“Social psychologists should treat interdependence not as a statistical nuisance that should be controlled, but rather as an important social psychological phenomenon that should be studied” Kashey & Kenny, 2002
Family researchers like this quote as much as social psychologists do because Kashey and Kenny are urging us to explore methods that allow us to study families--not to treat family data as though they were individual data.
Why is interdependence considered a nuisance? Even when families are selected for studies using random sampling, the data collected from multiple members of a family will be dependent. (Partners or married persons in a couple, for example, are more likely to be similar to each other than two randomly selected individuals are likely to be similar.) Regression models typically assume independence, along with linearity, normality, and homogeneity of variance of errors.
Researchers might be tempted to work around interdependence by studying individuals or by aggregating data or by assigning the same values to each member of a group. The latter two solutions can be statistically problematic and the former, well, we are back to the point of this entry: much can be gained by understanding the ways in which family members are and are not interdependent.
There are statistical methods, such as SEM or HLM, that accommodate--or take advantage of interdependence, depending on your point of view. These methods and others require a firm grasp of regression so it is best to start there. Here are two links to David A. Kenny's web site if you want to explore issues on this topic in more depth: dyadic analysis and unit of analysis.