18.5 Properties of randomized experiments
Ignorability
Completely randomized: \(z \perp y^0,y^1\) implies that there will be no differences on average in potential outcomes between treatment and control group.
Randomized Block Experiments: \(z \perp y^0,y^1 | w\) no difference within blocks between treatment and control groups (on average)
Matched pair: No difference between potential outcomes of the two members of the pair.
Will revisit more general version of ignorability in Chapter 20.
Efficiency
- Ideally blocks create subgroups where the members are more similar to each other in the blocks
- This should enable sharper estimates of block specific effects, which can be combined in a weighted average. (Same effects can be achieved with regression on block indicators)
- Regression also increases efficiency by adjusting for pre-treatment variables. “It is as if nature created a randomized block experiment and we were taking advantage of it.”
Question: Isn’t there some colinearity problem if you include block indicators and pre-treatment variables, many of which were used to define the blocks?