Cross-national analyses test hypotheses about the drivers of global variation in national outcomes. However, since nations are connected in various ways, such as via spatial proximity and shared cultural ancestry, cross-national analyses often violate assumptions of non-independence, inflating false positive rates. Here, we show that, despite being recognised as an important statistical pitfall for over 200 years, cross-national research in economics and psychology still does not sufficiently account for non-independence. In a review of the 100 highest-cited cross-national studies of economic development and values, we find that controls for non-independence are rare. When studies do include controls for non-independence, our simulations suggest that commonly used methods continue to produce false positives. In reanalyses of twelve cross-national relationships, we show that half are no longer significant after controlling for non-independence using global proximity matrices. We urge social scientists to sufficiently control for non-independence in cross-national research.