# Logistic regression: variable coefficient is statistically significant but not statistically significant as an exponentiated odds ratio?

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

• Please explain what the title means: how exactly did you make the two determinations of statistical significance?
– whuber
May 6, 2022 at 21:48
• 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. May 6, 2022 at 22:09
• Could be this one: 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. May 7, 2022 at 10:27
• The answer is really very simple: your second procedure is invalid. Use the first.
– whuber
May 9, 2022 at 19:34
• @haaris This happens because you are using Wald CIs which depend on the scale chosen for the parameter (i.e. the parametrization) May 9, 2022 at 19:34