[PLEASE PLACE ALL OFF-TOPIC COMMENTS IN THE MOST RECENT OPEN THREAD.  THEY WILL NOT BE POSTED IN THIS THREAD]

[WARNING:  THIS ARTICLE IS NOT AN ENDORSEMENT OF THE OLD SAT AS AN IQ TEST, IT SIMPLY EXPLAINS WHAT YOUR IQ ON THE OLD SAT WOULD BE IF THE SAT WERE AN IQ TEST.  THE LINE BETWEEN IQ AND ACHIEVEMENT TESTS IS PARTLY SEMANTIC]

Many high IQ societies accept specific scores from the pre-1995 SAT for admission, as if all SATs taken before the infamous recentering in April 1995 had the same meaning.  And yet Mensa, which only accepts the smartest 2% of Americans on a given “intelligence test” makes a curious distinction.  Prior to 9/30/1974, you needed an SAT score of 1300 to get into Mensa, yet from 9/30/1974 to 1/31/1994, you needed a score of 1250.

Well, that’s odd I thought, since all SAT scores from the early 1940s to 1994 are supposedly scaled to reflect the same level of skill, why did it suddenly become 50 SAT points easier to be in the top 2% in 1974?  And if such an abrupt change can occur in 1974, why assume stability every year before and since?  It didn’t make any sense.

And I wasn’t the only one who was wondering.  Rodrigo de la Jara, owner of iqcomparisonsite.com, writes:

If someone knows why they have 1300 for scores before 1974, please send an email to enlighten me.

 

The mean verbal and math SAT scores, if ALL U.S. 17-year-olds had taken the old SAT

To determine how the old SAT maps to IQ I realized I couldn’t rely on high IQ society cut-offs.  I need to look at the primary data.  Now the first place to look was at a series of secret studies the college board did in the 1960s, 1970s, and 1980s.  These studies gave an abbreviated version of the SAT to a nationally representative sample of high school juniors.  Because very few Americans drop out of high school before their junior year, a sample of juniors came close to representing ALL American teens, and then scores were statistically adjusted to show how virtually ALL American teens would average had they taken the SAT at 17. The results were as follows (note, these scores are a lot lower than the actual mean SAT scores of people who take the SAT, because they also include all the American teens who usually don’t):

 

The verbal and math standard deviations if ALL U.S. 17-year-olds had taken the old SAT

 Once I knew the mean SAT scores if ALL American teens had taken the SAT at 17 in each of the above years, I needed to know the standard deviations.   Although I knew the actual SDs for 1974, I don’t know them for other years, so for consistency, I decided to use estimated SDs.

According to the book The Bell Curve, since the 1960s, virtually every single American teen who would have scored 700+ on either section of the SAT, actually did take the SAT (and as Ron Hoeflin has argued, whatever shortfall there’d be would be roughly balanced by brilliant foreign test takers).  This makes sense because academic ability is correlated with taking the SAT, so the higher the academic ability, the higher the odds of taking the SAT, until at some point, the odds likely approach 100%.

Thus if 1% of all American 17-year-olds both took the SAT and scored 700+ on one of the subscales, then we know that even if 100% of all U.S. 17-year-olds had taken the SAT, still only 1% would have scored 700+ on that sub-scale.  By using this logic, it was possible to construct a graph showing what percentage of ALL U.S. 17-year-olds were capable of scoring 700+ on each sub-scale, each year:

 

 

What the above graph seems to show is that in 1966, a verbal score of 700+ put you in about the top 0.75% of all U.S. 17-year-olds, in 1974 it put you around the top 0.28%, in 1983 about the top 0.28% and in 1994 about the top 0.31%.

Similarly, scoring 700+ on math put you around the top 1.25% in 1966, the top 0.82% in 1974, the top 0.94% in 1983, and the top 1.52% in 1994.

Using the above percentages for each year, I determined how many SDs above the U.S. verbal or math SAT mean (for ALL 17-year-olds) a 700 score would be on a normal curve, and then divided the difference between 700 and each year’s mean (table I) by that number of SDs, to obtain the estimated SD. Because table I did not have a mean national score for 1994, I assumed the same means as 1983 for both verbal and math.  This gave the following stats:

 

Calculating verbal and math IQ equivalents from the old SAT

Armed with the stats in chart III, it’s very easy for people who took the pre-recentered SAT to convert their subscale scores into IQ equivalents.  Simply locate the means and SDs from the year closest to when you took the PRE-RECENTERED SAT, and apply the following formulas:

Formula I

Verbal IQ equivalent (U.S. norms)  = (verbal SAT – mean verbal SAT/verbal SD)(15) + 100

Formula II

Math IQ equivalent (U.S. norms) =  (math SAT – mean math SAT/math SD)(15) + 100

 

