# Test if counts in two conditions are significantly different without knowing the population size

The data are counts of cell structures in different (independent) conditions. For N cells per condition, in which N is different for each condition and unknown, the total number of X and Y structures were counted. Here is what the data looks like (R):

dat
Z   Y
control    198 198
condition1 155 257
condition2  41 101
condition3  93 107
condition4  79 111


Structures Z and Y co-occur in the same cell, and there might be more than one structure per cell.

Biological question: Are the number of Z features changed in conditions vs control (and which condition)?

Since we don't have N, or a distribution of Z counts per cells, the number of Y features could be used as "normalization" factor and the question be: are the number of Z features in relation to Y affected in the mutants (is the Z / Y ratio changed in the mutants)?

Is there any test I could use to test our hypothesis that the number of Z features is affected in the conditions?

My first instinct was to look at the chi-squared test, but (ii) these are aren't proportions and (ii) I guess we would be testing if there is an association between condition and structures (at best). I also looked at other tests, without knowing at least N per condition, or the number of structures per cell I couldn't find anything appropriate.

Reprex

dput(dat)
structure(list(Z = c(198L, 155L, 41L, 93L, 79L), Y = c(198L,
257L, 101L, 107L, 111L)), class = "data.frame", row.names = c("control",
"condition1", "condition2", "condition3", "condition4"))