I have two main independent variables - gender (0/1) and extraversion (continuous) in a logit regression. In the full sample, the gender X extraversion interaction shows no statistical significance. However, when I split the sample into male vs female subgroups, extraversion is statistically significant (p<0.05) among women, but not among men (p=0.09). The coefficient of extraversion in both subgroups are positive. What does this mean? Can I conclude that extraversion significantly predicts women's outcomes, but not for men? Thank you!
Can I conclude that extraversion significantly predicts women's outcomes, but not for men?
Yes and no. Yes it is significant in one subgroup. But, is the association significantly different between men and women? No - the interaction is not significant. What is going on? You didn't tell us the main effect of extraversion, but probably it is also significant? The fact that you don't have a significant interaction means that this association doesn't differ between men and women. Probably it is just non-significant in men due to the loss of power, because the sample is smaller.