The Unz Review seems to be a site that attracts all kinds of crackpots, but some articles are interesting if you have studied conspiracy theories, like I have in the recent years. But the site is not nice and there are too many trolls.
There was nothing interesting, so I read one of the IQ articles by James Thomson. There are many people there who are obsessed by IQ. I had a very unpleasant discussion with two Unz commenters, who had great difficulties in understanding simple mathematical things, basically, that you can sometimes move the place of a summation in an equation. Later one of them did write two non-offensive and non-contemptuous comments, which was unusual from these two, but even those comments did not clearly show that he had understood the problem. It was pretty much useless to try to explain the problem to those people, so I explain it here.
The issue was that one Davide Piffer has for several years been publishing papers where he plots country average IQ against a country score for genes related to educational achievement, and he gets a very good correlation. In case you have never heard of Piffer’s results, look at this Unz article by James Thomson.
Human Biodiversity (HBD) people are happy for these results as they seem to show that genes determine intelligence and colored people are less intelligent than Whites. They seem to have no special problem with East Asians and Ashkenazi Jews being more intelligent than Whites.
What is rather odd is that these supremacists accept Piffer’s plot that claims that Finns are more intelligent than other Europeans. Should they not object to that? After all, Mongol-hybrids, that is what the Nazis thought of us.
I, of course, do object to that claim. It is not the Finnish IQ score I object to. The claim of a bit higher IQ of Finns is justifiable, as IQ researchers use PISA results for determining country average IQs and Finnish children have done very well in PISA, so I agree that one can set 101 or 102 as the average IQ for Finns at the moment, but I do not agree that it is genetically determined. The reason for this slightly higher score is the school, though some part of it can come from the language that is easier to spell and of Finnish personality. Who knows, maybe there is a bit less pollution also, but all these reasons are environmental. Though, about pollution, I guess Saami still suffer from PCB. That dangerous chemical was forbidden in 1970s, but it did not disappear. Winds blew it to the North.
I do not deny that there are genetic differences in IQ between nations and that also in Finland Somali refugees do worse in the school even though it is exactly the same school. But it is not justified to claim that Piffer’s results show that Finns have higher genetic IQ than other Europeans. Not so long ago Finns were measured to have a lower average IQ, thus, average IQs of countries depend quite much on environmental factors and we should not expect to get a so clear correlation as Piffer gets. And Saami are not genetically so close to Finns, yet have the same IQ. So far it is more justified to say that it is the environment, not the genes, making these small IQ differences in Europe. Maybe one day the genetic argument can be proven and Finns turn out to be the smartest Europeans. But so far it is not proven.
So, there is something wrong with Piffer’s results, but what?
It is not that he calculated the genetic score (Polygenic Score, PGS) incorrectly. His calculations have been checked. The values are correctly calculated. It must be something wrong with the PGS. In the last paper Piffer used a PGS created by Lee et al (2018). It is a fine PGS, good for many things, but not intended to be used for calculating IQ differences between populations. Yet, that is what Piffer uses it for. He is not the only one. Dunkel et al (2019) applied the same PGS for comparing PGS scores of two populations: American Ashkenazi Jews and American Christians, and got a result that also looks suspicious. Also this Dunkel et al usage is not a correct usage of the PGS made by Lee et al (2018).
So, what is wrong with it?
I will explain it in a very simple way. You are able to follow this easily, and there is no bullshit and no error, I can do this level math. quite fine.
Assume that scientists have found a set I of SNPs (short pieces of DNA where a single nucleotide is different, they are caused by mutations) that are linked to some property P. In this case the property is educational achievement and it is used as a proxy for IQ, but for this calculation P can be anything. The size of the set I is denoted by S(I).
Each of these SNPs has an effect in educational achievement, positive of negative. We will denote the effect of SNP number i by wi. The test sample is used to determine wi. So far let us assume we do not know it.
We have a set J of test people that we will use for making a predictor for P, that is, fixing the values of wi. Each person j in this set either has an SNP number i or does not have it. Let us denote this situation using a number mji. Then mji=1 if the person j has the SNP number i, and mji=0 if he does not. The size of the set J is denoted by S(J).
When we have assigned values to wi, the predicted score for the property P for the person j is
Ȓj=∑i mji wi
We know the real value Rj of property P because we make tests for the tests people. We would like to find such weights wi that the predicted score Ȓj is as close to the real value Rj as possible. Naturally, if the size S(I) of I and the size S(J) of J are equal, we can simply solve the weights from a matrix equation. We set Ȓj=Rj for each j and solve
Rj=∑i mji wi
which in matrix form is
R=MW
and the solution is
W=M-1R
but we want to use a larger test set, thus S(I)<S(J) and the equation is over-determined. The reason why J must be larger is that the SNPs do not in reality predict P so well. If we solve the weights for one set of test persons and then for another, the values for the weights are different. In fact, we cannot demand that Ȓj=Rj for each j. The most we can demand is that the error
E= ∑jd(Ȓj,Rj)
is minimized. Here d(A,B) is the distance between A and B. It may be the eigenvalue |A-B| or the square (A-B)2, or something else depending on our choice of the distance.
