The study of cognitive development hinges, largely, on the analysis of infant looking. But analyses of eye gaze data require the adoption of linking hypotheses: assumptions about the relationship between observed eye movements and underlying cognitive processes. We develop a general framework for constructing, testing, and comparing these hypotheses, and thus for producing new insights into early cognitive development. We first introduce the general framework – applicable to any infant gaze experiment – and then demonstrate its utility by analyzing data from three studies investigating the role of attentional cues in infant learning. Finally, we discuss general implications for construction and testing of quantitative linking hypotheses.