Calculating the mean and SD of the COMBINED SAT if all U.S. 17-year-olds had taken the test

Now how do we convert combined pre-recentered SATs (verbal + math) into IQ equivalents.  Well it’s easy enough to estimate the theoretical mean pre-recentered SAT for each year by adding the verbal mean to the math mean.  But estimating the standard deviation for each year is trickier because we don’t know the frequency for very high combined scores for each year, like we do for sub-scale scores (see Chart II).  However we do know it for the mid 1980s. In 1984,  23,141 people scored 1330+ on the combined SAT.  Of course most American teens never write the SAT, so we’ll never know precisely how many could have scored 1330+, but Hoeflin argued that virtually 100% of teens capable of scoring extremely high on the SAT did so, and whatever shortfall there might be was negated by bright foreign test-takers.

Thus, a score of 1330+ is not merely the 23,141 best among nearly one million SAT takers that year, but the best among ALL 3,521,000 Americans who were 17 in 1984.  In other words, 1330 put you in the top 0.66% of all U.S. 17-year-olds which on the normal curve, is +2.47 SD.  We know from adding the mean verbal and math for 1983 in Chart I, that if all American 17-year-olds had taken the SAT in 1983, the mean COMBINED score would have been 787, and if 1330 is +2.47 SD if all 17-year-olds had taken it, then the SD would have been:

(1330 – 787)/2.47 = 220

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

Formula III

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

Formula III requires you to know the correlation between the two subscales.  Herrnstein and Murray claim that for the entire SAT population, the correlation between SAT verbal and SAT math is 0.67 however we’re interested in the correlation if ALL American young adults had taken the old SAT, not just the SAT population.

However since we just estimated that the SD of the combined SAT if all 17-year-olds took the SAT in 1983 would have been 220, and since we know from Chart III that the 1983 verbal and math SDs if all 17-year-olds had taken the SAT would have been 116 and 124 respectively, then we can deduce what value of r would cause Formula III to equal the known combined SD of 220.  That value is 0.68 (virtually the same as in the SAT population)*

Now that we know the correlation between the verbal and math SAT if all U.S. 17-year-olds had taken the SAT would have been 0.68 in 1983, and if we assume that correlation held from the 1960s to the 1990s, using the sub-scale SDs in chart III, we can apply Formula III to determine the combined SDs for each year, and of course the combined mean for each year is just  the sum of the verbal and math means in chart III.

 

 

Calculating full-scale IQ equivalents from the old SAT

Armed with the stats in Chart IV, it’s very easy for people who took the pre-recenetered SAT to convert their COMBINED scores into IQ equivalents.  Simply locate the means and SDs from the year closest to when you took the PRE-RECENTERED SAT, and apply the following formula:

Formula IV

Full-scale IQ equivalent (U.S. norms)  = (combined SAT – mean combined SAT/combined SD)(15) + 100

*Note: the IQ equivalent of SAT scores above 1550 or so will be underestimated by this formula because of ceiling bumping.  See below for how to convert stratospheric scores.

Was Mensa wrong?

Based on chart IV, it seems Mensa is too conservative when it insists on SAT scores of 1300 prior to 9/30/1974 and scores of 1250 for those who took it from 9/30/1974 to 1/31/1994.  Instead it seems that the Mensa level (top 2% or + 2 SD above the U.S. mean) is likely achieved by scores of 1250 for those who took the SAT close to 1966, and 1216 for those who took it closer to 1974.  For those who took the pre-recentered SAT closer to 1983 or 1994, it seems Mensa level was achieved by scores of 1227 and 1249 respectively.

Of course all of my numbers assume a normal distribution which is never perfectly the case, and it’s also possible that the 0.68 correlation between verbal and math I found if all 17-year-olds took the SAT in 1983 could not be generalized to other years, so perhaps I’m wrong and Mensa is right.

And in Mensa’s defense, they were probably erring on the conservative side (better to turn away some Mensa level scores, than accept non-Mensa level scores).  But it would be nice to know how they arrived at their numbers because it’s obviously way too simplistic to have only two Mensa cut-offs (one before and one after 9/30/74) for all the decades the pre-re centered SAT was used, given the fluctuations that occurred from the 1960s to the 1990s.

Extreme SAT scores in the mid 1980s

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.

 

 

 

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

What if you scored extremely high on the old SAT in the 1990s, 1970s, or 1960s?

No precise solution is possible for these people until I get more data, but my tentative advice is to map your scores to the mid 1980s distribution and then use table V.  For example, Bill Gates took the SAT circa 1973 and reportedly scored 1590.  According to table III, 1590 was +3.68 SD in the mid 1970s, since the mean and estimated SD were 770 and 223 respectively .  But in the mid 1980s, the mean and estimated SD were 787 and 220 respectively, so +3.68 SD would be 1597 which converts to an IQ of 170+ according to table V.

