How To Tell How Much Of “IQ” Is Inherited & How Much Is Environment

Due to the length of tomorrow’s and today’s post, there will be no post Wednesday. Video at bottom.

Word is out (I learned via, naturally, Steve Sailer) about a new paper on IQ, this one on monozygotic (“identical”) twins. Thinking of which leads many to this perennial question: Can IQ be inherited?

No. It is impossible. Unless you mean that a man’s score on his IQ test is printed on a certificate (or the like), and he then wills that certificate to his son. Then IQ can be inherited. Otherwise, no.

IQ, as I often remind us, is a score on a test. The score itself is either a crude measure of one part of intelligence, or the crude smoothing (mushing together) of more than one part, conjoined with the natural variability found in test taking (underdone bits of potato, hidden cultural clues, etc.). IQ is not intelligence. I want us to remove the horrible Deadly-Sin-of-Reification habit of speaking of “IQ” as it if were intelligence. Saying “He has a high IQ” when you meant “He is intelligent” is like saying “He has a high yardstick” when you meant “He is tall” and where the yardstick is a piece of uncalibrated crooked branch with fading notches.

All history teaches that that which leads to intelligence, or aspects of intelligence, can be inherited, in the same way as all material things can be inherited. How much can be inherited, in what forms, under what conditions, coupled with the complex and far-from-settled definitions of intelligence are all themselves fascinating questions. Which can be hinted at in studies of twins reared apart. We need to do this carefully.

The paper is “IQ differences of identical twins reared apart are significantly influenced by educational differences” by Jared C. Horvath and Katie Fabricant in Acta Psychologica.

They gathered data from several studies of monozygotic twins reared apart. There is, of course, apart and apart. One twin raised on one east side of New York City and the other raised on the west side are not the same as one bred on the west side and one in the Far East, say, Shanghai. Environmental conditions are a lot the same in the first case, and maybe not even that different in the second. Tracing conditions and causes (as I have tried to teach us) is hideously complex.

Given all these warnings and caveats, let’s now look at the data. Our authors only printed out a table (and did some modeling) and produced no pictures. Let’s do some pictures. In the table there are 84 complete pairs of twin IQ test scores. They have no measure of how far “apart” is in reared apart, except for the rough proxy of “ED” or educational “difference”. The scoring of this is far from perfect or trustable. Example (you can skip this):

With regards to curricula, seeing as different educational systems (eg – catholic, military, public, etc.) employ markedly different curricula [for review: (Anderson, 1996)], any TRA pair attending different school systems received +1 point. The max points for system differences was +1. Any TRA pair without sufficient data to estimate this dimension received +0.5 points.

With regards to pedagogy, seeing as different countries employ different governing bodies which, in turn, embrace different pedagogical frameworks and practices [for review: (Mortimore, 1999)], any TRA pair attending school in different countries received +1 point. In addition, seeing as the United States has always employed a non-standardized system where each state varies with regards to pedagogical frameworks and practices, any TRA pair attending school in different states within the US received +1 point. 

Et cetera.

The IQ scores are also fixed at a point, so we’ll have to take them as they come, understanding that each study used to provide data would have to be examined in depth, which I did not do. I have added all data together, and have 84 complete pairs.

Addendum: after I wrote this, Scott Bury sent me an article that questioned some of the data used in studies like this, including fraudulent data by Burt; that Burt data is not included in the paper here, which the authors also acknowledge was bad. I hadn’t seen the Paul Graham tweet (he blocks me) nor so-called Cremieux’s analysis (which I still haven’t had time to examine).

Here is a plot of the lowest IQ score of each pair by the highest IQ score of each pair. (And because we are miles away from understanding the shorthand “IQ” always means “IQ test score” and not “intelligence”, I have to laboriously spell it out each time. For bounds, I guessed a maximum possible score of 160 and a minimum possible of 40.)

A one-to-one line is added. This is not a probability model or, Lord help us, a regression. It is only a picture of the data. The idea is simple. The low score can only equal the high score, or be less, for two twins. All points that fall on the line see the pairs have the same IQ score, and so on. Points above the line (look vertically from the line) show how much higher is the score of the second twin.

