One thing that constantly saddens me about statistics is that a large amount of energy is expended using is almost correctly to "prove" something that was already the gut feel. Even unbiased practitioners can be lead astray [1] but standards on how not to intentionally lie with statistics are very useful. [1] http://euri.ca/2012/youre-probably-polluting-your-statistics...
There's no way to tell whether or not that "gut feel" is accurate without proof. Often it's right, but occasionally it's very, very wrong (cancer risk and Bayes theory provides a good illustration: http://betterexplained.com/articles/an-intuitive-and-short-e... ). Consequently it's still worthwhile proving things even when they're seemly obvious.
Or maybe I'm projecting?