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Alicorn comments on What's In A Name? - Less Wrong
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I don't think you could get together enough people who changed their names away from any particular name to see overall trends. The set of people who changed their names in adulthood is probably decent-sized, but the set of people who changed their names away from, say, David, and not because they are transitioning to female or for some other reason besides not liking it, and who have had the opportunity to move as adults to a city that sounds like "David", is probably tiny.
You could maybe do Bayesian updates on this if you had a large enough pool of name-changers and a large enough pool of names previously investigated, but it probably wouldn't end up being "statistically significant" by journal standards.
Can you expand on what sort of "statistically insignificant" Bayesian update would be a useful thing to do?