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As mentioned in the title. I came across this instance using GLM in R. Is this an error?

EDIT: The p-value of the coefficient was calculated by GLM in R and is less than 0.05.

I then plotted the odds ratios (OR's generated using tidy exponentiation method) and generated the confidence intervals by multiplying the std. error * 1.96 (+/-). When I plot it, the CI includes 1. My understanding is that a CI that includes 1 is not significant for logisitic regression. My confusion is how the coefficient is significant before exponentiating, but the odds ratio includes 1 and is thus not significant. I hope this edits helps, please let me know if I can provide more information. Thanks for your help! @whuber @Schortchi

haaris
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    Please explain what the title means: how exactly did you make the two determinations of statistical significance? – whuber May 06 '22 at 21:48
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    The coefficient has a p-value of less than 0.05 but after converting it to an odds ratio, the 95% confidence error includes 1. – haaris May 06 '22 at 22:09
  • Thank you. This has been noticed and resulted in several identical questions here on CV. https://stats.stackexchange.com/search?q=confidence+overlap+logistic might turn up a few answers; if not, keep hunting. – whuber May 06 '22 at 22:18
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    Could be this one: https://stats.stackexchange.com/q/5304/17230. If you don't find a post on your exact issue, you'll need to edit your question to explain just how you're calculating the p-values & confidence intervals. – Scortchi - Reinstate Monica May 07 '22 at 10:27
  • I have edited the original post, thanks – haaris May 09 '22 at 19:29
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    The answer is really very simple: your second procedure is invalid. Use the first. – whuber May 09 '22 at 19:34
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    @haaris This happens because you are using Wald CIs which depend on the scale chosen for the parameter (i.e. the parametrization) – user277126 May 09 '22 at 19:34
  • May I ask why it is invalid? Is the Wald CI not appropriate here? – haaris May 09 '22 at 21:21
  • It assumes the distribution of the exponentiated estimated OR is approximately symmetric. It's not--and that assumption is inconsistent with the assumptions used to compute the original CI. – whuber May 10 '22 at 14:34
  • Thanks, whuber. I have found that tidy has a conf.int option that has created CIs that appear consistent with coefficient significance. The code I am using now reads: tidy(exponentiate = TRUE, conf.int = TRUE) – haaris May 10 '22 at 14:41

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