By contrast Chuck Schumer reportedly scored a perfect 1600 in the mid-1960s (though Steve Sailer is skeptical) which would put him at +3.43 SD according to table III.  +3.43 equals 1542 in the mid 1980s according to table III, and that equates to IQ 157 in table V.

I am not suggesting that a 1600 in the mid-1960s reflects the same level of academic skill as 1542 in the mid-1980s, (the college board worked very hard to keep old SAT scores equal over the decades) but they may reflect the same percentile, relative to the general U.S. population of 17-year-olds, assuming the shape of the distribution stayed roughly constant, and the correlation between verbal and math did too.  Because IQ is never an absolute measure of intelligence, only a measure of where one ranks compared to his age mates in a specific population (typically the general population of the U.S. or U.K. or just the white populations thereof)

*in a previous article I estimated a 0.36 general population correlation between verbal and math by estimating the combined SD from a freakishly high point on the curve, but now that I have more data,  I prefer to do the calculations from a less extreme percentile given the ceiling bumping that distorts the SAT distribution at the extremes.

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

 

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 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+.

Meanwhile a national norm study found that if all Americans 17-year-olds took the SAT in the mid 1980s, not just the college bound elite, the average score would have been 787, so 787 implies an IQ of 100.

Armed with these three data points:

1590+ = IQ 170+

1330 = IQ 138

787 = IQ 100

Sadly, because the line is not linear, but rather positively accelerated (because of ceiling bumping on the SAT) no simple equation could be created, so I made a polynominal equating 1984 combined SAT to IQ (not sure how accurate this is since I only used 3 data points):

IQ = 114.13423524934914 – 0.06999703795283904(SAT) + 0.00006612121953074045(SAT)²

In 1993, The New York Times reported:

On the verbal test, the average scores of black students rose to 353 this year, up 1 point from last year and 21 points from 1976. In comparison, the average score of white students was 444 this year, up 2 from last year and down 7 points from 1976.

I estimate that if all American 17-year-olds (not just the college-bound elite) had taken the SAT in the mid 1970s and mid 1990s, the verbal SAT would have had a mean of 368 (SD = 119) and 376 (SD = 119) respectively.

From here we can deduce that the mean verbal IQ (U.S. norms) of college bound blacks (as measured by the SAT) increased from 95 in the mid 1970s to 97 in the mid 1990s.  By contrast, the mean verbal IQ of college bound whites dropped from 110 to 109 over the same period.

 

On the math test, the average score of black students rose to 388 this year, up 3 points from last year and up 34 points from 1976. In comparison, the average score of white students was 494, up 3 points from last year and up 1 point from 1976.

I estimate that if all American 17-year-olds (not just the college-bound elite) had taken the SAT in the mid 1970s and mid 1990s, the math SAT would have had a mean of 402 (SD = 124) and 411 (SD = 133) respectively.

From here we can deduce that the mean math IQ (U.S. norms) of college bound blacks (as measured by the SAT) increased from 94 in the mid 1970s to 97 in the mid 1990s.  By contrast, the mean math IQ of college bound whites dropped from 111 to 109 over the same period.

From the article it can be deduced that the combined score (verbal + math) of college bound blacks increased from 686 in the mid 1970s to 741 in the mid 1990s.  By contrast, the combined score for college bound whites dropped from 941 in the mid 1970s to 938 in the mid 1990s.

I estimate that if all American 17-year-olds (not just the college-bound elite) had taken the SAT in the mid 1970s and mid 1990s, the combined SAT would have had a mean of 770 (SD = 200) and 787 (SD = 208) respectively.

From here we can deduce that the mean full-scale IQ (U.S. norms) of college bound blacks (as measured by the SAT) increased from 94 in the mid 1970s to 97 in the mid 1990s.  By contrast, the mean math IQ of college bound whites dropped from 113 to 111 over the same period.

So the bottom line is that among college-bound 17-year-olds, the black-white IQ gap (as measured by the SAT) shrunk from 19 points to 14 points as measured by U.S. norms, or 20 points to 14 points as measured by U.S. white norms.

This is the same story as told by the NAEP, which showed an even more dramatic reduction of the black-white IQ gap in the general U.S. population (not the college bound elite).  However no such reduction was observed on the Wechsler intelligence scales where the black-white gap has remained 15 points from the 1970s to the 2000s.

Tentative conclusion: scholastic tests gave biased measures of black IQ at least until the mid 1970s, but by the mid 1990s, they gave results commensurate with official IQ tests like the Wechsler.  Black Americans who use the scholastic tests to estimate their IQs should add 5-10 points if said tests were taken before 1975 or so.

