# How do I properly interpret latent factor means for multi-group CFA after I've established measurement equivalence?

I have two latent factors, F1 and F2, with 3 indicators each. I have two groups, males and females so I'm doing multi-group CFA.

I also got partial scalar equivalence (all but one of the 6 indicator variable intercepts are set equal).

I understand everything pretty well except the latent factor means. For identification, they are set to zero for one group and estimated for the other group.

So for the first group (males) they are both zero, for the 2nd group (females):

F1 latent mean = -.15, standardized latent mean = -.7 (p-value .00)

F2 latent mean = -.17, standardized latent mean = -.2 (p-value .06)

I'm not sure how to interpret these. I'm pretty sure F1's mean is significant because the indicator variable for F1 who's loading is fixed to 1 is on a scale of 1-2 (yes or no), whereas for F2 the variable who's loading is fixed is on a scale of 1-5. So it makes sense that -.15 is significant for F1 but that -.17 is not significant for F2, because the scale of F1 and F2 are 1-2 and 1-5 respectively...but I'm still not sure how to interpret this.

Does it mean that for females, they are at a "baseline"/"expected value" of .7 standard deviations below men for F1? Does it mean that even if males and females have the same factor loading and same intercept (which is true for 5/6 of my variables) that females are still expected to have a lower value for the item?