The percentage of people who received one fecal transplant and were cured (\(13\) out of \(16\), or \(81\%\)) is higher than the percentage of people who received vancomycin and were cured (\(4\) out of \(13\), or \(31\%\)), which seems promising, but the sample sizes seem kind of small. The other nominal variable was outcome: each patient was either cured or not cured. One nominal variable was the treatment: some patients were given the antibiotic vancomycin, and some patients were given a fecal transplant. (2013) studied patients with Clostridium difficile infections, which cause persistent diarrhea. You want to know whether the proportions for one variable are different among values of the other variable. Use Fisher's exact test when you have two nominal variables.
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