Causal Inference Lecture Notes: Classical Approaches to Statistical Analysis of Randomized Experiments

Building upon the statistical framework of causal inference, we consider classical approaches to statistical analysis of randomized experiments. The use of randomized experiments in scientific inquiry goes back at least to the 19th century, but formal statistical methods to analyze these experiments were developed in early 20th century by J. Neyman and R. Fisher. The methods they developed were different but shared one important feature; both were design-based and nonparametric. That is, Neyman and Fisher provided ways to make causal inferences from randomized experiments by exploiting their design and avoiding arbitrary assumptions. We examine their proposed methods in detail.