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):

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).

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.

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 sat	iq equivalent(u.s. norms) based on normalized Z scores(sd 15)
1600	170+
1590	170
1580	164
1570	163
1560	161
1550	159
1540	157
1530	156
1520	154
1510	153
1500	152
1490	150
1480	150
1470	148
1460	147
1450	146
1440	146
1430	145
1420	144
1410	143
1400	142
1390	141
1380	141
1370	140
1360	139
1350	139
1340	138
1330	137

Commenter RR has a left a series of comments on this blog denying the very idea of culture fair IQ tests.

For example he writes:

. CULTURE-FREE IQ TESTS ARE AN IMPOSSIBILITY AS ALL HUMAN COGNIZING TAKES PLACE IN A CULTURAL CONTEXT!

This is a tautology not a testable hypothesis. The concept of culture bias needs to be operationalized if it wants scientific credibility.

In the field of psychometrics, a test is typically defined as culturally biased if the regression line predicting school performance from IQ is different in one group than another. For example, if blacks with an IQ of 120 get an A in algebra (on average), but whites with IQs of 120 get only a B, then the test is said to be culturally biased against blacks.

Why? Because if the test is underpredicting the grades of black kids, then it’s probably also underpredicting their intelligence as well.

The literature on predictive bias is extensive and it turns out that by this definition, neither IQ tests nor college admission tests are biased against any visible minority group in the United States. Indeed just the opposite, the tests tend to overpredict black achievement, and thus might even be considered biased against whites!

However this definition assumes that the criterion that test is predicting (i.e. school grades) is itself free from bias, but what could be more culturally loaded than school (the place where culture is explicitly taught).

Perhaps a better criterion than school grades would be real world survival skills. We could dump people in the middle of the woods and see how long they take to find their way out (each person would have a GPS locator they couldn’t use but could be used to find them) or have people compete in mock warfare like paintball. Again, if blacks with an IQ of 120 performed as well as whites with an IQ of 120 on these tasks (equating for practice and physical fitness), then IQ tests are unlikely to be culturally biased. But if 120 IQ blacks dominated 120 IQ whites, then it’s likely the tests are underestimating their intelligence.

Another way of testing for culture bias, as Jensen has alluded to, is to compare groups on physiological measures of intelligence like MRI brain size, evoked brain potentials, nerve conduction speed, neural adaptability reaction time etc. Jensen estimates that a comprehensive battery of such tests would correlate > 0.5 with IQ and this would be ideal for testing for culture bias. If for example, the nation of Nepal scored 3.8 standard deviations below the UK mean on tests like the Raven we would want them to take the physiological measure of intelligence.

The > 0.5 correlation would between IQ and its physiological proxies predicts that Nepal would score at least 3.8(0.5) = 1.9 SD below UK norms on physiological measures, but if they would score much better than this (and they would) we would know that the IQ test was culturally biased against them, and thus is dramatically underestimating their neurology.

We can never say, categorically, than any given test is culture fair, but what we can say is that test A is culture fair with respect to cultures B and C. For example in the 1920s it was proven that hardcore performance tests (similar to Block Design and Object Assembly subtests on the WAIS) are culture fair to people with and without schooling. I wrote the following in 2014:

… excellent research in the 1920s showed that canal boat children who lived a nomadic existence where they were virtually deprived of schooling, showed massive declines in IQ as they got older. Because IQ tests are normed for age, and because these kids were kept out of school they fell further and further behind their chronological age-mates on the type of knowledge that IQ tests measure. Young canal boat kids would have an IQ around 90, but older canal boat kids would have an IQ of 60. However in a footnote on page 1001 of this document, scholar Arthur Jensen writes:

When the canal boat children were tested on nonverbal performance tests, there was much less decline in scores and the average IQ of the children was 82, which is a typical value for unskilled workers, as the canal boat people were. Fewer than 1 in 10 obtained performance IQs below 70, and in fact there was a slight positive correlation between performance IQ and age

This demonstrates that some IQ tests really do come close to the culture fair ideal. People understood that in the 1920s, but decades of post-modern propaganda has brainwashed generations of credulous university students into thinking otherwise.