Chapter 1 - Bias - More Clarity on Bias association is not causation maths

[MichaelOgunmakin]

There is a slight friction for me on chapter 1, under bias in the following paragraph

Now, let’s add and subtract E[Y0 | T=1] This is a counterfactual outcome. It tells what would have been the outcome of the treated, had they not received the treatment.

For more clarity, it would be great to understand why we are adding and subtracting. Could be a friction point for some readers.

Something like "Now, let’s add and subtract E[Y0 | T=1] This is a counterfactual outcome. It tells what would have been the outcome of the treated, had they not received the treatment. Adding and subtracting this term preserves the mathematical expression while allowing us to reorder the formula into causal effect and selection bias"