Go Bayesian
By "doing data analysis in a patternless way," I meant statistical methods such as least squares, maximum likelihood, etc., that estimate parameters independently without recognizing the constraints and relationships between them. If you estimate each study on its own, without reference to all the other work being done in the same field, then you're depriving yourself of a lot of information and inviting noisy estimates and, in particular, overestimates of small effects.
Couldn't agree more.
See also: ESP paper rekindles discussion about statistics
Not directly related, but quite relevant.
If you are interested in statistics, I really recommend Andrew Gelman's books and blog.