Most appropriate statistical test for count data (2x2 contingency)

Question

This is a dummy dataframe resembling my real-life data:

structure(list(cond = c("WT", "WT", "WT", "WT", "WT", "WT", "WT", 
"WT", "WT", "WT", "WT", "WT", "WT", "WT", "WT", "WT", "WT", "WT", 
"WT", "WT", "WT", "WT", "WT", "WT", "KO", "KO", "KO", "KO", "KO", 
"KO", "KO", "KO", "KO", "KO", "KO", "KO", "KO", "KO", "KO", "KO", 
"KO", "KO", "KO", "KO"), class = c("N", "N", "N", "N", "N", "N", 
"Y", "Y", "Y", "Y", "N", "N", "N", "N", "Y", "Y", "N", "Y", "N", 
"N", "Y", "N", "Y", "N", "N", "N", "Y", "Y", "Y", "N", "N", "Y", 
"N", "N", "N", "Y", "Y", "N", "N", "N", "N", "N", "N", "N"), 
    lattice = c(72.4394527831179, 70.1486049154573, 71.2024262282001, 
    70.095774734531, 73.1687587160835, 73.4725521658284, 71.1213324059112, 
    69.4426450566097, 67.7407461727878, 67.3598397689386, 69.5170866395342, 
    68.751790570905, 73.2734806165999, 72.0386374169852, 70.293510845974, 
    68.9576642114016, 69.4472846093111, 70.8520303262601, 69.967844969872, 
    69.7957750105144, 76.3165495002798, 70.8237308152673, 70.5087804854601, 
    70.0768856496865, 49.4569953395058, 52.0898768763027, 44.3112116723351, 
    53.0069841435797, 49.6755152863985, 50.3014101181505, 49.0856479592249, 
    48.3511098818039, 50.0812079766985, 50.4035212282794, 54.0992908724316, 
    43.4055868143946, 50.1834254159389, 54.7298925145524, 55.1516389972744, 
    51.4685454381875, 52.253317158648, 52.8558395390657, 51.5377616093217, 
    57.7792154694597)), row.names = c(NA, -44L), class = "data.frame")

Those are two experiment conditions ("WT" & "KO"). In each condition, observations might be classified as "Y" or "N" depending on whether the organism exhibits some measured trait or not.

I would like to compare those 2 groups (experimental conditions) & to infer, whether there is a statistically significant difference in amount of observations regarded as "Y" between the groups (and if it is the case, whether there are more or less "Y"-s in "KO" with respect to "WT" or not).

I do not know what type of statistical test would be more appropriate for this task: Fisher's, Chi-squared, etc.

Info: the "lattice" is another feature of the dataset, I am comparing this parameter between conditions using the Wilcoxon rank test. For this question it might be ignored. I just decided to show an entire structure of df, including this column.

EDITS:

1. the experiment does not have fixed marginals.
2. there was a time window, in which the data were collected.
3. conditions are independent (those were cell-sorting experiments).
4. afaik, this cannot be addressed with McNemar's test which is applicable for dependent variables, so the question was incorrectly assigned as duplicate.

Answer 1

It is easier to present these data in a 2x2 contingency table.

$$\begin{array}{c|cc|c} &\text{Y}&\text{N} & \text{marginal sum}\\ \hline \text{WT} & 15 & 9 & 24\\ \text{KO} & 14 & 6 & 20 \\\hline \text{marginal sum} & 29 & 15 & 44 \\ \end{array}$$

The type of test to be performed depends on the boundary conditions (whether one or more marginals are fixed or not, e.g. whether the experiment selected a fixed number of cases with WT/KO and/or Y/N) and on the stopping rule (whether the test had a fixed number of the total 44 cases, or whether the test was continued untill some number of a particular class had been observed).

You can read about this in an article by Lydersen, Fatherland and Laake Recommended tests for association in 2×2 tables, but possibly also in many other places and also question already asked here.

Depending on the number of marginals that are fixed

• both marginals fixed: the values have one degree of freedom which follows a hypergeometric distribution.

  You can perform Fisher's exact test.

  Example: the lady tasting tea experiment

• one marginal fixed: the values have two degrees of freedom which follow a binomial distribution.

  You can perform several types of tests. For instance Barnard's test. Also a z-test for differences in proportions is commonly used.

  Example: a/b testing.

• no marginal fixed the values follow a multinomial distribution.

  You can perform a chi-squared test, which approximates the multinomial distribution with a multivariate normal distribution. The null hypothesis is that the cell probabilities are a product of class probabilities.

  Example: an observational study where both of the two variables are not controlled.

A situation based on a stopping rule.

• When we have fixed number of two classes, and observe untill a number of cases have occurred, then the distribution follows a binomial distribution and you can perform tests for that distribution.

  Example: testing the vaccins against Covid. (Which statistical model is being used in the Pfizer study design for vaccine efficacy?)