Comparing percentages! Here is the problem I need help with,
I have two stem cell lines (line A and Line B). These cell lines were generated from one source.
I have six flasks, three of the flasks contain cells line A and the other three flasks contain cells line B. All the flasks contain cells of the same passage, cultured in the same media, and otherwise treated identically (other than being different lines).
I have the proportion of cells that are DB positive in each flask (in percentage) and want to know if there is a difference in the proportion of cells that express gene DB between cell line A and B. How can I analyse this data statistically?
 A: You need the raw numbers. Otherwise, you have no idea how strong your evidence is. As an analogy, consider flipping two coins. One comes up heads half the times, while the other comes up heads a third of the times. Is this strong evidence of the coins being weighted differently if:

*

*You flipped each coin six times?


*You flipped each coin six-thousand times?
In the former scenario with six flips each, it is fairly reasonable to think that the coin that came up heads a third of the time ($2/6$) actually is weighted toward favoring heads but came up tails more often just by some bad luck. Thus, such a test is inconclusive, perhaps even misleading.
However, in the second scenario, it would be quite the event for the coins to have an unlucky run of flips, because of the sheer number of flips. A fluke in six flips is plausible. A fluke in thousands (millions, billions, etc) flips is less plausible.
This is related to something called the consistency of a hypothesis test which means that, somewhat loosely speaking, a consistent hypothesis test gets more and more likely to give the right answer as the sample size increases.
A caveat to this is that, by doing research at the level of individual cells, you probably have millions of cells. Consequently, your sample size is reasonably described as “huge” and will cause even small differences in the proportion to be statistically significant at the usual thresholds like $0.05$ (since the usual proportion tests are consistent and the truth is likely that the proportions differ by at least a little bit). If you don’t have a huge number of cells, however, or if you need an exact p-value, then you need the full information on the counts.
