There is considerable controversy over the factors that shape infants’ developing knowledge of grammar. Work with artificial languages suggests that infants’ ability to track statistical regularities within the speech they hear could, in principle, support grammatical development. However, little work has tested whether infants’ performance on laboratory tasks reflects factors that are relevant in real-world language learning. Here we tested whether the language that infants hear at home, and their receptive language skills, predict their performance on tasks assessing the ability to learn non-adjacent statistical dependencies (NADs) at 15 months, and whether that in turn predicts sensitivity to native-language NADs at 18 months. We found evidence for some (though not all) of these relations, and primarily for females. The results suggest that performance on the artificial language-learning task reveals something about the mechanisms of grammatical development, and that females and males may be learning NADs differently.