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Do people know how smart they are? This question motivated a recent meta-analysis of 41 studies (Freund & Kasten, 2012) published in Psychological Bulletin. The authors investigated whether self-reported estimates of cognitive ability associated with psychometric measures of intelligence and found a moderate positive correlation (r = .33), indicating that people do indeed have some idea of how smart they are relative to others. The correlation between self-reported and psychometric intelligence measures was higher in cases when people were asked to evaluate their numerical ability and lower when asked to indicate their general cognitive ability or cognitive abilities other than spatial or verbal ability. People were also more accurate when given a specific comparison group rather than asked to rate their abilities relative to people in general.
Freund, Philipp Alexander, & Kasten, Nadine. (2012). How smart do you think you are? A meta-analysis on the validity of self-estimates of cognitive ability. Psychological Bulletin, 138(2), 296-321. doi: 10.1037/a0026556