 

 

Arthur Jensen noted how measuring a trait indirectly can often lead to misleading conclusions.  He compared it to measuring a person’s height by measuring the height of their shadow.  The correlation between actual height and shadow height could be extremely strong under controlled conditions, but when the position of the sun moves, the measurements become meaningless.

I think giving someone an official IQ test like the Wechsler, is somewhat analogous to measuring their height directly on a stadiometer, while giving someone the SAT is like measuring height from one’s shadow.  Because you’re not directly observing how fast one can learn like you do on many Wechsler subtests, you’re indirectly inferring it from how much they know.

Of course shadow measurements can be extremely accurate.  If everyone is measured at the same time of day,  shadow height will correlate near perfectly with actual height, and when everyone takes the SAT with a similar academic background, the SAT correlates near perfectly with general intelligence (the g factor) as found in a sample from the University omTexas at San Antonio.

.However in America, there’s a strong class divide, so you have the upper class, who studies AP algebra, geometry, calculus and Shakespeare, and then you have the lower class, who attends working class schools and is dissuaded from going to college at all.  The lower class tend not to even take the SAT, but when they do, they tend to score below their genetic potential.  For example Bill Cosby had an IQ equivalent around 80 on the SAT despite being very intelligent on an official IQ test and known for his comic wit.  Other quick comic minds from working class backgrounds who underperformed on the SAT include Rosie O’Donnell and Howard Stern.

A good analogy would be the upper class has their shadow height measured in the morning where shadows are quite long.  The lower class has their shadow height measured in the afternoon, when shadow height is quite short.  Now within each class, shadow height may correlate near perfectly with stadiometer height, just as within each class, the SAT may correlate near perfectly with official IQ.  But when the ENTIRE population is aggregated, the correlation between shadow height and stadiometer height plummets because of the class inequality, just like the correlation between SATs and official IQ scores plummet.

This explains why people who are 46 IQ points above the U.S. mean on the new SAT regress to only 21 IQ points above the U.S. mean on the Raven IQ test, suggesting the new SAT correlates 21/46 = 0.46 with the Raven in the general U.S. population.  Arthur Jensen noted that the correlation between two tests is a product of their factor loadings, so assuming the only factor the SAT and Raven share is g, then dividing their 0.46 correlation by the 0.68 g loading of the Raven tells us the SAT also has a g loading of 0.68, or roughly 0.7 if you like round numbers.

A g loading of 0.7 is not low, and tells us the SAT is a reasonable proxy for g in the general U.S. population, but it’s nowhere near the 0.9 g loading the SAT enjoys in more socioeconomically homogenous subsets of America such as students at the University of Texas at San Antonio.  This is because the general U.S. population is analogous to people having their shadow heights measured at different times of day, while the students at a given local university are analogous to students all having their shadow height measured at the same time of day, thus maximizing the correlation between shadow height and real height. 

I apologize to my readers for recycling so much old material, but certain crucial issues must be resolved before we can move forward knowledgeably.

In this post, I summarize all I have learned to date about how much high SAT performers regress to the mean when faced with official IQ tests and what this implies about the SAT’s correlation with said tests.  Some of the data may contradict previous posts, as new information has come to light, causing me to revise old numbers.

Study I: New SAT vs the Raven

A study by Meredith C. Frey and Douglas K. Detterman found a 0.48 correlation between the re-centered SAT and the Raven Progressive Matrices in a sample of 104 university undergrads, but after correcting for range restriction, they estimate the correlation to be 0.72 in a less restricted sample of college students.  I don’t buy it, but I’m not interested in how well the re-centred SAT would correlate with the Raven among college students, but among ALL American young adults. (including the majority who never took the SAT).

Using the Frey and Detterman data, I decided to look at the Raven scores of those who scored 1400-1600 on the re-centred SAT, because 1500 on the new SAT (reading + math) corresponds to an IQ of 143 (U.S. white norms), which is 46 points above the U.S. mean of 97. Now if the new SAT correlated 0.72 or higher among ALL American adults, we’d expect their Raven scores to only regress to no less than 72% as far above the U.S. mean, so 0.72(46) + 97 = IQ 130.

