The CR test is significant given that path loadings for individual groups were in different signs (male : positive and female: negative) but insignificant.
Assuming I understand your question correctly, yes, the moderator has a "statistically significant" effect. The conclusion would be that neither the path coefficient for males nor for females differs significantly from zero, but that they DO differ significantly from one another (hence the significant effect of the moderator, sex).
Thank you for your inputs. However, is there any relevance in terms of difference if the individual effects themselves are insignificant?
It is possible to have a situation where neither coefficient is different from zero, but the two are far enough apart to be different from each other, but this can only occur when one is positive and the other is negative.
Dear Mr Morgan,
Yes that is the situation - the coefficients for the male and female group are positive and negative respectively but insignificant so am confused as to whether a significant critical ratio test is worthwhile to evaluate?
Yes, you should evaluate the fit of the overall model because a positive value may be different from a negative value, even if neither is itself different from zero. Imagine a positive coefficient that had p < .06 and a negative coefficient with a similar p value. Neither would be different from zero, but they would be far enough apart to be different from each other.
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