Most online tests give score around 10-15 points too high, so that is a big source of error.
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You have to beware the sampling issue here. Smart people take more online IQ tests, so the online IQ testee sample will be somewhat above average, but probably not 10-15 IQ, more like 5 IQ. You can see some evidence of this in this study. https://www.sciencedirect.com/science/article/pii/S0160289614000051 …
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Do you have to take an official test to get a reliable score?
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You can get a realistic eyeballing with online tests. Afaik http://iqtest.dk is alright and tends to give lower scores.
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So, many ppl will really have 0.5 SD (7-8 points) higher than what that site says.
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But even official tests won't be perfect and could have a few points variation from test to test.
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I find the online ones to be highly reliable (= test retake and get similar result), but the norms may be off. Here's a good vocabulary test. https://openpsychometrics.org/tests/VIQT/
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Intriguing implications. Heavy-tailed distributions are often associated with autocorrelation in cumulative effects. This seems to imply that the autocorrelation and impact of successive educational progression is insufficient to create heavy tails (unless samples all young).
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Population substructure. Yes. Clear in SMPY results.
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Memory distortion? I think he means like "remembering" your score was higher than it really was.
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