# What is a “high” standard error (in logistic regression)?

I can't find in any statistics book what would start to be considered a large standard error of a regression coefficient.

In my research, I have a group of a categorical variable with a small number of cases that in a logistic regression reports what I think is a rather large Standard Error (0.647), but since the B is big (-1.394) the coefficient is significant (p=0.031).

Is a standard error of 0.6 or 0.7 indeed an indicator that something is wrong? (in my case, it could be that there is incomplete information from the predictors, i.e. there isn't data for all combinations of my predicting variables)

• If a standard error should be considered large not only depends on its value, but also on the magnitude of the corresponding effect, on units (for continuous predictors), on your application (what do you intend to do with the coefficient's estimate?), ... Can you give more context regarding your question? – Roland Jan 4 '17 at 11:13
• There are circumstances where this matters. If your coefficient is large (say 10 or more) and your se is also large say about the same (all on the log scale) then you may have separation. But otherwise @Roland has offered you good advice. – mdewey Jan 4 '17 at 13:19
• This seems like a perfectly reasonable question to me. – gung Jan 4 '17 at 16:12

The odds ratio can assume values up to and including 0 and $\infty$ for a sample of any size. Inference is based on the Wald statistic: inspecting the log odds ratio divided by its standard error, it is compared to a normal distribution. In your case, the two-tailed test based on the Wald statistic of -1.394 / 0.647 = -2.15 was statistically significant at the 0.05 level so we conclude these data are highly inconsistent with a null hypothesis of no association. The upper bound of the 95% CI is exp(-1.394 + 1.96*0.647) = 0.88 which is a small odds ratio in some circumstances and large in others.
Inspecting the $2 \times 2$ contingency table of a binary predictor and binary response, the cell frequencies $ad/bc$ give the odds ratio estimate and the variance of the log odds ratio is $1/a + 1/b + 1/c + 1/d$. If any of the cell entries is 0, the variance is infinite which is undesirable.