Difference of mean with unequal sample sizes and nesting (and non-independence!)


I've never posted here before; hopefully this query isn't redundant. (I have tried to look through previous posts for an answer!). My problem involves difference of means, unequal sample sizes, and nested groups. The basics:

I want to know whether the difference between two means is statistically significant. The means are averages of time periods over which individuals sustained relationships; the variable = continuous.

I have a mean for individuals in Group A (say, n~60). I have a mean for individuals in Group B (n~20). However, *all* the individuals in Group B are also in Group A. Group B is nested in Group A.

From a substantive perspective, it is not helpful for me to calculate the means for people who are only in Group A and for the separate group of people who find themselves in both A and B, and then compare the A versus A+B means. This comparison won't have meaning for my research.

(Oh, and to further complicate things, I can't actually assume independence . . . respondents appear more than once in each group, and provide more than one value subsequently used in the mean calculation. That is, Sally is in Group A. She had two different relationships of different lengths. Both relationship time intervals are included in the list of values that went into the calculation of the Group A mean. I'm ignoring this non-independence for now, though, because I think I can explain why substantively it doesn't matter too much.)

Does anyone have suggestions about how to do what I thought was quite simple -- compare two means -- given these complications?

Any help is much appreciated.