Since we have the ability to intervene in the data-driven world, we can carry out counterfactual regression where we can estimate the effect of treatment (Intervention) on an outcome by comparing what would have happened if same group had not been treated.

This brings us to Potential outcomes framework. To wrap our heads around this, we will talk in terms of potential outcomes. They are potential because they didn’t happen. Instead, they denote what would have happened in the case some treatment was taken. We sometimes call the potential outcome that happened, factual, and the one that didn’t happen, counterfactual.

As for the notation, we use an additional subscript:

Y_i0 is the potential outcome for unit(i) without the treatment.

Y_i1 is the potential outcome for the same unit(i) with the treatment.