I personally looked at the scatter plot carefully and did my best to write down the RAPM IQs of every single participant with an SAT score from 1400-1600. This was an admittedly subjective and imprecise exercise given how small the graph is, but I counted 38 top SAT performers and these were their approximate RAPM IQs: 95, 102, 105, 108, 108, 110, 110, 113, 113, 113, 113, 113, 117, 117, 117, 117, 117, 120, 120, 120, 122, 122, 128, 128, 128, 128, 134, 134, 134, 134, 134, 134, 134, 134, 134, 134, 134, 134

The median IQ is 120, and it does not need to be converted to white norms because the Raven was normed in lily white Iowa circa 1993, but as commenter Tenn noted, I should have perhaps corrected for the Flynn effect since the norms were ten years old at the time of the study.  Correcting for the Flynn effect reduces the median to 118 (U.S. white norms) which is 21 points above the U.S. mean of 97.

For people who are 46 IQ points above the U.S. mean on the new SAT to regress to only 21 points above the U.S. mean, suggests the new SAT correlates 21/46 = 0.46 with the Raven in the general U.S. population.

Study II: New SAT vs the abbreviated WAIS-R

Harvard is the most prestigious university in the World with an average SAT score in the stratosphere, thus it’s interesting to ask how Harvard students perform on an official IQ test. The best data on the subject was obtained by Harvard scholar Shelley H Carson and her colleagues who had an abbreviated version of the WAIS-R given to 86 “Harvard undergraduates (33 men, 53 women), with a mean age of 20.7 years (SD 3.3)… All were recruited from sign-up sheets posted on campus. Participants were paid an hourly rate…The mean IQ of the sample was 128.1 points (SD 10.3), with a range of 97 to 148 points.”

It should be noted however that the WAIS-R was published in 1981, and that the norms were collected from 1976 to 1980. Carson’s study was published in 2003, so presumably the test norms were 25 years old.

James Flynn cites data showing that from WAIS-R norms (circa 1978) to WAIS-IV norms (circa 2006) the vocabulary and spatial construction subtest (used in the abbreviated WAIS-R) increased by 0.53 SD and 0.33 SD respectively. These gains would result in the composite score of the abbreviated WAIS-R becoming obsolete at a rate of 0.26 IQ points per year, meaning the Harvard students’ scores circa 2003 were 6.5 points too high. This reduces the mean IQ of the sample to 121.6 (U.S. norms) which is about 120 (U.S. white norms); 23 points above the U.S. mean of 97 (white norms).

However Harvard’s median re-centered SATs of 1490 equate to IQ 143 (U.S. white norms) which is 46 points above the U.S. mean of 97.  Assuming the sampled Harvard students were cognitively representative of Harvard and assuming Harvard is cognitively representative of all 1490 SAT Americans, the fact they regressed from being 46 IQ points above average on the SAT to 23 IQ points above average on the abbreviated WAIS-R, suggests the re-centered SAT correlates 23/46 = 0.5 with the abbreviated WAIS-R.

Study III:  Old SAT vs the full original WAIS

Perhaps the single best study was referred to me by a commenter named Andrew.  In this study, data was taken from the older more difficult SAT, and participants took the full-original WAIS.  In this study, six samples of  seniors from  the extremely prestigious Dartmouth (the 12th most selective university in America) averaged 1357 on the SAT just before 1974. Based on my latest research, an SAT score of 1357 circa 1974 would have equated to an IQ of 144 (U.S. norms); 143 (U.S. white norms).  Because this is much higher than previously thought; the degree of regression is quite devastating.

Assuming these students are typical of high SAT Americans, it is interesting to ask how much they regress to the mean on various subtests of the WAIS.

Averaging all six samples together, and then adjusting for the yearly Flynn effect from the 1950s through the 1970s (see page 240 of Are We Getting Smarter?) since the WAIS was normed circa 1953.5 but the students were tested circa 1971.5, then converting subtest scaled scores to IQ equivalents, in both U.S. norms and U.S. white norms (the 1953.5 norming of the WAIS included only whites), we get the following:

	iq equivalent (u.s. norms)	iq equivalent (u.s. white norms)	estimated correlation with sat in the general u.s. population inferred from regression to the mean from SAT IQ 44 points above U.S. mean.
sat score	144	143	44/44 = 1.0
wais information	128.29	127.2	28.29/44 = 0.64
wais comprehension	122.22	120.9	22.22/44 = 0.51
wais arithmetic	120.37	119	20.37/44 = 0.46
wais similarities	119.16	117.75	19.16/44 = 0.44
wais digit span	117.37	115.9	17.37/44 = 0.39
wais vocabulary	125.93	124.75	25.93/44 = 0.59
wais picture completion	105.87	104	5.87/44 = 0.13
wais block design	121.82	120.5	21.82/44 = 0.50
wais picture arrangement	108.33	106.55	8.33/44 = 0.19
wais object assembly	113.65	112.05	13.65/44 = 0.31
wais verbal scale	126	125	26/44 = 0.59
wais performance scale	116	114	16/44 = 0.36
wais full-scale	123	122	23/44 = 0.52

