On page 694 of the book The Bell Curve by Richard J. Herrnstein and Charles Murray, they mention that the U.S. average on the verbal SAT during the 1980s if all U.S. 17-year-olds took the test, not just the college-bound elite. This data was arrived at using special studies by the college board, where they recruited a nationally representative sample of teens to take the SAT.

But I wanted to know the standard deviation of the math SAT. I knew over a decade ago, but had since forgotten. I reached out to the author of the study Murray cited, but he no longer had a copy of his own paper.

“Why don’t you ask Charles Murray?” somebody said.

“Charles Murray is the most influential social scientist on the planet. He ain’t gona respond to some nobody blogger” I replied.

“But you’re not just any blogger, you’re Pumpkin Person! Never underestimate the power of that brand” they said citing my lucrative advertising deal with wordpress which has been earning money on top of money.

So I sent off a message to the World’s most influential social scientist, not expecting any reply.

He responded IMMEDIATELY.

“Okay, okay, I’ll see if I can find it” he wrote on February 18, 2019.

Precisely 12 minutes later he wrote:

“Verbal mean 375.8, SD 102. Math mean 411.5, SD 109…”

The most influential social scientists on the planet managed to dig up a paper he hadn’t cited in a quarter century with incredible speed and was kind enough to also take an iphone photograph from one of the pages.

But how do we determine the SD for the combined old SAT?  Well since we know the estimated means and SD of the subscales, then the below formula is useful for calculating the composite SD (from page 779 of the book The Bell Curve by Herrnstein and Murray):

formula

r is the correlation between the two tests that make up the composite and σ is the standard deviation of the two tests.

Herrnstein and Murray claim that for the SAT population, the correlation between SAT verbal and SAT math is 0.67. Assuming it would be the same for the general U.S. 17-year-old population, then the 1980s SAT had an SD of 192.8

Some might argue that the 0.67 correlation in the SAT population would underestimate the correlation in the general U.S. 17-year-old population, because the SAT sample is a restricted group and thus should be corrected for range restriction. .

However surprisingly, the math SAT standard deviation for the SAT population was 119 in the 1980s (higher than the 109 in the general population).

Source: Trends in educational achievement
By Daniel M. Koretz, United States. Congressional Budget Office

So assuming that if all U.S. 17-year-olds had taken the SAT in the 1980s, the combined mean would be 787.3 with an SD of 192.8, then a near perfect score of 1590 would have equated to +4.16 SD or an IQ equivalent of 162.

However as I wrote back in March 2018:

The above conversions were based on the assumption that the SAT would have a roughly normal distribution in the general U.S. population, which is likely true for 99% of Americans but likely false at the extremes.

Below is incredibly rare data of the total number of people in 1984 who scored high on the combined SAT.

sat1984

Table IV

We see that of the 3,521,000 Americans born in 1967, roughly 964,739 would grow up to take the SAT at age 17 in 1984.  And of those who did, only 20,443 scored above 1330.  If one assumes, as the great Ron Hoeflin does, that virtually all the top SAT talent took the SAT in 1984 (and whatever shortfall was madeup for by foreign students), then those 20,443 were not just the best of the 964,739 who actually took the SAT, but the best of all 3,521,000 Americans their age.  This equates to the one in 172 level or IQ 138+ (U.S. norms).

Meanwhile, only five of the 3,521,000 U.S. babies born in 1967 would grow up to score 1590+ on the SAT, so 1590+ is one in 704,200 level, or IQ 170+.  However above I claimed that in the mid 1980s, the combined SAT had a mean of 787 and an estimated SD of 220, which means 1590 is “only” +3.65 SD or IQ 155.  Clearly the SAT is not normally distributed at the high extreme, so Z scores start to dramatically underestimate normalized Z scores, and modern IQ scales only care about the latter.

Thus, for extremely high SAT scores obtained in the mid 1980s, please use table V and not formula IV:

Table V:

1984 satiq equivalent(u.s. norms) based on normalized Z scores(sd 15)
1600170+
1590170
1580164
1570163
1560161
1550159
1540157
1530156
1520154
1510153
1500152
1490150
1480150
1470148
1460147
1450146
1440146
1430145
1420144
1410143
1400142
1390141
1380141
1370140
1360139
1350139
1340138
1330137
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