The human sciences should seek generalisations wherever possible. For ethical and scientific reasons, it is desirable to sample more broadly than ‘Western, Educated, Industrialised, Rich, and Democratic’ (WEIRD) societies. However, restricting the target population is sometimes necessary; for example, young children should not be recruited for studies on elderly care. Under which conditions is unrestricted sampling desirable or undesirable? Here, we use causal diagrams to clarify the structural features of measurement error bias and target population restriction bias (or ‘selection restriction’), focusing on threats to valid causal inference that arise in comparative cultural research. We define any study exhibiting such biases, or confounding biases, as weird (wrongly estimated inferences due to inappropriate restriction and distortion). We explain why statistical tests such as configural, metric, and scalar invariance cannot address the structural biases of weird studies. Overall, we examine how the workflows for causal inference provide the necessary preflight checklists for ambitious, effective, and safe comparative cultural research.