

The causal effect for you depends in some way on whether I get treatment or control. That violates first part of SUTVA.

Basic Concepts of Statistical Inference for Causal Effects in Experiments and Observational Studies Donald B. Rubin. P 6