Data on the languages of the world are complex from a statistical point of view: sparse on many important dimensions, noisy and fostering complex layers of (genealogical, areal and other) dependencies. As a response to this situation, the language sciences have embraced experimental methods, computational modelling as golden standards for evaluating and discovering the processes and factors that shape human languages. This host of methods has provided new insights and opened new research venues, yet I will argue in this presentation that the assumptions behind these approaches are by no means less problematic than the ones underlying the analyses of cross-linguistic distributions for the same purpose. While experimental techniques allow us to test online human behavior (which is the ultimate source of language structure) and computational methods provide a thorough control of the target variables and perfect replicability, their ecological validity as models of language structure is limited in a number of ways cross-linguistic distributions are not. I will illustrate these points with a number of examples and case studies (taken from my own work and others.)​