0

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?

  1. Are there any good tests for the case of replicated paired data I have described, especially non-parametric tests?
  2. Is taking the average between replicates, then applying a non-parametric paired test on the averages a good enough option?
  3. Will taking averages lose too much information about the data, espeicially when $n \geq m$, leading to underpowered tests?
YEp d
  • 1
  • The design is not totally clear to me, maybe you could clarify, but I would start by looking into mixed models – kjetil b halvorsen Nov 10 '23 at 01:53
  • @kjetilbhalvorsen What is specifically unclear to you? – YEp d Nov 11 '23 at 01:28
  • You start with $m$ cultures, for each of the two strains. Then you sample from the cultures. How do you assing growth condition to each sample, randomizing? Then the $n$ replicates, do you get it by subsampling from the same cultures, or do you start new cultures? How do you measure growth condition? (numeric or categorical, say) How do you measure cell viability? Please edit your post to include this information! – kjetil b halvorsen Nov 14 '23 at 21:24
  • Each culture of bacteria is subjected to a different growth condition, cell viability is the measure used to compare the two strains of bacteria across all different growth conditions. Other clarifications have been reflected in the edit. I hope that helps. – YEp d Nov 21 '23 at 09:52
  • Say we have $k = mn$, what is the difference between performing $n$ experiments with $n$ cultures, and performing $1$ experiment with $k$ cultures? In both cases you have in the end independent measurements with $k$ cultures. Or, can't we assume that the measurements are independent and do you expect a variation from the $n$ different experiments? – Sextus Empiricus Nov 21 '23 at 14:26
  • What are the results of an ANOVA seperating the variance of the experiments and strains? – Sextus Empiricus Nov 21 '23 at 14:28

0 Answers0