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gwern comments on More "Stupid" Questions - Less Wrong
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Don't worry; the people whose responses the tests were built on didn't have access to a random sample either! Still seems to work, though.
So combining two biased samples balances out? Or is it more testing self perception? E.g. do you think of yourself as X not whether you are objectively X. Probably thinking about this question in detail ruins its usefulness as a text question anyway....
Offhand I don't entirely know, but the tests do work so your comparison issues can't be serious. If they've been normed for your group, perhaps that screens off the worst of the issues.
I'm only talking about myers briggs here, but I'm really confused about why you say the tests seem to work. They don't seem to work to me. I can get any of handful of different results and so can many people I know. Not only that, but I've studied the underlying theory enough to know that a lot of people I've met who only go by the tests are mistyped. They don't even know what the letters mean. They don't know if they use extroverted or introverted thinking/intuition/feeling/sensing. They think that if they're smart, they have to have a T in their type.
One of the main criticisms of MBTI is actually its lack of reliability - that is, its lack of consistency from test to test. MBTI in general is rubbish and when I talk about personality tests or correlations, it's always Big Five or some other decent test.