Conclusion

In three different studies (New SAT vs Raven, New SAT vs abbreviated WAIS-R, Old SAT vs WAIS), people averaging exceptionally high SAT scores averaged only 46%, 50%, or 52%, respectively, as far above the U.S. mean on the official IQ tests as they did on the SAT, suggesting the SAT (old or new), only correlates about 0.5 with official IQ tests.  Correlations in the range of 0.5 are about all you’d expect most educational measures (school grades, years of school) to correlate with IQ, but it’s a surprisingly low correlation given that some consider the SAT to be more than a mere education measure, but an IQ test itself.  So either the SAT is NOT equivalent to an IQ test, or it’s only equivalent to an IQ test among people with similar educational backgrounds, or my method of inferring correlations from the degree of regression is giving misleading results (perhaps because Spearman’s Law of Diminishing Returns is flattening the regression slope at high levels or because of ceiling bumping on the tests involved).

The potentially low correlation between the SAT (and presumably other college admission tests like the GRE, LSAT, etc) with official IQ has some positive implications.  It means that to whatever extent IQ and success are correlated in America, the correlation is a natural consequence of smart  people adapting to their environment, and not the artificial self-fulfilling prophecy of a man-made testocracy.

It also suggests that there’s no substitute for a real IQ test given by a real psychologist with blocks, cartoon pictures, jig-saw puzzles, and open-ended questions.  I can see David Wechsler, chuckling from the grave, saying “I told you so.”

Many high IQ societies accept specific scores from the pre-1995 SAT for admission, as if all SATs taken before the infamous recentering in April 1995 had the same meaning.  And yet Mensa, which only accepts the smartest 2% of Americans on a given “intelligence test” makes a curious distinction.  Prior to 9/30/1974, you needed an SAT score of 1300 to get into Mensa, yet from 9/30/1974 to 1/31/1994, you needed a score of 1250.

Well, that’s odd I thought, since all SAT scores from the early 1940s to 1994 are supposedly scaled to reflect the same level of skill, why did it suddenly become 50 SAT points easier to be in the top 2% in 1974?  And if such an abrupt change can occur in 1974, why assume stability every year before and since?  It didn’t make any sense.

And I wasn’t the only one who was wondering.  Rodrigo de la Jara, owner of iqcomparisonsite.com, writes:

If someone knows why they have 1300 for scores before 1974, please send an email to enlighten me.

 

The mean verbal and math SAT scores, if ALL U.S. 17-year-olds had taken the old SAT

To determine how the old SAT maps to IQ I realized I couldn’t rely on high IQ society cut-offs.  I need to look at the primary data.  Now the first place to look was at a series of secret studies the college board did in the 1960s, 1970s, and 1980s.  These studies gave an abbreviated version of the SAT to a nationally representative sample of high school juniors.  Because very few Americans drop out of high school before their junior year, a sample of juniors cam close to representing ALL American teens, and then scores were statistically adjusted to show how virtually ALL American teens would average had they taken the SAT at 17. The results were as follows (note, these scores are a lot low than the actual mean SAT scores of people who take the SAT, because they also include all the American teens who usually don’t):

The verbal and math standard deviations if ALL U.S. 17-year-olds had taken the old SAT

 Once I knew the mean SAT scores if ALL American teens had taken the SAT at 17 in each of the above years, I needed to know the standard deviations.   Although I knew the actual SDs for 1974, I don’t know them for other years, so for consistency, I decided to use estimated SDs.

According to the book The Bell Curve, since the 1960s, virtually every single American teen who would have scored 700+ on either section of the SAT, actually did take the SAT (and as Ron Hoeflin has argued, whatever shortfall there’d be would be roughly balanced by brilliant foreign test takers).  This makes sense because academic ability is correlated with taking the SAT, so the higher the academic ability, the higher the odds of taking the SAT, until at some point, the odds likely approach 100%.

Thus if 1% of all American 17-year-olds both took the SAT and scored 700+ on one of the subscales, then we know that even if 100% of all U.S. 17-year-olds had taken the SAT, still only 1% would have scored 700+ on that sub-scale.  By using this logic, it was possible to construct a graph showing what percentage of ALL U.S. 17-year-olds were capable of scoring 700+ on each sub-scale, each year:

What the above graph seems to show is that in 1966, a verbal score of 700+ put you in about the top 0.75% of all U.S. 17-year-olds, in 1974 it put you around the top 0.28%, in 1983 about the top 0.28% and in 1994 about the top 0.31%.

Similarly, scoring 700+ on math put you around the top 1.25% in 1966, the top 0.82% in 1974, the top 0.94% in 1983, and the top 1.52% in 1994.

