# Idea > [!tldr] Counterfactual thinking > What would have happened if circumstances were different? In the [[causal inference]] [[potential outcomes|potential outcome]] framework, counterfactual outcomes are ones that would have been observed had the treatment been different. If my treatment was $A = 1$ (and thus my **observed outcome** is $Y^1$, the alternative I could have received would be $A = 0$, and thus, my **counterfactual outcome** is $Y^0$. Note that sometimes $Z$ is used instead to refer to treatment assignment. - **Observed** outcome: I got the vaccine ($A = 1$) and I did not get sick. My observed outcome was $Y^a = Y^1$. - **Counterfactual/unobserved** outcome (contrary to the fact): Had I not gotten the vaccine, would I have gotten sick? That is, if ($A = 0$), what would my $Y^0$ have been? When $A$ or $Z$ is binary (0, 1), the two potential outcomes are represented with $Y^1$ and $Y^0$. ## Examples Does interacting with dogs reduce cortisol/stress? Applying the [[potential outcomes]] framework, we must consider what each person's cortisol level would be in two different "universes." - universe T (treated): patient X interacts with dog - universe C (control): patient X does not interact with dog The cortisol levels in these two parallel universes are called [[potential outcomes]]: Either could be potentially observed. But in reality, we can only observe on cortisol level for a particular patient at one specific moment in time. The potential outcome that was actually observed or happened is the **observed or factual outcome**. The other outcome is the **counterfacutl outcome**. ![[po-universes.gif]] # References - Potential outcomes and counterfactuals