intelligence me psychology

# Estimating My IQ

## ACT

Based on my own statistical analysis of NLSY NLSY97 and ACT ACT High School Profile: HS Graduating Class National Report data, we can compute the correlation between ACT scores and IQ (ASVAB scores) from 2002. In doing so, we find that for people with ACT scores between 25 and 36, the line of best fit between their highest composite ACT score and their IQ is

IQ = 1.59 * (ACT - 25) + 113
r = 0.61

My highest ACT score 36, so this predicts an IQ of 130 (12).

For the sake of completeness, I should mention an earlier study that was actually peer-reviewed examined data from the early 1980s Koenig and estimated the relationship between g and the sum of the ACT's English and Math scores. They found

g = 0.685 * ACT + 87.76
r = 0.77

which predicts my IQ is 137 (10)

## SAT

Another study looked at the correlation between g and the math and verbal SAT test scores Scholastic assessment or g? The relationship between the scholastic assessment test and general cognitive ability. They found

g = 40.063 + 0.126 * SAT - 4.71E-5 * SAT^2
r = 0.82

I got a 740 on each SAT subtest, which suggests a 1600-point score of 1480. From this, I achieve an estimated IQ of 125 (9).

## LSAT

As part of a misguided attempt to evaluate whether creatine boosted IQ, I took the LSAT at home twice, a week or two apart, scoring 168 the first time and either 172 or 173 the second time. I couldn't find any academic analysis linking LSAT to IQ, but Mensa accepts members with a score above 167 Mensa, suggesting a score of 167 corresponds to the 98th percentile in IQ (IQ~131). Likewise, the Triple Nine Society accepts a score of 173 Triple Nine Society, suggesting a score of 173 corresponds to the 99.9th percentile in iQ (IQ~146). These with my my score of 172 suggests an IQ of ~144.

## Credentials

I attended Carleton College, where the middle 50% of students have ACT scores between 31 and 34 Class of 2023 Profile. If the ACT were the only filter, it'd suggest an average IQ of 125. In practice, there are other filters, some of which indirectly select for lower IQ and others that indirectly select for higher IQ.

The College Board publishes the average SAT score of test takers by intended major SAT: Total Group Profile Report. The relevance here is that the average score for "Computer and Information Sciences and Support Services" is 1580 and the average score for "Mathematics and Statistics" is 1681. The median overall score is 1480, which suggests (but does not prove) that CS and Math majors tend to have average SAT scores 100 and 201 higher than normal.

We can use this and the SAT correlation discussed above to adjust the estimate by my majors. First, we convert the 3-test scores to two test scores by averaging the critical reading and writing scores to estimate verbal scores. This suggests gaps of 71.5 and 152 points for my two majors, respectively.

Since the relationship between SAT and IQ is non-linear, it's hard to adjust my IQ estimate from getting into Carleton College, but my impression from the numbers is that this bumps the expected IQ score by 2-5 points, bumping the estimate up to ~128.

Subjectively, at Carleton I felt like I was significantly above average at computer science and stats compared to the average major and and a bit above average at math. Given this, I think it's reasonable to bump my expected IQ up a few points: into the mid 130s.

## Overall

 Method 95% Confidence Human 100 ±30 ACT [a] 130 ±24 ACT [b] 137 ±20 SAT 125 ±18 LSAT 144 ±? Carleton Experience Mid 130s

It's really not obvious how these pieces of evidence can be synthesized, but the fact Mensa and the Triple Nine Society accept the LSAT but not the ACT or SAT as a valid IQ test suggest we take its evidence the most seriously.

Another thing to note is that compiling an IQ estimate from multiple tests is not the same as just taking a weighted average of the test scores. For instance, if you score 75 on ten IQ tests, then your implied IQ (statistically) is 66 Schneider.

If we do an appropriate analysis of my test scores using reasonable assumptions, I end up estimating that my IQ is in the low 140s.

On the other hand, my performance in my major is, I think, pretty important too. All in all, I think a fairly unbiased estimate of my IQ is the high 130s, but there is significant uncertainty - probably ±10 points in either direction.

NLSY97 (National Longitudinal Survey of Youth 1997). (n.d.). Retrieved from https://www.nlsinfo.org/investigator/pages/search ACT High School Profile: HS Graduating Class National Report. (2002). https://www.act.org/content/dam/act/unsecured/documents/Natl-Scores-2002-t4.pdf Koenig, K. A., Frey, M. C., & Detterman, D. K. (2008). ACT and general cognitive ability. Intelligence, 36(2), 153-160. https://doi.org/10.1016/j.intell.2007.03.005 Carleton College. Class of 2023 Profile. (2020). https://www.carleton.edu/admissions/apply/steps/profile/ College Board. (2014). SAT: Total Group Profile Report. https://secure-media.collegeboard.org/digitalServices/pdf/sat/TotalGroup-2014.pdf Frey, M. C., & Detterman, D. K. (2004). Scholastic assessment or g? The relationship between the scholastic assessment test and general cognitive ability. Psychological science, 15(6), 373-378. https://doi.org/10.1111%2Fj.0956-7976.2004.00687.x Th Princeton Review. Good LSAT Scores for Law School. https://www.princetonreview.com/law-school-advice/lsat-scores Qualifying Test Scores. Mensa. https://www.us.mensa.org/join/testscores/qualifying-test-scores/ Test Scores. Triple Nine Society. http://www.triplenine.org/HowtoJoin/TestScores.aspx Schneider, J. (2014). Misunderstanding Regression to the Mean. https://youtu.be/aLv5cerjV0c