Using the above percentages for each year, I determined how many SDs above the U.S. verbal or math SAT mean (for ALL 17-year-olds) a 700 score would be on a normal curve, and then divided the difference between 700 and each year’s mean (Chart I) by that number of SDs, to obtain the estimated SD. Because Chart I did not have a mean national score for 1994, I assumed the same means as 1983 for both verbal and math.  This gave the following stats:

Calculating verbal and math IQ equivalents from the old SAT

Armed with the stats in chart III, it’s very easy for people who took the pre-recentered SAT to convert their subscale scores into IQ equivalents.  Simply locate the means and SDs from the year closest to when you took the PRE-RECENTERED SAT, and apply the following formulas:

Formula I

Verbal IQ equivalent (U.S. norms)  = (verbal SAT – mean verbal SAT/verbal SD)(15) + 100

Formula II

Math IQ equivalent (U.S. norms) =  (math SAT – mean math SAT/math SD)(15) + 100

 

Calculating the mean and SD of the COMBINED SAT if all U.S. 17-year-olds had taken the test

Now how do we convert combined pre-recentered SATs (verbal + math) into IQ equivalents.  Well it’s easy enough to estimate the theoretical mean pre-recentered SAT for each year by adding the verbal mean to the math mean.  But estimating the standard deviation for each year is trickier because we don’t know the frequency for very high combined scores for each year, like we do for sub-scale scores (see Chart II).  However we do know it for the mid 1980s. Ron Hoeflin claimed that out of a bit over 5,000,000 high-school seniors who took the SAT from 1984 through 1988, only 1,282 had combined scores of 1540+.

Hoeflin has argued that even though only a third of U.S. teens took the SAT,  virtually 100% of teens capable of scoring extremely high on the SAT did so, and whatever shortfall there might be was negated by bright foreign test-takers.

Thus, a score of 1540+ is not merely the 1,282 best among 5 million SAT takers, but the best among ALL fifteen million Americans who were 17 years-old anytime from 1984 through 1988.  In other words, 1540 was a one in 11,700 score, which on the normal curve, is +3.8 SD.  We know from adding the mean verbal and math for 1983 in Chart I, that if all American 17-year-olds had taken the SAT in 1983, the mean COMBINED score would have been 787, and if 1540 is +3.8 SD if all 17-year-olds had taken it, then the SD would have been:

(1540 – 787)/3.8 = 198

But how do we determine the SD for the combined old SAT for other years?  Well since we know the estimated means and SD of the subscales, then Formula III 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.

However Formula III requires you to know the correlation between the two subscales.  Herrnstein and Murray claim that for the entire SAT population, the correlation between SAT verbal and SAT math is 0.67 however we’re interested in the correlation if ALL American young adults had taken the old SAT, not just the SAT population.

However since we just estimated that the SD of the combined SAT if all 17-year-olds took the SAT in 1983 would have been 198, and since we know from Chart III that the 1983 verbal and math SDs if all 17-year-olds had taken the SAT would have been 116 and 124 respectively, then we can deduce what value of r would cause Formula III to equal the known combined SD of 198.  Shockingly, that value is only 0.36!

Now that we know the correlation between the verbal and math SAT if all U.S. 17-year-olds had taken the SAT would have been only 0.36 in 1983, and if we assume that correlation held from the 1960s to the 1990s, using the sub-scale SDs in chart III, we can apply Formula III to determine the combined SDs for each year, and of course the combined mean for each year is just  the sum of the verbal and math means in chart III.

 

Calculating full-scale IQ equivalents from the old SAT

Armed with the stats in Chart IV, it’s very easy for people who took the pre-recenetered SAT to convert their COMBINED scores into IQ equivalents.  Simply locate the means and SDs from the year closest to when you took the PRE-RECENTERED SAT, and apply the following formula:

Formula IV

Full-scale IQ equivalent (U.S. norms)  = (combined SAT – mean combined SAT/combined SD)(15) + 100

*Note: the IQ equivalent of SAT scores above 1550 or so will be underestimated by this formula because of ceiling bumping.

Was Mensa wrong?

Based on chart IV, it seems Mensa is too conservative when it insists on SAT scores of 1300 prior to 9/30/1974 and scores of 1250 for those who took it from 9/30/1974 to 1/31/1994.  Instead it seems that the Mensa level (top 2% or + 2 SD above the U.S. mean) is likely achieved by scores of 1218 for those who took the SAT close to 1966, and only 1170 for those who took it closer to 1974.  For those who took the pre-recentered SAT closer to 1983 or 1994, it seems Mensa level was achieved by scores of 1183 and 1203 respectively.

Of course all of my numbers assume a normal distribution which is never perfectly the case, and it’s also possible that the 0.36 correlation between verbal and math I found if all 17-year-olds took the SAT in 1983 could not be generalized to other years, so perhaps I’m wrong and Mensa is right.  But it would be nice to know how they arrived at their numbers.

