Let's say we are asking if a vaccine is effective in mice. We test the vaccine vs control in groups of 10 mice, and the vaccine does confer a significant immune response (based on a linear mixed model with repeated measures, if that makes any difference).
We repeat the experiment twice more, keeping as much as possible the same between experiments, and in these two replicate experiments there is not a significant level of protection.
What conditions (if any) would have to be true for pooling data to be appropriate? By pooling data, I mean that instead of considering three separate groups of 10 mice each, we would treat the data as if they came from a single group of 30 mice.
Intuitively, it doesn't seem to me that three separate 10-mouse experiments should be the same as a single 30-mouse experiment, but whether that's right or not I'd like to understand the explanation.