Causal Inference in Python

Chapter 2. Randomized Experiments and Stats Review

Now that you know the basics about causality, its time to talk about the inference part in causal inference. This chapter will first recap some concepts from the previous chapter in the context of randomized experiments. Randomized experiments are the gold standard for causal inference, so it is really important that you understand what makes them special. Even when randomization is not an option, having it as an ideal to strive for will be immensely helpful when thinking about causality.

Next, I’ll use randomized experiments to review some important statistical concepts and tools, such as error, confidence interval, hypothesis tests, power, and sample size calculations. If you know about all of this, I’ll make it clear when the review will start so you can skip it.

Brute-Force Independence with Randomization

In the previous chapter, you saw why and how association is different from causation. You also saw what is required to make association equal to causation:

$$E\left[Y\right|T=1]-E\left[Y\right|T=0]=\underset{ATT}{\underbrace{E[Y_1-Y_0|T=1]}}+\underset{BIAS}{\underbrace{\{E\left[Y_0\right|T=1]-E\left[Y_0\right|T=0]\}}}$$

To recap, association can be described as the sum of two components: the average treatment effect on the treated and the bias. The measured association is only fully attributed to causation if the bias component is zero. There will be no bias if $E\left[Y_t\right|T=0]=E\left[Y_t\right|T=1]$. In other words, association will be causation if the treated and control ...