Predictor is significant in logistic regression, but not in Mann-Whitney I have run a logistic regression using several predictor variables (call them $p_1, p_2,  p_3,  p_4$) to predict a binary dependent variable (call it $y$). $p_1$ is a significant predictor of $y$ in the regression. However, a Mann-Whitney test of $p_1$ shows no significant difference by category of $y$.
Is it normal to have a significant logistic regression predictor that doesn't significantly differ by groups, or is there potentially something screwy with the data?
 A: There are several issues here:

*

*Your multiple logistic regression model includes other variables that may well improve the performance of the model even if they aren't 'significant', thus increasing the power of the test of $p_1$.  If you want to learn more about this phenomenon, it may help you to read this thread: How can adding a 2nd IV make the 1st IV significant?


*The Mann-Whitney U-test isn't a single-variable analog of multiple logistic regression, simple logistic regression is.


*Reverse regression (i.e., regressing $X$ on $Y$) isn't the same thing as 'regular' regression (i.e., regressing $Y$ on $X$).
Based on these facts, if you wanted to see the relationship of $p_1$ in isolation, you should fit a simple logistic regression of $y$ on $p_1$.


*I suspect these data came from an observational study, not an experimental study.  As a result, causal conclusions are not valid.  That is, you cannot "recommend addressing $p_1$ to increase the number of people who do $y$".
In addition, that phrasing implies that you may think of $y$ as the actual predictor variable here.  If so, in combination with point 3 above, you probably should be fitting a multivariate model (such as a MANOVA) instead.
