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

arXiv: https://arxiv.org/abs/2302.12878 · HTML: https://mlsanity.com/paper/2302.12878/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2023.

## Built on by (most cited first, 4 of 4)

- [This human study did not involve human subjects: Validating LLM simulations as behavioral evidence](https://mlsanity.com/paper/2602.15785/) (2026)
- [Performance is not enough: the story told by a Rashomon quartet](https://mlsanity.com/paper/2302.13356/) (2023)
- [A Conceptual Framework for Ethical Evaluation of Machine Learning Systems](https://mlsanity.com/paper/2408.10239/) (2024)
- [Position: Prioritize Identifying Structure, Not Complex Models, for Scientific Discovery](https://mlsanity.com/paper/2606.02632/) (2026)

## Abstract (arXiv)

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.