As a numerical incompetent and math-phobe, I found psych statistics to be one of the few classes that has had a long-term positive effect on my thinking. I actually learned how to do some basic correlations, thought about what they might mean, and considered the applicaitons of analysis of variance.

Was it mathematically rigorous? Well, no, but if it was I would have failed. The formulas simply make no sense in and of themselves, and the class was happy to treat them as mysterious black boxes. I would not trust myself to use them in real research situations, then or now. However, it helped sharpen up my general thinking a little bit, and I remain far more aware of research design issues and the various potential flaws of data than most of my humanities-oriented peers. It's an incredibly low bar, but still.