Unless you are in the grip of the theory of Equality (meaning no differences between any two people except for environmental causes), it’s easy to see twins with larger lowest-scores see their siblings with large highest-scores, and vice-versa. The variation in differences in scores inside pairs doesn’t seem to change depending on the scores. Which is important.

This picture says it is possible whatever aspects of intelligence are used to produce scores on IQ tests “runs in families” to some degree. That is, those material aspects of intelligence that are heritable could have been inherited by each of the monozygotic twins reared apart.

It is also possible that environment accounts for all these differences. (There are always an infinite number of possible explanations: see the Class). But the environment theory is weakened by these twins being reared apart. The Equality thesis is also made less likely by all observations of families throughout history. The evidence for Equality relies almost entirely on desire (and there is no more powerful force).

Let’s think. If environment did nothing, and inheritance was everything (for taking IQ tests), then all scores would fall on the one-to-one line; since they don’t, we deduce environment plays some role (including the environment of the tests themselves and their circumstances; the environment is large!).

If Equality (i.e. no inheritance) were true, we’d see something like this instead (I used the same minimum scores and distribution of differences in scores in this simulated fictional made-up artificial not-real data); here this shows the average or mean high score; actual data would be scattered equally around this line under Equality:

For those twins (still reared apart, mind) in which the minimum in a pair scores very low, his sibling is expected to score much higher, because obviously the low-scoring child was in a lousy environment and it is unlikely (but far from impossible) his separated twin was, too. Yet for those twins in which the minimum one scores very high (and near the “top”), his sibling is also expected to score near the “top”. Remember: the maximum score of a pair has to be at least as large as the minimum score. And there will be some topping out because of the test itself. IQ scores are not unbounded (at the top or bottom; it is of course an entirely separate question whether intelligence is unbounded).

The data of these two curves together should average out to match the observed median and variation in the real twins data, minus whatever shared environmental conditions and causes that cannot be eliminated (maybe Mandarin speakers have average higher scores for certain reasons of the language; e.g. languages “rewire” brains). If Equality holds.

Here’s the Equality thesis minimum IQ score (of a pair) by average (simulated) difference in scores, contrasted with the in-real-life observed minimums by difference:

Obviously, under Equality we’d expected much higher differences when the lowest score is small, because that low scores reflects a bad environment; and vice versa for high scores, recalling that the difference must go to 0 at whatever the maximum on the test is.

And now here’s the real data: not the simulation, but the data itself:

That the difference in IQ score is roughly the same regardless of minimum IQ score suggests Equality is false. There is a hint differences grow smaller as minimum IQ scores increase, as they do in Equality, but this is not surprising for the two reasons we discussed: we have already deduced environment plays some role and IQ scores still top out, not matter which thesis is true, so differences must tend to 0 as IQ scores increase.

Heredity Vs Environment

Equality has nothing going for it. Except, as mentioned, desire. So powerful is the desire for Equality, it is pointless to argue with anyone in its deadly grip.

So we pass by arguments over Equality and ask: since it is clear inheritance plays some role, and we have deduced environment also is important, can we say how important each is using data like this? And the answer is: only a little.

First, here is a series of plots using the “ED” score the authors created. The first is ED difference predicting IQ score difference, then each of minimum IQ score and maximum IQ score:

There is a slight signal, which may be spurious. Perhaps those with the largest ED score in pairs with the lowest IQ scores saw greater IQ score differences. A long-winded way of suggesting that bad environments might have suppressed some IQ scores. Assuming ED scores equal to or greater than 2.5 somewhat more often meant better environments.

But it was too much to expect a measure as crude as a single-number score for goodness of environment would have given much information. Can your life be given in one unambiguous number?

Still, we are not powerless. We have a theoretical limit, or four limits, that aide in our task. The first is IQ is bounded below, and the second is that it is bounded above. These bounds are fixed by how the tests are scored: there will be a maximum and minimum. Given these, the third bound (so to speak) is we can guess what the average signal would look like if Equality held, i.e. if only purely environmental factors were causative. The fourth is we know what the signal would look like if Heritability held, i.e. if only purely inheritance is causative.