Finding weights that minimize the distance is a normal optimization problem and can be solved without any difficulties. We can allow the weights to have any real number values, or we can restrict the weights in any way we want. For instance, we can demand that the weights can only be integers or signed binary numbers (+1, -1, 0).
OK, this is what is normally understood by a predictor. It is how you would do a GWAS. You can do it a bit differently, possibly the GWAS people do it a bit differently, but not much can differ. Basically it is always like this with predictors: you make a predictor for some data. The predictor looks at your input data (here, the genes) and predicts what value you should get for some property P.
Assume now that the weights have been found. Let us go to the problem in Piffer’s method. Assume that the set of test people is an union of several subpopulations Jk, k=1,…, N, and that these subpopulations differ in gene frequencies so that the frequencies of all SNPs in I are not the same in each subpopulation. Assume also that these subpopulations have different average values for the property P. We denote the average value of P for the subpopulation Jk by Rk,ave. The subpopulation PGS score for the subpopulation Jk is
PGSk=S(Jk)-1 ∑jϵ Jk Ȓj
The average P score for the subpopulation Jk is
Rk,ave=S(Jk)-1 ∑jϵ Jk Rj
Piffer plots Rk,ave as a function of PGSk and gets an almost straight line. But notice that
PGSk– Rk,ave =(S(Jk)-1 ∑jϵ Jk Ȓj) – Rk,ave
and it can be expressed in two ways (notice that the weights are fixed, this time we have a different sample, we use our predictor on some sample, we do not any more modify weights.)
PGSk– Rk,ave =S(Jk)-1 ∑jϵ Jk ( Ȓj – Rk,ave)
PGSk– Rk,ave =S(Jk)-1 ∑jϵ Jk ( Ȓj – Rj)
That is, the PGS score you get by averaging over Jk is exactly the same score that you would get if each person j has for property P the average value for P in his subpopulation. We can just as well think about Piffer’s test in the following way. He has a test set of N subpopulations. There is zero variance for educational achievement in all subpopulations, but the subpopulations have different genes and different average educational achievements.
Reflect on it for a while: what does the predictor use the SNPs for? It does not need them for the value it assigns to a person for the property P. That value is taken directly from the subpopulation P values. The SNPs are needed only for identifying the subpopulation where the person belongs to. The predictor could use SNPs that have no association with property P. The SNPs can have negatively or positively weights and you can change the negative to positive and still get the almost same correlation because the real effect of these SNPs does not matter to the predicted value. (The effect of an SNP in the predictor is given by the weights determined in the prediction stage. The real effect is what you noticed in the discovery phase.) The predictor looks at the SNPs in a person’s genes. From these SNPs it can detect to which subpopulation the person most likely belongs to and it gives the country average value for P as the prediction for P to this person. If the person does not clearly belong to any subpopulation, the prediction is a combination.
Think what happens e.g. in Dunkel et al (2019) test. They use PGS from Lee et al (2018), where the prediction test sample includes White Americans of European descent and a part of them (1% in the HRS sample) are Ashkenazi Jews. Dunkel makes just as Piffer, just as described above. US Ashkenazi Jews have an average IQ of 110 and US White Christians have an IQ of 100. The predictor can usually tell that if a person is a Jew from SNPs, as these populations are genetically different. To a Jew it gives the score 110, to a Christian it gives 100. This happens in any sample with White Americans. It does not need to be the test sample. The weights of the predictor are set so that when summed over a subpopulation it works as a predictor of the subpopulation and gives the subpopulation average as the prediction. Consequently, this predictor gives US Ashkenazi Jews a very high PGS score. It is built that way. This has nothing to do with the real influence of the SNPs to educational achievement. This result comes merely from the facts that the average IQs of these two subpopulations differ and that the genes of the subpopulations are different enough for the predictor to detect to what subpopulation a person belongs to.
Did you get it? Piffer’s, and Dunkel et al’s, correlation is a mathematical consequence of the way the PGS is created. It is not any research result. It does not prove anything of the importance of genes to IQ. It is similar to a case where you put a stone in your pocket and later find it, or where you, at some less obvious step multiply your number by three and at the end show, look, it is divisible by three. Of course there is a correlation between the country PGS score and the country average IQ, because the country average IQ highly correlates with country average educational achievement, and you created a predictor which should give a linear correlation between country PGS and country educational achievements.
Some people are impressed that Piffer’s results repeat in each test. Of course they must repeat. The reason there is the correlation is a mathematical identity. It must always repeat, but it does not mean anything. You would get the correlation even if the SNPs had no influence to the property P.
