# 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. Note, however, the low r value, which implies a standard error of 12 points after accounting for this formula.

For the sake of completeness, I should mention an earlier by a real research 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

## 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.

## LSAT

As part of a misguided attempt to evaluate whether creatine boosted IQ, I took the LSAT at home and scored 172. I couldn't find any academic analysis linking LSAT to IQ, but Mensa accepts it as a valid IQ test, assuming a score of 167 corresponds to the 98th percentile in IQ. Assuming they're correct a score of 167 corresponds to an IQ of 132. A score of 167 corresponds to the about the 95th percentile of LSAT test-takers (z=1.65) Good LSAT Scores for Law School while my score of 172 puts me in the 98.7th percentile (z=2.27), which using somewhat handwavy math, suggests my IQ is 5-10 points higher than that 132, putting me in 137-142 territory.

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

## 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. In all, my intuition is that this IQ estimate is biased downwards.

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 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.

## Overall

Looking at these4 estimates independently suggests my IQ is somewhere between the high 120s and low 140s. However, looking at these estimates independently is equivalent to assuming they're all merely g-factor with independent noise. While this is probably partly true, these estimates probably include independent information.

To see why this is a problem, if the four estimates are completely independent information, then you simply add up how much each estimate differs from 100 to get an overall estimate. Under that hypothesis, my IQ rises to ~200, which is obviously ridiculous.

Still its really not obvious how these pieces of evidence can be synthesized, but the fact that such synthesis would generally result in a higher estimate than the average of the individual estimates is worth pointing out.

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