# Choosing the right test for cell count data and categorical data

I have recorded data from a lot of cells viewed under a microscope, and am now stuck trying to do a useful analysis of it.

I have two types of cells (genotype; WT and null), and I treated them with a chemical and recorded data before and after treatment (treatment; treated and untreated). There were two biological replicates of each condition (cultures grown from different colonies but should be genetically identical) and I recorded observations from 200 cells for each condition.

I was effectively doing two separate experiments: experiment 1) the number of a cellular component I could see in each cell (foci per cell) experiment 2) an observation of for another cellular component, which was placed into one of 5 categories

For experiment 1; I want to know if: 1) the number of foci per cell is different between the two genotypes 2) the number of foci per cell is different before and after treatment 3) the biological replicates are the same as each other

I don’t believe this data is normally distributed so the test which makes the most sense to me so far has been Kruskal-Wallis with Dunn’s post test. But I read that this is not designed for discrete data which may be a problem here.

This is what the data looks like for experiment 1

|   WT  |  null |   WT  |  null |   WT  |  null |   WT  |  null |
|   untreated   |    treated    |   untreated   |    treated    |
|           sample 1            |           sample 2            |
|   4   |   3   |   2   |   3   |   3   |   3   |   2   |   3   |
|   2   |   3   |   3   |   2   |   4   |   1   |   3   |   2   |
|   2   |   1   |   5   |   2   |   2   |   3   |   1   |   3   |
|   1   |   2   |   3   |   2   |   4   |   3   |   6   |   1   |


Another problem I encountered was that when I run Kruskal Wallis on all 8 columns some of the column comparisons come out with difference significance values than if I run it on just the 4 from sample 1. For example, WT untreated vs WT treated in Sample 1 is not significant when all the data is analyzed, but is significant when only Sample 1 data is analyzed. Which one should I use, or should I do a different test?

For experiment 2 the data is a little different. Each cell was placed in a category based on the appearance of an organelle, so I’m looking to see if there is a shift away from the normal appearance in to one of the other categories as a result of treatment and whether it is genotype dependent. So far I have this in a contingency table in Prism and have tried a Chi squared test but I’m not sure this is answering my question. When I have done this before it was with just two categories, as are most of the examples I see for chi squared analyses.

In Excel I have averaged the value for each comparable sample and displayed as a column chart with error bars, and the shift is obvious in some comparisons, but I was hoping to be able to do something to show statistically that the distribution of cells between categories is different. This is what one of the excel tables/graphs look like;

Is there a better way to approach category data like this?