What does it mean to explain data patterns? Cognitive psychologists and other scientists face this question when observable phenomena have to be explained in theoretical terms. Frequentist null-hypothesis testing – one prominent approach in psychology – controls error rates. Machine learning – an alternative prominent outside of, but not yet inside psychology – focuses on precise predictions. However, both alternatives often provide little insight into the data. We propose a combination of formal modeling and Bayesian statistical inference to ground explanations in data analysis. We support this approach by reference to philosophy of science and discussions of the current methods crisis in several empirical sciences and illustrate it with an example from visual attention research.