A colleague asked me about some results with logistic regression. He had
two predictors of a binary outcome, call them A and B. When used alone,
predictor A was significantly related to the outcome and predictor B was
not. Moreover, the correlation between A and B was zero. When the
outcome was regressed on the two predictors simultaneously using logistic
regression both were significantly related to the outcome. In effect, the
coefficient for predictor B became larger. However, when OLS regression
was used instead, the coefficients for each predictor were the same as
when entered alone, which is what one would expect.
I discuss this in these two handouts: