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NancyLebovitz comments on Statistical checks on some social science - Less Wrong Discussion
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Maybe this isn't a job for anyone who knows statistics, it's a job for research psychologists who know statistics and have found they're too pugnacious to be happy in a conventional academic career.
That would still not help them make their criticism, based on technical statistical grounds, understood or accepted among other psychologists who are poorly trained in statistics.
Note the last paragraph I quoted-- Simonsohn's inbox is full of tips about iffy research of many kinds.
There are two issues: having influence within a profession (difficult) and getting paid (not obvious, but possibly easier than having influence). The path isn't as easy as I thought. Perhaps the best route is looking for a job teaching good statistical practice.
If psychologists want and accept being taught good statistical practice, as Douglas_Knight suggested, then that seems likely to work.