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Kindly comments on 2012 Less Wrong Census/Survey - Less Wrong
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What I would do is compute a linear (or otherwise) regression between random number and height guessed. It would have also helped to have a control group to answer the question without anchoring, to determine what sort of background information people have, but that's not strictly necessary.
I would only do that with respondents from the US -- having to convert from metres to feet is likely to weaken the anchoring effect for respondents from elsewhere.
Of course, I'm a respondent from the US and I answered the question by converting from meters. So this approach isn't foolproof.