I am looking for the optimal test to use on a contingency table with 2 categorical variables (first variable has 2 levels, second has 4 variables). The cell counts can be as low as 1 or 2 and the overall sample size is about n=150.

Based on basic textbook knowledge, I would use the Fisher exact test. However, I recently saw an article arguing against this common logic. It stated that unconditional tests are more powerful then Fisher's exact test for small samples.

Which test should be used then on these n=150 observations to compare a binary variable across levels (4) of an unordered categorical variable? Fisher, fisher with simulation, chi-square with some mid-p correction and simulation, etc?


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