Suppose I have $m$ cultures of each of two strains of bacteria. I subject each culture of bacteria to different growth conditions, and measure the cell viability at the end of the experiment. This leads to $2m$ data points where growth conditions are measured categorically whereas cell viability is measured numerically.
To test if there is any significant difference between the two strains of bacteria across the different conditions, I can apply one of many different paired hypothesis tests.
However, imagine now that I repeat this experiment $n$ times by creating new cell cultures, leaving me with $2mn$ data points. It becomes difficult to use any test that I know of, since the replicates themselves cannot be paired.
I have read suggestions, like in this post, to simply average across the replicates and apply a paired t-test. But what if $n$ is too small for the assumption of normality to apply and the data is known to have a non-normal distribution?
- Are there any good tests for the case of replicated paired data I have described, especially non-parametric tests?
- Is taking the average between replicates, then applying a non-parametric paired test on the averages a good enough option?
- Will taking averages lose too much information about the data, espeicially when $n \geq m$, leading to underpowered tests?