How to deal with differences in subgroup analysis but no significant interaction? In case of a multiple linear regression I found a significant effect in a subgroup analysis (sample restricted to males). In the subgroup analysis restricted to females there is no effect. However in a model of the whole sample the interaction term of gender is not significant. 
I am aware of the fact that significant result in one group and the lack of significant effect in another group does not necessarily mean that there is a significant difference of the association with the dependent variable between the two groups. However I would like to hear your opinion how to interprete such finding. Could one argue that there is limited evidence for a difference in the sense of that evidence is not as strong as it would be in case of a significant interaction effect of gender?
 A: One problem is that you are using "significance" as your criterion. Look at the effect size. 
This can easily happen if the effect for men and women is in the same direction, but stronger for men. The effect size of the interaction relates to the difference in effect size between women and men.
Indeed, it could be (because of the nature of significance) that the effect for men and women is almost identical. 
Here's an example: Interaction not sig., effect for males sig., effect for females not sig.
#set up model
set.seed(19749)
sex <- c(rep('M', 500), rep('F', 500))
x1 <- rnorm(1000)
y <- 1.2*x1 + 1*(sex == 'M') + 1.5*x1*(sex == 'M') + rnorm(1000, 0, 10)
m1 <- lm(y~x1 + sex + sex*x1)

#significant interaction
summary(m1)

#subgroup of men
m2 <- lm(y[1:500]~x1[1:500])
summary(m2)

#subgroup of women
m3 <- lm(y[501:1000]~x1[501:1000])
summary(m3)

A: Given Peter Flom's point, that lack of evidence is not evidence of lack, you may wish to consider those inevitable two errors, evidence of an effect when it is not present and no evidence of an effect when it is present AND their respective probabilities and importances. Roughly, only if there is a low probability of no evidence of an effect when it is present (high power for detecting the interaction) can one take any defensible assurance from a small observed difference. And when there is an important difference it likely should be shrunk somewhat. And, and there are multiplicities. So once past the first hurdle, it's tough and perhaps worth a survey of modern approaches for sub-group analysis methods. 
