proptesti one-sided confidence interval uses the same critical value as a two-sided CI

[viqule11]

We can see in the image below that when prompting for a 1-sided confidence interval, the critical value used is still Z_{alpha/2} instead of Z_{alpha}. The upper bounds are the same for each; this issue also occurs in the analogous case where we set alternative="greater"

[adw96]

Thanks @viqule11 !

@svteichman would you mind taking a crack at this? It should be a one-line fix 🙏

[svteichman]

@adw96 a few questions for you on this:

• should the confidence intervals here match stats::prop.test()? It seems that stats::prop.test() uses the Wilson score method to calculate confidence intervals, while in the code for proptesti() the confidence interval is calculated using the typical Wald approach. I just wanted to double check here that in rigr we want to use the Wald approach, which will provide different confidence intervals than simply running stats::prop.test().

• how do you want the one sided intervals to be calculated? When the alternate is "less", should the interval be $[0, \hat{p} + z_{1-\alpha}*SE]$, and when the alternate is "greater", should the interval be $[\hat{p} - z_{1-\alpha}*SE, 1]$? Right now, when the alternative is "less" the upper bound is calculated as $\hat{p} + z_{1-\alpha/2}*SE$ and the lower bound is set to be the lower bound from the confidence interval in stats::prop.test() (similarly with the "greater" alternative), and I wasn't quite sure what the thinking was behind this.

[adw96]

Great catch, @svteichman ! This is adopted code, so I don't know whether this was all intentional. Here are my best guesses:

• let's ensure that results are consistent between rigr::proptesti() and rigr::proptest(). I don't think that they need to be consistent with stats::prop.test(). I certainly trust my UW colleagues to make better choices about uncertainty quantification over computational statisticians from the 80's. (asymptotically they're equivalent, tg)
• seems right?! (but I never think about one-sided tests...) do those intervals always respect the bound? does that roughly match with stats? (I'm drawing it out now...)

[svteichman]

@adw96, right now rigr::proptest() returns the same two-sided CI regardless of alternative (always using critical value $z_{1-\alpha/2}$), and rigr::proptesti() when doing a test with a single group updates the CI based on the alternative (i.e. one-sided CI's like $(0, x)$ and $(x, 1)$ for "less" and "greater") and when doing a test with two groups uses the same two-sided CI regardless of alternative. In order to make them all consistent, would you like CIs to always be two sided, or for them to be one-sided if alternative is "less" or "greater"?

[adw96]

I think I'd like them always to be two-sided, thanks!!

[svteichman]

Closing because this is implemented in PR #167