I see where gathering information about all participants before starting the intervention might not be possible. It should still be possible to maximize balance with each batch added, but that means a tradeoff between balancing each batch and balancing the experiment as a whole. For a given experiment, we would have to decide the relative likelihood that that there would be a confounding variable which in the batches or a confounding variable in the demographics.
The undetected confounding variable is always a possibility. That doesn’t mean that we can’t or shouldn’t do as much about it as the expected gains offset the expected costs, and doing some really complicated math to divide the sample into two groups isn’t much more expensive than collecting the data to go into it.
I see where gathering information about all participants before starting the intervention might not be possible. It should still be possible to maximize balance with each batch added, but that means a tradeoff between balancing each batch and balancing the experiment as a whole. For a given experiment, we would have to decide the relative likelihood that that there would be a confounding variable which in the batches or a confounding variable in the demographics.
The undetected confounding variable is always a possibility. That doesn’t mean that we can’t or shouldn’t do as much about it as the expected gains offset the expected costs, and doing some really complicated math to divide the sample into two groups isn’t much more expensive than collecting the data to go into it.