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Control group had 2/200 people quit their jobs. Experimental group had 3/90 people quit their jobs. My gut tells me that this result not statistically-significant, but how can I show it using a statistical test?

juju b
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    Welcome to Cross Validated! You want to compare two proportions, right? What methods have you learned for doing so? – Dave Oct 31 '22 at 22:12

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You can use the Fisher exact test, obtaining

fisher.test(matrix(c(2,198,3,87),2,2))
Fisher's Exact Test for Count Data

data: matrix(c(2, 198, 3, 87), 2, 2) p-value = 0.1752 alternative hypothesis: true odds ratio is not equal to 1 95 percent confidence interval: 0.02415544 2.61654673 sample estimates: odds ratio 0.2943426

Some will object to this because they say the marginals are not fixed (only one of them is), but we can condition on the marginals, which by itself gives no information on possible dependence. For the discussion see What does the assumption of the Fisher test that "The row and column totals should be fixed" mean?