I recently did flow cytometry to quantify cell numbers on 4 similar samples from one group and 4 from another different group (n=4). The samples each contained millions of cells and I wanted to compare the cell populations for a difference. For simplicity let's say n=1 million (mixed cells). For specific cell types in that mix, I created a contingency table and tested for a difference between mean cell proportions in the sample. I used the Chi squared test for a difference between two different non-parametric samples.

So for example, if I had a mean of 10,000 type A cells in group 1 and 1,000 type A cells in group 2, I also had 990,000 other cells in group 1 and 999,000 other cell types in group 2.

So the p value with these large numbers of cells comes out tiny.

My question is, if I only sampled 4 individuals, but then ran my stats tests against very large numbers of something contained within those 4 individuals, is this valid? To take it to its extreme, I could have compared 1 individual against 1 other (n=1) and still have done stats tests on cell numbers which would seem very high powered, but it's only powered for those two individuals. How do I describe this? Can/should I do the test at all? If not, then what n number of individuals do I need before I can say this is valid (given that when I test the cells I will have very high n numbers and no issue with the tests being underpowered)?

Also, is the chi squared test the correct test (I assumed the data are not normally distributed, but should I assume normality, or test for it, and then potentially run a t test)?

  • $\begingroup$ I find this question interesting and gave an upvote, but you might have better luck on the bioinformatics Stack. $\endgroup$
    – Dave
    Mar 13, 2021 at 4:13

1 Answer 1


It depends on what you consider your unit of analysis, the cell or the subject from whence the cells came. Most consider the subject is the unit of analysis and therefore you have a sample size of 8 (4 per group). Ultimately, a hierarchical/multilevel model adresses this perfectly.

  • $\begingroup$ Thanks for setting me off down the hierarchical (nested data) track, which seems to be the right one. So I can put this into a nested table and run a t test (graphpad PRISM has useful info about this here graphpad.com/guides/prism/8/statistics/…). As I am not taking replicate samples on the same subjects I just have to switch the rows and sub-columns (instead of individual 1, 2, 3 as my subcolumn headings I have B Cells, Macrophages etc and the rows represent the 4 individuals in each sample). $\endgroup$
    – croc7415
    Mar 16, 2021 at 6:20
  • $\begingroup$ Only slight concern about this, is there a non-parametric test for this? PRISM gives two options for nested data (nested one way ANOVA or nested t test) and as far as I know both are for normally distributed data. How can I tell if my data are normally distributed? If I sampled random cell numbers then I can see how this would be normally distributed, but I've done an intervention which will surely mean that my intervention could change this? Any advice on this point? $\endgroup$
    – croc7415
    Mar 16, 2021 at 23:42

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