Sander Greenland, speaking today on the oft-heard demand of classical statisticians to “let the data speak for themselves”:

If you hear the data speaking to you, seek professional help.

There’s no such thing as a-theoretical data analysis. There’s always a model lurking there somewhere. All statistical analysis can tell you is how consistent the data are, or aren’t, with some set of parameter values for that model. If the model is wrong – if, for example, you’ve assumed away an interaction effect or a sample bias – the results will be equally wrong. Properly used, statistics is an aid to thought, not a substitute for it.