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L4-06 · Potential outcomes and randomization

Define an average treatment effect and identify the assumptions that connect it to an observed contrast.

Level 4 icon Level 4 · Undergraduate
Objective. Define an average treatment effect and identify the assumptions that connect it to an observed contrast.
Before this lesson. L4-01, L3-10
Hands-on lab. Confounding and intervention

Learn

A potential outcome describes the outcome a unit would have under a specified treatment. Write Y(1) and Y(0) for two treatment options. The individual effect is their difference. Only the potential outcome corresponding to the received treatment is usually observed for each unit.

The average treatment effect is the population average of those individual differences. Random assignment makes treatment independent of potential outcomes in the assignment distribution. Together with consistency, positivity, and an appropriate treatment and interference definition, this permits identification by a comparison of treatment groups.

Randomization does not make every realized sample perfectly balanced. It supports uncertainty calculations based on the assignment design. Missing outcomes, treatment nonadherence, or interference can change the target and the analysis. Distinguish the effect of assignment from the effect of treatment actually received.

Practice

Solution

The individual effects are two, zero, three, and minus one. Their sum is four across four units, so the average treatment effect is one outcome unit.

Check your understanding

What does random assignment establish in its assignment distribution?

Show the answer

A. Treatment is independent of potential outcomes

Random assignment provides independence by design. Perfect realized balance and full adherence are different properties and do not follow automatically.

Sources

This lesson draws on Hernan & Robins, 2020.

Next: L4-07 · Identification before estimation

References
  1. Hernan, M., & Robins, J. (2020). Causal Inference: What If. https://miguelhernan.org/whatifbook
  2. Bareinboim, E. (2025). Causal Artificial Intelligence: A Roadmap for Building Causally Intelligent Systems. https://causalai-book.net/