[NOTE: Pumpkin Person does not endorse the SAT (old or new), as a great measure of IQ, BUT, if one wants to express their old SATs on the IQ scale, here are simple ways of doing so]

I have previously cited a rare study showing that if all American young adults (in the early 1970s) had taken the old SAT (pre-1995), not just the college bound elite, the mean verbal score would have been 368 with an SD of 111, and the mean math score would have been 402 (SD = 112).

Thus converting old SAT verbal and math scores into IQ equivalents (U.S. norms) was simply a matter of converting them to Z scores, then multiplying by 15 and adding 100.

So,

formula 1:

verbal IQ (U.S. norms) = [(verbal SAT – 368)/111][15] + 100

formula 2:

math IQ (U.S. norms) = [(math SAT – 402)/112][15] + 100

Now what happens if you want to convert the composite old SAT score (verbal + math) to IQ.  Well we know the mean score if all Americans had taken the test would have been about 770 (the mean verbal + the mean math), but we don’t know the standard deviation.

On page 779 of the book The Bell Curve by Herrnstein and Murray, they cite the formula for calculating the standard deviation of a composite score.

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 also claim that for the entire SAT population, the correlation between SAT verbal and SAT math is 0.67.  Of course we’re interested in the correlation if ALL American young adults had taken the old SAT, not just the SAT population.  If they had, it’s possible the correlation would have been higher than 0.67 given less range restriction in the general population compared to the college bound population.  On the other hand, the college bound population had studied verbal and math skills more diligently during high school, thus perhaps inflating the correlation.  Assuming these two factors cancel out, and the correlation was probably the same for the college bound population as for the general population, then applying the above formula gives a general population combined standard deviation of 203.77.

So,

formula 3:

full-scale IQ (U.S. norms) = [(combined SAT) – 770)/203.77][15] + 100

This formula appears to give fairly good results, at least up to the mid 1550s.  For example, scholar Ron Hoeflin claimed that out of a bit over 5,000,000 high-school seniors who took the SAT from 1984 through 1988, only 1,282 had combined scores of 1540+.

Hoeflin has argued that even though only a third of U.S. teens took the SAT,  virtually 100% of teens capable of scoring extremely high on the SAT, did so, and whatever shortfall there might be was negated by bright foreign test-takers.

  Thus, a score of 1540+ is not merely the 1,282 best among 5 million SAT takers, but among ALL fifteen million Americans who were 17 years-old anytime from 1984 through 1988.  In other words, 1540 was a one in 11,700 score, which on the normal curve, equates to an IQ of 157 (sigma 15).

Using formula 3, 1540 also equates to exactly IQ 157.

However above 1560, the formula seems to yield IQs that are too low, given their actual rarity.  This is because people who scored above 1560 typically hit the ceiling on the math section and approach the ceiling on the verbal, so people capable of scoring well above 1600 if the test had more hard items, tend to cluster in the high 1500s.

 

 

 

 

 

A guy named Shaan Patel acquired HUNDREDS OF THOUSANDS OF DOLLARS in scholarship money by scoring perfect on his SAT.  What’s interesting about his case is that he claims that when he first took an SAT practice test, he scored 1760 out of 2400 which on the IQ scale, equates to a score of 120 (U.S. white norms) but after studying hard, he raised his score to a perfect 2400 (IQ 155).  That’s equivalent to going up 35 IQ points!

 

 

If his story is true, and assuming he didn’t take the practice SAT at an abnormally young age thus explaining his lower practice score, this suggests the SAT is way too coachable to be considered a good IQ test.  Of course all IQ tests are coachable, but the difference is, official IQ tests are taken cold, because few people have any incentive to get coaching on a private test given by a psychologist for diagnostic reasons.  By contrast, the SAT is supposed to measure coachable skills, but folks like Charles Murray believes that because we have been coached all our lives in reading and math, any additional coaching has diminishing returns and so the SAT functions as a measure of g (general intelligence).

But in Patel’s case, that clearly wasn’t the case.  Perhaps the writing section added in 2005 made the SAT more coachable?  I wonder how much his scores improved when that section is excluded.

Of course, as Charles Murray would argue, anecdotal evidence can be misleading.  For every person who shows such a huge increase, there might be ten others who show almost no increase, or even a decrease.

And even if the SAT is extremely coachable, it could still function as an IQ test if the vast majority of people who take it get similar preparation.

One reason to think the SAT is a valid measure of g is that it’s extremely long (4 hours).  It would be almost impossible to create a comprehensive paper-pencil test that long, on almost any broad subject, that didn’t load substantially on g.