# 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?

• I don't think it's a fair comparison. As how the question is worded, it seems the first result from the regression for p1 is adjusted for p2, p3, and p4. And the Mann-Whitney test only uses p1. Perhaps you can clarify? In addition, p1 joins the logistic regression as a (I am guess) continuous variable, while in the Mann-Whitney test it's turned into a rank variable. These two are related and yet can be very different. What is the premise/purpose of using Mann-Whitney anyway? Commented Mar 11, 2014 at 13:44
• @Penguin_Knight I'm using the Mann-Whitney test to try to make some real-world recommendations based on the regression. Without getting too specific, y measures whether or not people performed a certain desirable activity. So, if p1 was a significant predictor of y and significantly differed between people who did and did not perform y, then I might be able to recommend addressing p1 to increase the number of people who do y. However, I think the interpretation is a bit more cloudy if p1 doesn't significantly differ among people who did and did not do y. Does that make sense? Commented Mar 11, 2014 at 13:55
• I see. The problem is that whatever MW test says does not necessarily equate to logistic regression, because they are different types of analysis. If you want to do some bivariate exploration, an approach more parallel to logistic regression is to bin your p1 into some categories, calculate the percent of Y=1 in each category, and then examine if the percentage of Y=1 climbs/declines along the binned categories. You can also change the percentage of Y=1 into logit of Y to examine linearity as well. I wouldn't recommend MW. Commented Mar 11, 2014 at 14:04
• Among other potential explanations (M-W and logistic regression shouldn't be expected to correspond --- indeed, M-W doesn't normally apply for the data you'd use logistic regression on), the most obvious thing to mention is Simpson's paradox -- leave out an important covariate and this can easily happen ... or you can get significance in both, but in opposite directions. Commented Mar 11, 2014 at 22:04

There are several issues here:

1. 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?

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

3. 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 $$p_1$$.

4. 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.