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JoshuaZ comments on A few questions on International Rationality - Less Wrong
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While I think I see why the parent was downvoted, I would add that in my experience atheism doesn't correlate very strongly with rationality, insofar as rationaltiy can be said to mean anything. I know plenty of successful scientists who are Christian. I know plenty of atheists who repeatedly make poor life choices. Telling me someone is religious does not help me predict whether I will be able to beat them on any practical contest of wits or reasoning.
The majority of Chinese I have encountered both inside and outside of China believe in traditional Chinese medicine, including the healing powers of chi and all the other aspects that are no better than homeopathy. Of course all of these individuals have claimed to be atheists. There are many flavors of systematic irrationality.
It should do so but it is only a weak predictor. See for example,the GSS data which shows a correlation between vocab (as measured by WORDSUM) and lack of belief in God. Vocabulary is a predictor of general intelligence (high correlation with IQ and Wonderlic for example) whether or not one one corrects for education level (although some complicated things happen in terms of parental education level). The GSS is not the only data set which shows this sort of pattern. The result is weak but statistically robust.
BTW, correlation is not an equivalence relation, especially weak correlation.
Er, of course not. What's your point?
Your argument was atheism is weakly correlated with vocab. Vocab is weakly correlated with intelligence. Therefore, atheism is weakly correlated with intelligence.
Ah, I see your point. However, a) vocab is highly correlated with intelligence, not weakly so, b) vocab is not just highly correlated with a single intelligence metric, but is correlated with such in a variety of different metrics of intelligence. While it is possible to construct variables such that A and B are correlated, with B and C correlated, and A and C anti-correlated, it is quite difficult to do so with a large set of distinct variables that all have such correlations with each other and have a single pair be anti-correlated, especially when one has the same set of correlations even when one controls for a variety of other variables. Moreover, as a probabilistic matter if one as three variables with two pairs correlated, it is much more likely that the remaining pair will be correlated than anti-correlated, assuming that variables don't have too pathological a distribution.
Where you you get that? The intended probability space isn't clear, but if I take three random directions in N-dimensional space for large N, I find that the chance of two pairs having an angle less than pi/2 and the third an angle greater than pi/2 is about 1.4 times the chance of all three being less than pi/2. The ratio rises to about 3 if I add the requirement that the corresponding correlations are in the range +/- 0.8 (the upper liit of correlations generally found in psychology).
Hmm, that's a good point. I'm aware vaguely of theorems that say what I want but I don't have any references or descriptions off hand. It may just be that one is assuming somewhat low N, but that would be in this sort of context not helpful. I do seem to remember that some version of my statement is true if the variables match bell curves, but I'm not able at the moment to construct or find a precise statement. Consider the claim withdrawn until I've had more time to look into the matter.