The reductions in marginal variance and in conditional (on the observed imbalance) bias that you get from adjusting are two sides of the same coin, this is explained clearly in the chapter of What If reference earlier in this thread
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Indeed, but it is misleading to imply that imbalance should drive the decision of whether or not to adjust. Prespecify prognostic variables, and adjust for them.
I don’t think he’s implying you shouldn’t prespecify. But I guess he’s implying you should break your prespecification and adjust for large imbalances that might matter but you didn’t plan for. At least if your research question is more important than harm you might do to norms around prespec
Well I don’t want to put words in his mouth and get him trouble with the fda but that’s what I would do if an important experiment were “broken” based on my understanding of the arguments in what if. I think we all agree you should adjust for prognostic covariates
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