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naraburns  nihil supernum  1yr ago (text post)   3549 thread views

Friday Fun Thread for December 16, 2022

Be advised: this thread is not for serious in-depth discussion of weighty topics (we have a link for that), this thread is not for anything Culture War related. This thread is for Fun. You got jokes? Share 'em. You got silly questions? Ask 'em.

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Apparently, asymmetric confidence intervals are perfectly possible. See here and here.

Re the confidence interval, as I understand it, a p-value is an estimate of how likely it is that an effect is real, and a CI tells us the size of the effect. See here. So, a p-value can be low even if the CI is wide.

Edit: See also here ("The CI gives an indication of the precision of the sample mean as an estimate of the "true" population mean. A wide CI can be caused by small samples or by a large variance within a sample. . . . The p-value is the chance of getting the reported study result (or one even more extreme) when the null hypothesis is actually true.").

It's not a question of how wide the confidence interval is, but of how much of the interval is greater than 1. For a 95% confidence interval, a one-tailed p of 0.025 should correspond to a CI with an upper (or lower) bound of 1.0. Since the p value is only slightly greater than 0.025, I would expect the upper bound of the CI to be closer to 1.

I checked confidence intervals of hazard ratios for several other published studies and found that the CIs were consistently geometrically symmetrical (i.e. upper/point = point/lower) around the point estimate, but now that I think about it, they all had large samples. I'll have to look into why small sample can result in asymmetric confidence intervals.

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