Judging by the internet, law students have long wondered how to convert LSAT scores into IQ equivalents.  American IQ tests are typically designed such that the distribution of American IQs has a mean of 100 and a standard deviation (SD) of 15.  By contrast, the LSAT has been designed so the median LSAT taker has a mean score of around 151.5 and an SD of 10.  But since the average LSAT taker is presumabley smarter than the average American, one can’t simply equate the means and SDs.  A simple solution is to assume LSAT takers are equivalent to American college graduates.  The WAIS-III demographic norms report that Americans with 16+ years of education have a mean IQ of 112.8 (SD = 13.7).  From here one can assume that an LSAT score of 151.5 equals an IQ of 112.8, and each 10 LSAT points above or below the LSAT median equals 13.7 IQ points.  We’ll call this formula one:

IQ =  1.37(LSAT score) – 94.755

This formula assumes of course that the score distribution of both LSAT takers and college grads are roughly normal and that both groups have roughly the same IQ distribution.  Some might argue that LSAT takers are more intelligent than college grads (on average) since they are considering an additional degree.  On the other hand, there are probably a lot of people who take the LSAT under the mistaken assumption that they will go to law school, only to later discover they’re not smart enough to finish even their undergrad degree.  So on balance, assuming LSAT takers are as smart as college grads seems reasonable.

Another method is to find a sample of LSAT takers who have also reported their scores on some other validated intelligence test.  For example, I found a blog where the SAT scores of dozens of LSAT test takers were reported.  I don’t know how reliable the data is because it’s self-reported (in at least one case by someone other than the test takers themselves).  Nonetheless, I did my best to document all the score pairs (excluding one person because he took the SAT at 16 and the LSAT at 31, suggesting he had taken the old (pre-1995 SAT) which gave much lower scores).  Here is the raw data:
SAT, LSAT

1390, 161
1290, 164
1020, 145
1420, 167
1520, 163
1540, 178
1520, 174
1270, 175
1360, 177
1330, 167
1400, 163
1530, 173
1550, 167
1040, 169
1360, 157
1510, 176
1410, 176
1370, 169
1460, 170
1250, 164
1360, 165
1390, 160
1270, 172
1500, 166
1470, 173
1360, 177
1500, 166
1020, 172

The correlation between LSAT and SAT scores is +0.33, which sounds low for two tests that supposedly both accurately measure IQ, but keep in mind that the data is self-reported, the sample size is not huge, a few of the respondents may have reported old SAT scores (despite my effort to omit them), and the sample probably suffers from range restriction.

Nonetheless, the SAT distribution of this sample had a mean of 1372 and an SD of 147, which according to my research, would equate to a mean IQ of 133 and an SD of 10.    Meanwhile the LSAT distribution of this sample has a mean of about 168 and an SD of about 7.  According to the psychometric theory of equipercentile equating (score pairing), one can thus assume an LSAT of 168 equals an IQ of 133 and every 7 LSAT points above or below a 168 LSAT equates to 10 IQ points.  We’ll call this formula two:

IQ = 1.43(LSAT score) – 107

Even though both formulas were made using different data, they give similar results, suggesting they are accurate.

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