1 Defining counterfactuals

1.1 Observing versus intervening

Aug 22. Slides

Statistical inference is about observing: if I observe a sample from a population, what can I infer about that population? Causal inference is about intervening: if I take a sample from a population and intervene to change some exposure, what average outcome would result?

Today we will discuss observing, intervening, and why the difference is so important.

1.2 Lab: Designing a study

Aug 23

In this lab, we will start by getting to know one another. Then, we will discuss a hypothetical scenario.

A researcher (with whom you may disagree) says to you: > Coming to office hours frequently causes student success in the classroom.

In groups of about 3 students, discuss the following.

1. Imagine it is the start of the semester. How would you design a randomized experiment to assess this claim?
   • Imagine that you can assign students to a treatment condition and they will comply
   • Consider the details: who would you enroll, how would you define frequently, how would you assess success, etc.
2. Imagine it is the end of the semester. No randomized study was run. You want to conduct an observational study using administrative records (and you get IRB approval to do this). How would you design an observational study to assess this claim?

There is no expectation to have clear answers now. Over the course of the semester we will learn to formalize these types of questions and their solutions.

1.3 Defining causal effects

Aug 24. Slides. After class, read Chapter 1 of Hernán and Robins 2020 and begin Homework 1.

Today we will define average causal effects in the potential outcomes framework.

By the end of class, you will be able to

• define potential outcomes
• explain the Fundamental Problem of Causal Inference¹
• recall statistical concepts: random variables, expectation, conditional expectation