Obligatory link to Statistics Done Wrong: The Woefully Complete Guide, a book on how statistics can and has been abused in subtle and insidious ways, sometimes recklessly. Specifically, the chapters on the consequences of underpowered statistics and comparing statistical significance between studies.

I’m no expert on statistics, but I know enough that repeated experiments should not yield wildly different results unless: 1) the phenomenon under observation is extremely subtle so results are getting lost in noise, 2) the experiments were performed incorrectly, or 3) the results aren’t wildly divergent after all.