# What test should I use to compare two categorical distributions with replicate measurements?

So I have data from an experiment I did, and I'm at a loss for which test I should use to assess for significance.

I took some cells in vitro and subjected them to either a treatment or a control. Then, I harvest them, and categorize them into three unranked groups, I'll call them A, B, and C. For both the controls and treatments I have three biological replicates. So, for each sample I get a distribution of the cells into A, B, or C, and I'd like to compare the treatment and control to see if there is a statistically significant difference between the two distributions.

My data looks like this:

sample percent_A percent_B percent_C
control_1 0.70 0.17 0.13
control_2 0.71 0.16 0.13
control_3 0.70 0.17 0.13
treatment_1 0.90 0.03 0.07
treatment_2 0.90 0.02 0.08
treatment_3 0.90 0.01 0.09


I'm not sure how to assemble this to get a single value that shows the different distributions between the control and the treatments are significantly different. I know I can run pairwise t-tests for the percent in each group, comparing say "percent_A" between control and treatment, but it would be nicer if I had a single value looking at the whole distribution.

I thought about something like a Kolmogorov–Smirnov test, but that only works on continuous distributions, not nominal categories like I have. Since it's categorical data I thought about a chi-squared test, but I don't know how to make that account for the fact that I have replicates. I could do a chi-squared test on the mean of each of the proportions, but it feels like I'm losing information about the variance of the replicates by doing that. And I thought about a Mann-Whitney U test, but my categories aren't ordinal so I can't rank them. So... I'm not quite sure what test I can use.

It feels like I'm missing something completely obvious, but I'm not quite sure what. Could anyone help point me in the direction of the correct test to use?

Edit: Bumping this question, I could still use an answer for this. I kept searching and never found out what the appropriate way of doing this is.