No, they don't, they measure a persons current capacity for IQ test taking.
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In all, IQ testing is worthless.
Online IQ tests measure a person's ability to answer typical questions found in IQ tests..

We agree the online ones are worthless but the 'proper' tests, which have a high variety of questions that offset "test training" and which are done in a controlled environment, do shed some light on that person's capacity for abstract reasoning. That being said, abstract reasoning is only a small part of intelligence as a whole so I agree that all IQ tests are worthless when trying to measure it.