My data is from cells that are treated under two different conditions and then their response to the condition is measured by one output variable.
The cell populations in the two conditions are quite different, one has about 7 000 cells and one almost 30 000 cells. When I plot the histograms of the single output variable, one is heavily skewed with a long tail to the right and one is less skewed, but does not look normal. The histogram peaks are clearly separated and together with their different shapes, this make me inclined to think that there are different effects of the different conditions (biologically speaking).
However, I am having troubles expressing myself statistically. My current approach is to show the distributions in either overlapping histograms or a violin plot rather than a bar plot since I want to emphasize the difference in distribution shape as well as shift in means. I would like to accompany this with a statistical indicator of the difference between these two distributions.
When I perform a T-test or Welch test, I get super significant p-values of at least 10^-100, which, if I understand correctly, can largely be attributed to my high power from having big sample sizes and are not really indicative of a meaningful difference between the data. I am currently thinking of including the effect size of the difference in means together with this p-value and a distribution/violin plot as my final way of presenting this data. But before that, I wanted to ask here if my approach is sound or if there is a better way to show that these distributions are different from each other.
(I am sorry if there statistical language is not correct there, please ask if you need clarification of something. Many approaches I have seen to similar problems, employ a bar plot of means +-s.d. and then follow up with a T-test. I wanted to see if there is a more informative approach since feel that a lot of information is hidden by presenting it this way, but I understand it is preferred by many for practical reasons.)