Biology as a whole has entered a new era in which data analysis plays a prominent role; but in the field of evolutionary genomics, data analysis has so far yielded little of value. This relative failure has been due in large part to methodological problems. Frequently, researchers have not sufficiently considered alternative hypotheses, leading to a kind of “computer-assisted storytelling”. Moreover, there has been widespread use of model-based statistical methods that depend heavily on assumptions regarding evolutionary processes of which we have little knowledge. The field of evolutionary genomics would benefit from a greater use of “sturdy statistics” that are model-free and make few assumptions about processes we do not understand.