Why does everyone love a good RCT?

The individual treatment effect is defined as an individual’s potential outcome under treatment minus their potential outcome under control. This within-participant difference cannot be directly measured since only one of the two potential outcomes is realised depending on whether the participant was exposed to treatment or control.

Everyone loves a good randomised controlled trial because the mean outcome of people who were exposed to treatment minus the mean outcome of people who were exposed to control – a between-participant difference – is an unbiased estimator of the mean of within-participant individual treatment effects.

I’ve coded up a simulation in R over here to illustrate how they work. Note in particular the importance of confidence intervals!