Significance Natural selection is the force that underlies the spectacular adaptations of all organisms to their environments. However, not all traits are under selection; a key question is which traits have been shaped by selection, as opposed to the random drift of neutral traits. Here, I develop a test of selection on quantitative traits that can be applied to almost any genetic cross between divergent populations or species. The test is robust to a wide range of potential confounders and has greater power to detect selection than existing tests. Applied to empirical data, the test reveals widespread selection in both domesticated and wild species, allowing selection to be detected more easily and powerfully than previously possible.