Betsey Stevenson and Justin Wolfers, writing at Bloomberg's website, consider some rules of thumb for helping the layman decide whether they should trust someone's statistical analysis or not. Here's the first of them:
Focus on how robust a finding is, meaning that different ways of looking at the evidence point to the same conclusion. Do the same patterns repeat in many data sets, in different countries, industries or eras? Are the findings fragile, changing as one makes small changes in how phenomena are measured, and do the results depend on whether particularly influential observations are included? Thanks to Moore’s Law of increasing computing power, it has never been easier or cheaper to assess, test and retest an interesting finding. If the author hasn’t made a convincing case, then don’t be convinced.
It's hard not to recall the case of the Hockey Stick and its reliance on the bristlecones. And all the other paleoclimate studies that are said to support the Mannian stick, and which rely on bristlecones too.