neither of which should be assumed to be likely to result in an average score that's 30 points too high, as mistakes like these could go in either direction

Look. People misremember (and remember the largest value, and so on) in the way most favourable to themselves. While mistakes can of course go in either direction, they don't actually go in either direction. If you ask men to report their penis size (quite literally), they over-estimate; if you ask them to measure, they still overestimate but not by as much. This sort of error is absolutely the norm in any surveys. More so here, as the calibration (on Bayes date of birth question at least) was comparatively very bad.

The situation is anything but symmetric, given that the results are rather far from the mean, on a Gaussian.

Furthermore, given the interest in self improvement, people here are likely to have tried to improve their test scores by practice, which would have considerably lower effect on iqtest.dk unless you practice specifically the Raven's matrices.

The low scores on iqtest.dk are particularly interesting in light that the scores on the latter are a result of better assignment of priors / processing of probabilities (as, fundamentally, one needs to pick the choice which results in simplest - highest probability - overall pattern. If one is overconfident about the pattern they see being the best, one's score is lowered, so poor calibration will hurt that test more).

Even if every self-reported IQ is exactly correct, the average of the self-reported IQ values can still be (and likely will still be) higher than the average of the readership's IQ values.

Consider two readers, Tom and Jim. Tom does an IQ test, and gets a result of 110. Jim does an IQ test, and gets a result of 90. Tom and Jim are both given the option to fill in a survey, which asks (among other questions) what their IQ is. Neither Tom nor Jim intend to lie.

However, Jim seems significantly more likely to decide not to participate; while Tom may decide to fill in the survey as a minor sort of showing off. This effect will skew the average upwards. Perhaps not 30 points upwards... but it's an additional source of bias, independent of any bias in individual reported values.

*-1 points [-]Ah! Good point! Karma for you! Now I will think about whether there is a way to figure out the truth despite this.

Ideas?