# Causal quartets: Different ways to attain the same average treatment effect

## TL;DR

This paper explores how different underlying data patterns can produce the same average treatment effect, highlighting the complexity of causal heterogeneity through visual examples.

## Contribution

It introduces the concept of causal quartets, illustrating multiple data configurations that yield identical average effects but differ in heterogeneity patterns.

## Key findings

- Different data patterns can produce the same average causal effect.
- Visualizations reveal the complexity of heterogeneity in causal effects.
- Understanding heterogeneity is crucial for interpreting average treatment effects.

## Abstract

The average causal effect can often be best understood in the context of its variation. We demonstrate with two sets of four graphs, all of which represent the same average effect but with much different patterns of heterogeneity. As with the famous correlation quartet of Anscombe (1973), these graphs dramatize the way in which real-world variation can be more complex than simple numerical summaries. The graphs also give insight into why the average effect is often much smaller than anticipated.