# How to interpret coefficient standard errors for logistic regression

The coefficients estimated for logistic regression are in log odds, and I understand it is common -- at least when interpreting the output -- to convert the log odds to odds so they're more easily understandable.

When reporting results for logistic regression, should log odds and their standard errors be reported, say, in a table, and then odds used to interpret the coefficients?

Or, can odds (and, uh, standard error odds?) be reported in a table?

It's fine to report odds ratios rather than log-odds differences if that will be easier for your audience to understand. If you report odds ratios it probably makes sense to report the confidence intervals. That is, if $\beta_i$ are the log-odds differences, $\sigma_i$ is the standard error of $\beta_i$ (also on the log-odds scale), and $q$ is 1.96 for $\alpha=0.05$ (or whatever Normal quantile you want use), then you should report the back-transformed confidence intervals:
$$\exp(\beta_i \pm q \sigma_i)$$
rather than back-transformed values $\pm$ standard errors, as the confidence intervals are often asymmetric on the odds scale (they're not necessarily symmetric on the log-odds scale either, but generally much closer).
• Thanks, should $\sigma_i$ be in terms of odds ratios - or its original units (which I think are in terms of log odds)? – Joshua Rosenberg Nov 30 '16 at 13:10