I Still Don't Believe The Average American College Student Has an IQ of 102.

True average is 104-108

A preprint went viral on twitter, which claimed that the average IQ of a college student is only 102 in 2020:

Note that they have only 5 post 2010 studies, and that there is visual heterogeneity in means within the post 1970 samples. Depending on how high this heterogeneity is, the confidence invervals would have to be adjusted to accomodate for the fact that sampling error cannot account for all of the variance in means between studies. There is also the question of non-linear effects - the decrease from 1940 to 1980 is pretty large, but after that the decrease appears to attenuate. If that is the case, then a linear model would underestimate the mean of modern college students.

Theoretically speaking, there are three reasons why the average IQ of college students can drop. First, the average levels of intelligence in the whole population can decrease - there is little empirical evidence that the average cognitive ability of Americans has shifted in the last 50 years, so this cause can be ignored. In addition, intelligence tests are renormed every 10-20 years to correct for Flynn Effects and improve their quality, so this would not be expected to be an issue. Second, the correlation between IQ and educational attainment could decrease - this might be the case, but it’s hard to tell. The correlation between AFQT scores and educational attainment in the NLSY cohort born in 1955-1965 was 0.57, while it was 0.52 in the 80-84 cohort. The difference in the correlation does reach statistical significance, but the difference is small and could easily be a statistical artefact.

from here

Strenze also tested this in his old meta-analysis (admittedly, in 2007), and found that the correlation was increasing, though this increase barely passed statistical significance (p < 0.05), so I wouldn’t put any stock into it. Oddly enough, this doesn’t seem to be the case when other moderators are not controlled for - the correlation was 0.51 between 1960 and 1969, but 0.41 (!) between 1990-2003. Mysterious.

The meta-analysis aside, there is strong evidence that the correlation between education and IQ reduced in Norway, but there is no guarantee that this applies internationally.

The last thing that can affect the average IQ of a college student is enrollment rates - if more students enroll, than the process is by definition less selective. This is obviously the culprit of the decrease that is observed - fortunately college enrollment statistics are easy to access and highly precise, so they can be used to model the average IQ of a college student over time.

I suppose it’s possible that the average IQ of college students could decrease due to education becoming worse, but let’s be real here, what matters are the genes. The mathematical/reading skills of American children have also been fairly stagnant; if there was a massive decline in American education, we would have seen it already.

from here

II.

Making a few assumptions, it is easy to model what the average IQ of a college student/graudate is:

• Educational attainment is a normally distributed latent variable.

• “IQ” is a normally distributed.

• The relationship between latent educational attainment and IQ is perfectly linear.

• People become “college students” or “college graduates” after reaching a certain level of latent educational attainment. The concept of “selectivity” is relevant here: if the selectivity is 60%, then the 60% of the population who are above -0.25 in latent educational attainment pass, and the other 40% fail.

I discuss these assumptions in a prior article - a model that operated under these assumptions was able to predict the average IQs by degree of NLSY97 respondents perfectly - the model predicted that the average IQ of a HS dropout is 86.7, that the average IQ of somebody with a HS degree is 98, and that the average IQ of a college graduate was 109.2. The real averages were 86 for dropouts, 97 for high school graduates, and 109.7 for college graduates within the NLSY97.

There is the issue of determining how selective attending college is - about 63% of high schoolers enroll in university, but only 60% of those who enter finish with a Bachelors, so only about 36% of the population graduates. The true selectivity of being a college student is probably somewhere between 63% and 41% - I’ll assume it’s 55% for the sake of the model.

This model predicts that in 2022, the average college student has an IQ of 107.3. Making the least generous, but still possible model (selectivity of 66%, true correlation between educational attainment and IQ of 0.5) predicts an average of exactly 105. Note that, as of 2018, 33% of Americans aged 25-30 have never gone to college, so it’s unlikely that the true average is below this.

It is theoretically possible that there could be discrepancies between the reality and the model; this would happen if unintelligent people became increasingly likely to drop out late. Or perhaps there could be secular changes in the covariance between intelligence and time spent in college which cause the average of college students to lower past what would be expected from the correlation between education and IQ. I suppose these strange effects could alter the average by a few points - so I would peg the 100% credible interval to be 104-108.

III.

On the topic of IQ and educational attainment: the averages by degree within Whites have not changed much in the 20 years between the cohort born in 55-65 and 80-84.

I checked the averages within all races (IQ standardized to 100) - modern college graduates within the NLSY97 cohort had IQs of about 109.7 on average. The means by sex/degree were:

• Female, Bachelors: 106.6

• Female, Masters: 108.3

• Female, professional/PhD: 114.9

• Male, Bachelors: 111.2

• Male, Masters: 113.8

• Male, professional/PhD: 120.1

The sex difference in IQ within the whole dataset was about ~1-3 points favouring men if I recall correctly. Regardless of whatever the number was, it can’t account for the relatively large differences (4-5 points) that are observed within the degree categories - this is due to a collider bias, where men have slightly higher IQs, but have lower levels of educational attainment.

100 → dropout, 115→ highschool only, 130→associates, 145→bachelors, 160→masters, 175→professional degree or PhD

It is true that these averages aren’t what they used to be; of course they aren’t - college has become less selective over time, so the averages will inevitably decrease. What matters is the genes - education does not actually make people more intelligent. Unfortunately, we live in a time of cultural malaise and decline, so fake statistics like “the average IQ of a college graduate has an IQ of 102” will be injected into the veins of the zeitgeist like Heroin.

iq <- rnorm(1000000, 0, 1)
lated <- iq*0.6745 + rnorm(1000000, 0, 1)*sqrt(1-0.6745^2)
ed <- NA
d <- data.frame(iq = iq, lated = lated)
d$ed <- NA

d$ed[d$lated < -1.4757] <- 0
d$ed[d$lated > -1.4757 & d$lated < 0.1004] <- 1
d$ed[d$lated > 0.1004 & d$lated < 0.33185] <- 2
d$ed[d$lated > -0.431644 & d$lated < 0.33185] <- 3
d$ed[d$lated > -0.431644 & d$lated < 1.340755] <- 4
d$ed[d$lated > 1.880794] <- 5

cor.test(d$ed, d$iq)

d2 <- d %>% filter(lated > -0.1256613)
mean(d2$iq)*15+100
qnorm(.33)
###################################
iq <- rnorm(1000000, 0, 1)
lated <- iq*0.619 + rnorm(1000000, 0, 1)*sqrt(1-0.619^2)
ed <- NA
d <- data.frame(iq = iq, lated = lated)
d$ed <- NA

d$ed[d$lated < -1.4757] <- 0
d$ed[d$lated > -1.4757 & d$lated < 0.1004] <- 1
d$ed[d$lated > 0.1004 & d$lated < 0.33185] <- 2
d$ed[d$lated > -0.431644 & d$lated < 0.33185] <- 3
d$ed[d$lated > -0.431644 & d$lated < 1.340755] <- 4
d$ed[d$lated > 1.880794] <- 5

cor.test(d$ed, d$iq)

d2 <- d %>% filter(lated > -0.4399132)
mean(d2$iq)*15+100
#note: the correlation between latent ed and IQ was doctored to make it mirror the observed correlation between degree attainment and IQ a certain value (0.5 in the second example).