The problem clearly is in Dunkel et al (2019) as they compare two subpopulations, which have different genes and different IQs, and these two subpopulations were both in the prediction sample. This study must therefore be discarded. It does not matter that Jews were only one percent: the PGS score for them comes from this one percent. Piffer’s earlier papers have an IQ gradient in Europe. It seems that the prediction sample had multiple subpopulations from Europe. This is wrong. The last paper of Piffer does not show this North-South IQ gradient in Europe, because the sample was made from Americans of European origins. As they all live in similar circumstances in the USA, there is no IQ gradient. This naturally shows that Piffer’s earlier papers were incorrect because of the prediction sample. The new paper is also incorrect: Piffer includes Ashkenazi Jews, which belonged as a subsample to the prediction sample.
Can this problem be fixed?
Basically one would think that if we simply count the number of SNPs affecting IQ without any prediction stage, then we should have a correct method. But is it correct and can we do this way? IQ differences between countries are at least partially caused by environmental factors. It would be wrong to create a predictor, which tries to claim that the differences are only caused by genes. If one wants to make a predictor for country IQ differences, why would one not include to the predictor such factors, like many environmental ones, that are known to influence the average IQ of the country? The predictive value of all IQ related SNPs is still quite small. I think fixing this predictor to actually say something of IQ differences between countries is hopeless in this stage of research. There is lacking a scientific basis for it.
Some people may think that the problem maybe is a minor one. After all, Piffer calculates PGS scores to countries which were not in the prediction sample. Yes, maybe, but here we have another problem. These outliers are rather far from Europeans, the Fst distance is large, so they could have their own IQ affecting SNPs. They do not seem to, but the fact that they do not seem to have their own SNPs is a different reason than what Piffer’s correlation says. Piffer’s straight line says that Sub Saharan populations have low IQ because they do not have European SNPs. The correct way would be to say: naturally they do not have European SNPs as they are not admixed with Europeans. The problem is that they do not have their own SNPs. Thus, Piffer is wrong, even though his result agrees with the reality. If it does, as Lynn and Rushton have estimated that without environmental reasons Sub Saharan IQ would be some 15 points higher. But Piffer seems to be right with East Asians. They have the same SNPs as Europeans and probably more of them. Piffer’s plot works. This can very well be so. The IQ genes may have evolved in Ancient North Eurasian. If so, you would find them in Yamnaya, Uralic and East Asian populations.
The people, who do not understand this simple mathematical problem that I just explained, seem to be supremacists. They are people, who claim that many other people, like Africans, in fact, all colored people, are much more stupid than they are and it is for genetic reasons.
I hope these supremacists understand that people from hard science think exactly the same of people in soft fields: those people in soft fields, like psychology, just cannot think logically. Half of my former colleagues would place IQ researchers somewhere between chiropractors and astronomers.
Both of these supremacist opinions are in a way correct. IQ tests do show differences between populations and mathematically talented people are correct in saying that there is a difference. IQ tests do not show this difference, but only because they truncate the mathematical talent. It is so that the traditional meaning of intelligence is mathematical talent, also called logical thinking, and actually it is the problem solving capability. This is why one used to say that girls can talk and write better, but boys are more intelligent. Well, you see the problem when talking with soft field researchers. Remember to be patient, they are really slow thinkers. Just talking about very recent experiences.
Sadly, I must suspect that in Dunkel et al the “et al” must have understood that they are making an error. I mean, I could spot the error even without reading Piffer and Dunkel carefully. I had read earlier papers of Piffer carefully, but this one I just briefly scanned, and there is it, an obvious error. How could somebody who is working on the field not see it? Should I assume none of them understand, “et al” usually includes supervisors if the author is not experienced enough? No, I cannot assume that. Therefore the error was intentional. It was to prove that Ashkenazi Jews are the most intelligent. That is, it was fraud. The fraud explanation fits well to the fact that nobody uncovered the fraud: the main stream likes this meme. It wants it to be believed.
There is one good thing with this fraud: when fraud is found, the same claim cannot any more be so easily presented. Consider a case of a magician. He makes a trick and you may wonder if this was a real miracle. It is hard to believe in miracles, but maybe still… But when you have discovered that he made a trick and know where he cheated, can he come next day to you and make the trick again. Do you then believe that now it for sure is a miracle? It is not made exactly in the same way as he invented some new way of doing it. Do you need even to find out the new way in order to say that it must be a trick? I say, you do not. If it was a trick last time, it is a trick this time. There is no need to spend time debunking the trick every time. And it does not matter if it is next time presented by Piffer or Dunkel, or somebody else. It is still a trick.
Piffer fails, and the evidence of super high Ashkenazi Jewish IQ fails every time. It may be interesting to notice that James Thomson, who put the article to Unz, stayed quiet.