Subgoal interactions have received considerable attention in AI Planning. Earlier analyses by Korf and Joslin and Roach  were done in terms of the topology of the space of world states. More recent analyses by Barrett and Weld and Veloso and Blythe were done in terms of the nature of the planner. In this paper, we will argue that subgoal interactions are best understood in terms of the candidate sets of the plans for the individual subgoals. We will describe a generalized representation for partial plans that applies to a large class of refinement planners, and discuss the notion of mergeability and serial extensibility of these partial plans. The concepts of independence and serializability of subgoals are derived by generalizing mergeability and serial extensibility over classes of partial plans. Unlike previous work, our analysis also applies to multi-method refinement planners such as UCP. We will show that all existing characterizations of serializability differ only in terms of the specific class of partial plans that they implicitly address. Finally, we will use our interaction analysis to explore factors affecting the selection of a refinement planner for a given domain.