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In SAS, there are different CIs for proportion difference ($\pi_1-\pi_2$) to choose?

1.Continuity-corrected Wald CIs based on normal approximation

2.exact method

3.Miettinen-Nurminen CIs based on score test

4.Newcombe hybrid score CIs based on Wilson score CIs for binominal proportion

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  • $\begingroup$ I imagine that each style of CI has somewhat different properties and that each has people who think it is best. Maybe you can google each style and see which seems best for your application. // You might start by looking to see which style(s) may be useful in your currect application. In R, if $\hat\pi_1 = 10/100 = 0.100, \hat\pi_2 = 20/150 = 0.133,$ then code prop.test(c(10, 20), c(100, 150))$conf.int returns 95% CI $(-0.1218,\, 0.0551).$ The null hypothesis $H_0: \pi_1 = \pi_2$ is not rejected against the two-sided alternative, so it is reasonable that the CI includes $0.$ $\endgroup$
    – BruceET
    Sep 14 at 21:55
  • $\begingroup$ Questions that are only about software (e.g. error messages, code or packages, etc.) are generally off topic here. If you have a substantive machine learning or statistical question, please edit to clarify. $\endgroup$ Sep 15 at 1:46
  • $\begingroup$ Does stats.stackexchange.com/questions/123609/… answer your question? $\endgroup$
    – whuber
    Sep 20 at 13:04
  • $\begingroup$ I found this paper FYI $\endgroup$ Sep 20 at 13:12
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There are a lot of intervals out there for the binomial proportion. This paper does a fairly good job of comparing some of them on coverage and length (typically, you want coverage closest to nominal with smallest length. Shorter intervals are higher precision so close to nominal coverage and short length is desirable).

The paper linked does not compare those exactly, but should be sufficient to get you started.

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