3 ms·

Can you provide a source for that?

by Recursing 9y ago

thaumasiotes 9y ago
There's really no need; that's exactly what you would expect to see in a thresholded population ("elite players").
- gleb 9y ago
  Please elaborate
  - thaumasiotes 9y ago
    On the assumption that IQ and "chess skills" both contribute to "chess performance", then everyone achieving a threshold of "chess performance", such as being an "elite player", has been selected to have at least a certain sum of "IQ + chess skills". This means that, given high IQ, it's not necessary to have good chess skills to be in the elite group, whereas given low IQ, it is necessary to have good chess skills to be in the elite group. This will establish a negative correlation between "chess skills" and IQ within the elite group even though they are positively correlated overall. Similarly, SAT math and verbal scores tend to be negatively correlated within the student population of any particular university, because universities will reject applicants whose total scores are low, despite the fact that the math and verbal scores are very strongly positively correlated in the larger population.
    - gleb 9y ago
      Thank you, this makes a lot of sense
  - tzahola 9y ago
    Imagine a scatterplot of two correlated variables. Overall there’s a clear tendency for samples to be around the diagonal. Now zoom on the top 1% of the plot and surprise, you’ll see no apparent correlation.
- 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 ago
    I'm assuming he's referring to regression to the mean.
    - thaumasiotes 9y ago
      Regression to the mean would only be relevant if you sampled something twice.
  - thaumasiotes 9y ago
    There 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 ago
      Is this Simpson's Paradox, or something else?
      - thaumasiotes 9y ago
        Something 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.

Can you provide a source for that?

thaumasiotes 9y ago

There's really no need; that's exactly what you would expect to see in a thresholded population ("elite players").

gleb 9y ago
Please elaborate
- thaumasiotes 9y ago
  On the assumption that IQ and "chess skills" both contribute to "chess performance", then everyone achieving a threshold of "chess performance", such as being an "elite player", has been selected to have at least a certain sum of "IQ + chess skills". This means that, given high IQ, it's not necessary to have good chess skills to be in the elite group, whereas given low IQ, it is necessary to have good chess skills to be in the elite group. This will establish a negative correlation between "chess skills" and IQ within the elite group even though they are positively correlated overall. Similarly, SAT math and verbal scores tend to be negatively correlated within the student population of any particular university, because universities will reject applicants whose total scores are low, despite the fact that the math and verbal scores are very strongly positively correlated in the larger population.
  - gleb 9y ago
    Thank you, this makes a lot of sense
- tzahola 9y ago
  Imagine a scatterplot of two correlated variables. Overall there’s a clear tendency for samples to be around the diagonal. Now zoom on the top 1% of the plot and surprise, you’ll see no apparent correlation.
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 ago
  I'm assuming he's referring to regression to the mean.
  - thaumasiotes 9y ago
    Regression to the mean would only be relevant if you sampled something twice.
- thaumasiotes 9y ago
  There 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 ago
    Is this Simpson's Paradox, or something else?
    - thaumasiotes 9y ago
      Something 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.