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The p value in a logistic regression is given for the B estimates. But what if I'm reporting odds ratio instead of logit. Do the same p values apply?

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    $\begingroup$ The coefficients are the log odds ratio? $\endgroup$
    – Repmat
    Commented Apr 30, 2016 at 11:42

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First an aside- $p$-values as you are describing them are special cases that only apply when either (1) the predictor is continuous and linear or (2) it is categorical and has only 2 levels. More generally you need to only report $p$-values for the appropriate chunk/composite tests. For example if you have $x$ and $x^2$ in the model the most meaningful $p$-value is for the 2 d.f. test combining the two effects. For a $k$-level categorical predictor the most meaningful $p$-value is from a $k-1$ d.f. test.

To your question, the $p$-value is for a (sometimes silly) null hypothesis test that the odds ratio is 1.0 which is identical to saying that the log odds ratio is 0.0. The standard error is always on the latter scale. So the $p$-value goes for both.

But remember not to show anyone $p$-values for single coefficients when you should have done chunk tests. In R this is automatic with the rms package's anova function once you fit a logistic model with the lrm function.

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