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Converting SAT and ACT to IQ
A search of ‘SAT to IQ’ on google results in being presented with the website ‘iqcomaprisonsite.com’, which uses this table:
This man has directly converted the SAT percentiles to IQ scores, which is not what should be done. Tests like the ACT and SAT correlate with IQ at about 0.8-0.85 [rca], [my analysis], [emil article], [scholarly article]. The general factor of academic achievement and IQ correlate at about 0.81-0.88 [psychometric test], [GCSE grades]. This discrepancy occurs because they measure different abilities - an IQ test will test many different abilities, while the SAT/ACT only tests verbal/mathematical ability.
In addition, these percentiles are very outdated as the average SAT score has changed over time due to changes in the content of the test.
Instead, the ideal way to do this is to take the percentiles from the current versions of the SAT and then convert those into z-scores and then regress those z-scores by the mean by the estimated regression coefficient. Emil has already done this, but there are two differences in our methods:
He used the mean and SD to calculate the percentiles, while I took the percentiles straight from the table. This does lead to some difference at the high end, with his method yielding a z-score of 2.95 for a perfect SAT score, while mine yields a z-score of 3.29.
I used a regression coefficient of 0.84 while he used a coefficient of 0.8. The difference is negligible, and not worth discussing with the current amount of evidence.
Beyond this, I had to make some quick and dirty statistical adjustments. For instance, some of the SAT scores share a percentile, so I had to space out the percentiles manually by assuming that the distance in percentile between the scores was equal. For instance, if 1390 and 1400 share the 92nd percentile, I assign 1390 a percentile of 91.83 and I assing 1400 a percentile of 92.16. Also, due to the greater numeric spacing between ACT scores, I had to fill in the empty spaces with the nearest score.