We know environment is important to some degree, and we know conditions and causes are all over the place, they are hard to know, i.e. they are largely unknown or “random” (a synonym for unknown cause). Because of this, our answer thus must always and necessarily be probabilistic. We will not reach certainty.

Here is the idea:

The one-to-one line is perfect Hereditary, where the environment causes no differences between twins; the curved line is expected (average) Equality, and the bounds are indicated. The single dot is an IQ score we might see (one observation each pair of twins). In Equality, the dot is possible, just as any dot is possible, but it is not as likely as a dot falling on the upper line. Under strict Hereditary, the dot is not possible; it is impossible.

The relative distance to the one-to-one shows how much heredity can exist; it’s relative because at the top the distance is 0, recall. Under Equality, all points might ride on the one-to-one line, but it’s not likely (given what we know of varying environmental conditions; recall these are twins raised apart). Any point on the one-to-one line might be due entirely to environment because of coincidence.

To be clear: If Equality were true, any given person can score any number within the bounds, and there will be a spread in scores in people strictly because of environmental differences. A twin’s score will have similarities with his or her twin only because some of their environmental causes will be shared. Ordinarily, because of shared environments, we expect twins to score closer together than any other two people. However, in this data, shared environments are less likely because twins were reared apart; but of course there will still be some shared environmental causes, as noted above.

Now we must understand what is meant by inheritance. Suppose we have two identical machines, Twins, each coded (with the same code) to take IQ tests. Obviously, inheritance is 100% here, between the machines. But suppose each has inside its guts a diode that is sensitive to temperature, which can give varying voltages if temperature varies, and these voltages can sometimes result in different answers. The two machines could therefore score different results even though they are identical, because the environment differed in a causal way (hot the day Machine 1 took the test, and cold the day Machine 2 took it).

If you didn’t know about the diode, yet you see different answers from the machines, there are two possibilities. You assume identical structure and code, and therefore conclude something environmental is unaccounted for influencing the machines. You still say that inheritance is 100%; indeed, that is your assumption. Yet scores can differ even if inheritance is complete. By which I mean, the nature, essence, or quiddity of the machines is as one, but the powers those machines manifest can vary by conditions. This is crucial everywhere in science.

On the other hand, suppose you knew nothing about the machines, except that they take tests. You see they have different scores. What caused the difference? Could have been the differences in machines, could have been the environment, could have been both. Obviously, since we do have two machines, our background knowledge of machines tells us that there are likely many similarities between them; after all, electronics is electronics everywhere.

All we can do is to try and control (as in real control) the environment in all the ways we guess (and we might guess wrong) are causally important. Then have the machines retake the tests. And even if we did that perfectly, it could be that the two machines are in fact identical, and with no temperature-sensitive diodes or whatever, but have been trained on different data, hence have subtle differences in code (education). Even here we could say inheritance is 100%, since the machines as machines are identical.

People taking IQ tests face the same difficulties. Genetic determinism is absurd; people aren’t machines. Identical starting points (as far as anybody knows about biological makeup) cannot thus lead to identical ending points, because (as we saw before and will see again soon) genes are not the whole story. In other words, like the machines you can claim because of “identical” genetics that inheritance is 100%, and so all other differences must be environmental.

And the environment is vast! Every little thing affects us. Most imperceptibly, some perceptibly. Some of the environment remakes us and even our wiring (call it epigenetics), some remakes the code (education). And so on. One of a pair of abandoned monozygotic twins can be adopted by Dave Rubin and his roommate and have its mind ravaged, whereas the other can be taken in by nuns and become a priest. The differences in scores on their tests can be gaping. Yet the pair are still identical twins, and so have 100% genetic inheritance.

There we have our answer. If you see genetics as the basis, then because these are identical twins, inheritance must be 100%, and so any difference in scores between twins must be environmental, including the environmental causes that change the people taking the tests. Differences between pairs of twins or other people (here other pairs of twins) will vary because inheritance is less and because of different environments.

If you see Equality as all, then it is only because of shared or similarly causal environments that people score similarly: the environments can differ in any number of ways, but the causes added up must the same in effect for any people who have the same scores. Here, environments are known to be at least somewhat different for twins.

