Supposing that patients did better in the morning because, say, the nurses were more alert, no matter how many samples you take you'll find the patients do better in the morning. How does "more samples" help control for confounders rather than just confirm a bias?
> How does "more samples" help control for confounders rather than just confirm a bias?
I think you're correct that randomising patient assignments doesn't control for provider-side confounders. Curious if the study also randomised nursing assignments.
"more samples" is not what controls for confounders. Controlling for confounders is what controls for confounders, which you can only do with enough samples that you can randomize out the effect of the confounder.
Whether or not they controlled for nurse-alertness is something you'd have to read the paper (or assume the researchers are intelligent) for.
I imagine that that particular confounder is not possible to eliminate via randomization. Perhaps you collect a bunch of data on nurse awakeness--day shift vs night-shift, measuring alertness somehow, or measuring them on other activities known to be influenced by alertness--and then ensure your results don't correlate with that.
There is also the mechanistic side: if you have lots of plausible mechanism for what's going on, and you can detect indicators for it that don't seem to correlate with nurse alertness, that's a vote against it mattering. Same if you have of lots of expertise on the ground and they can attest that nurse alertness doesn't seem to have an affect. There are lots of ways, basically, to reach pretty good confidence about that, but they might not be as rigorous as randomized assignments can be.
The same thing it means in every context: that (with enough samples) you can control for confounders.