Expecting one person to be able to do psychology and neuroscience and stats and computer programming seems like an unreasonable demand
Most papers have multiple authors. If you need to do heavy lifting in stats, bring a statistician on board.
whether the development of some sort of automated stats program would help
I don't think so. First, I can't imagine it being flexible enough (and if it's too flexible its reason for existence is lost) and second it will just be gamed. People like Gelman think that the reliance on t-tests is a terrible idea, anyway, and I tend to agree with him.
My preference is for a radical suggestion: make papers openly provide their data and their calculations (e.g. as a download). After all, this is supposed to be science, right?
This "radical" suggestion is now a funding condition of at least some UK research councils (along with requirements to publish publically funded work in open access forms). A very positive move.... If enforced.
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