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Both adults and young children possess powerful statistical computation capabilities—they can infer the referent of a word from highly ambiguous contexts involving many words and many referents by aggregating cross-situational statistical information across contexts. This ability has been explained by models of hypothesis testing and by models of associative learning. This article describes a series of simulation studies and analyses designed to understand the different learning mechanisms posited by the 2 classes of models and their relation to each other. Variants of a hypothesis-testing model and a simple or dumb associative mechanism were examined under different specifications of information selection, computation, and decision. Critically, these 3 components of the models interact in complex ways. The models illustrate a fundamental tradeoff between amount of data input and powerful computations …