4 ms·
Maybe I'm just not that bright but I would expect to see a positive correlation between IQ and exceptional chess ability.
by lgas 9y ago
Maybe I'm just not that bright but I would expect to see a positive correlation between IQ and exceptional chess ability.
- jcranmer 9y agoI'm assuming he's referring to regression to the mean.
- thaumasiotes 9y agoRegression to the mean would only be relevant if you sampled something twice.
- thaumasiotes 9y agoThere is a positive correlation between IQ and chess ability. That does not imply that there should be a positive correlation between IQ and chess ability in a group that has been selected for strong performance in chess.
- 0xcde4c3db 9y agoIs this Simpson's Paradox, or something else?
- thaumasiotes 9y agoSomething else. https://en.wikipedia.org/wiki/Statistical_conclusion_validity#Restriction_of_range https://en.wikipedia.org/wiki/Statistical_conclusion_validit... > Restriction of range, such as floor and ceiling effects or selection effects, reduce the power of the experiment, and increase the chance of a type II error.[5] This is because correlations are attenuated (weakened) by reduced variability If you want to try this for yourself, try generating some fake SAT scores: (a,b) pairs where a and b are normally distributed with mean 500 and sd 100, and where a and b correlate at about 0.8. Then, from your unbiased data set, select all the pairs for which 1600 >= a + b >= 1300, and check the correlation of a with b in the new, smaller data set. Just examining this as a thought experiment, you can see that someone with an 800 math score might have a verbal score anywhere from 500 to 800. If we lower the math score, our expectation for the verbal score rises -- someone with a 600 math score will have a verbal score between 700 and 800. That is the basis of the negative correlation in the subgroup, but it's purely an artifact of the way we chose to label data points as being in or out of the subgroup.
- thaumasiotes 9y agoPast the edit window: the 600 math score will of course imply a verbal score between 700 and 1000; the data I described has no caps on individual scores.