A counterfactual is a what-if statement. Like “what if 911 had not happened?”, or “What if Trump had not won the election?” I read that historians don’t entertain counterfactuals, partially because they hardly know what actually did happen.
Why would a statistician use a counter-factual argument?
It turns out that we use them all the time: a \(p\)-value is a counterfactual – It is a statement about what could have happened, as opposed to what actually happened.1 Despite this issue, the \(p\)-value is widely considered to be statistical evidence. It may be that statistics is the only discipline where a counter-factual can count as hard evidence, but we have a pretty narrow definition of evidence. I should probably spend more time here.
On the other hand, I believe that the counterfactual \(p\)-value makes sense as evidence in a small number of experiments. For example, in asserting the existence of the Higgs particle.
In statistics we can model what happened, and we can model what didn’t happen (missing data) or what partially happened (censored data).↩