If Heritability is false and Equality true, then the distance in IQ scores between a twin and his brother (or sister) would be the same on average as between a twin and anybody else, more or less, because shared environments (in all the meanings of that word) will still cause similarity. If Heritability has any truth to it, then the distance in IQ scores between a twin and his or her sibling would be less on average than between any two others, accepting that changing environment also is important (if not, then the distance between twins would always be 0).

Here is a plot of the normalized frequency of IQ score differences for twins and between all pairs of people in the data. The blue bars are a histogram (High IQ test score — Low IQ test score) for all pairs of twins; whereas the pinkish bars are (High IQ test score — Low IQ test score) for all possible pairs of people in the data.

Obviously, the difference between IQ scores for twins is often much smaller on average than for differences between other pairs. Assuming the differences in environments for twins is the same, in a causal sense, as for other pairs, then we have a rough measure of heritability and environment.

The mean IQ difference for twins was 8.3, and for all pairs was 18.5; (more relevant) medians were 6 and 15.5. The standard deviation for twins was 6.4 and for all pairs was 13.8.

Our goal, here and everywhere in science, is to figure the probability our theory or hypothesis is true given all the data we think relevant. What, what precisely, are our hypotheses?

One in Genetic Heritability in a strict sense. This says identical twins must score the same on IQ tests, because their intelligence used in answering IQ test questions is identical. This hypothesis is false, given our observations: the probability it is true is 0.

A second hypothesis is Equality in a strict sense. This says identical twins are the same as any two other people on average, in their intelligence used in answering IQ test questions. This hypothesis is possible, given our observations. But it doesn’t have much going for it for all the reasons we know.

It’s obvious from looking at this data, and from all experience, that a third hypothesis is likely true: Some Heritability + Environment. That is, identical twins share certain and variable aspects of intelligence used in answering IQ test questions, and that environmental causes and conditions affect twins as much as they affect anybody.

And that is our answer.

Video

Most Can Stop Here: The rest is needless math to confuse minds

We could leave it at that, and not risk trying to put a number on this probability. We don’t have to put numbers to everything. Still, it isn’t wrong to do so here, though in order to do so we have to make assumptions.

We know

Pr(Equality|XB) = Pr(X|Equality B)Pr(Equality|B) / [D]

where

D = Pr(X|Equality B)Pr(Equality|B) + Pr(X|Not Equality B)Pr(Not Equality|B)

and where we take “Not Equality” to mean “Some Heritability + Environment”, X is our differences in IQ scores, and B is whatever background information we bring to bear.

The key is calculating Pr(X|Equality B) and Pr(X|Not Equality B); of course, we also need Pr(Equality |B), but that will vary a lot by how devoted one is to Equality (i.e. by individual Bs). It’s anyway just a number between 0 and 1. Interestingly, if one insists, as Equality mavens do, that Pr(Equality |B) =1, then no observations of any kind will ever convince them Equality is false (the math for that is easy).

We can take the data of all pair differences as indicative of Reality; though this is a large assumption! This is only 84 pairs of data from a small period in history. Meaning I don’t believe it will hold everywhere all time. We have to add all this skepticism about data purity and representativeness into our B. But we can only do that in a hand-wavy way. That, my friends, is a common limitation in science.

Anyway, if we take that pinkish distribution as correct, then the probability of seeing a median difference of 6 (rounding all differences to the nearest whole number) in a sample is 0.043. More ambitiously, we ought to do the whole distributions and not just medians, so consider this only an example of the right direction of how this analysis ought to go. More research is needed (thank you).

So much for Pr(X|Equality B) (which equals 0.043). What about Pr(X|Not Equality B)? That depends entirely on what precisely we mean by Some Heritability + Environment. I don’t know what we mean. That is, for this data, I haven’t had time to figure what it might mean.

But one guess is this: we’d get what we got. Meaning a median of 6 is certain, or close enough to it, is Some Heritability + Environment is true.

If we take, for fun, Pr(Equality |B) = 0.5, and using the other numbers, then we get

Pr(Equality|XB) = 0.04.

Or

Pr( Some Heritability + Environment|XB) = 0.96.

Where “Some Heritability” means the amount necessary to produce intelligence in twins reared apart and their ability to answer IQ test questions.

Very loose. But yet I find it accords with observations in history.

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