Which test to use - Binomial or Fisher's Exact?


I am trying to compare 2 random binary samples, and I am confused on which test to use.

This is to test the effectiveness of an algorithm in identifying risk factors in patients.

If the patient is diagnosed with at least 1 risk factor that is a success (1) and if they are not diagnosed with a risk factor that is a failure (0).

I have a random sample of 200 patients that were chosen prior to the algorithm being implemented and a random sample of 200 different patients that were chosen after the algorithm was implemented. I would like to compare the two samples.

I am questioning whether to use the Binomial Exact Test with the testing mean as the mean of the pre-algorithm data, or whether a Fisher's Exact Test (or any other test) would be more appropriate?

Any insight that anyone could give me would be greatly appreciated!
You basically have a comparison of two groups on the percentage with "success". That would be a contingency table chi-square. Fishers Exact is probably too conservative for 200 subjects per group, but you could also use it.
Definitely do not calculate the pre-test proportion (is that what you mean by a "mean"?) and use it as a parameter for an exact binomial -- doing that would assume that the proportion calculated pre-test was a population-level, known proportion, whereas it is actually as subject to random error as the post-test proportion. Chi-square considers that both pre and post test proportions (or percentages) are subject to random error.


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Agree with EdGr. Chi-square test will be appropriate here considering contingency table with sufficient sample size (200 subjects).