A non-conservative, size-α modified Fisher exact test for comparing two proportions. Its p-value, confidence interval, and power all agree with one another by construction, and it controls the Type I error rate strictly while recovering most of the power that the ordinary exact test gives up to conservativeness. It implements the test of van der Meulen, Raymond and van der Meulen (2021), building on van der Meulen (2008).
Usage
The main function takes the two success counts (u, v), the two group sizes (m, n), and a null odds ratio, and returns a familiar htest object.
# Example 1 of the paper: 5/12 successes versus 7/11, H0: OR = 1, alpha = 0.05.
res <- modified_fisher_exact_test(u = 5, m = 12, v = 7, n = 11, odds_ratio = 1)
res$estimate # sample odds ratio
res$p.value # two-sided, test-based p-value
res$conf.int # agreeing (1 - alpha) confidence intervalLearn more
-
Introduction to modifiedfisher: an introduction to
modified_fisher_exact_test(), its arguments, power, and diagnostics. -
Background and comparison: why the test exists, and a comparison with
fisher.test()andexact2x2::fisher.exact()(both similar to SAS PROC Freq). - Overview of algorithm: a step by step overview of how the test is built in R.
- Reproducing the paper’s figures: rebuilding the size and power curves, and adapting them to your own design.
Reference
van der Meulen EA, Raymond K, van der Meulen PJ (2021). Consistent Confidence Limits, P Values, and Power of the Non-Conservative, Size-α Modified Fisher Exact Test. Journal of Biostatistics and Biometric Applications 6(1):102.
van der Meulen EA (2008). A Nonrandomized, Nonconservative Version of the Fisher Exact Test. Communications in Statistics - Theory and Methods, 37:699-708.