An alt-right web site, "Red Ice" (apparently belonging to Henrik Palmgren), proposes that there's a nearly worldwide decrease in IQ due to immigration. The Red Ice piece apparently originated from unz.com so clearly this story was more widely circulated in the alt-right circles, circa 2016. (It was listed on the first page of results on my google search for IQ and immigration.) The author of the piece is Anatoly Karlin, whose science-related qualifications are unclear (to me), unlike his political views.

The average IQ score cannot really drop due to the way it's calculated (as discussed at Is global IQ dropping over time?), but what the Karlin piece seems to be talking about is a decrease in PISA scores:

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The author's interpretation is (for instance) that:

Western Europe is a complete disaster zone, getting a harder cognitive hit even though the immigrant share of their population is considerably smaller than the US, where they constitute almost a quarter of the PISA-taking population. The German national average takes an astounding 2.4 IQ point hit due to immigrants. [...]
The situation in the US is actually considerably better than in Europe – the low-IQ Central Americans, who are not sending their best, are counterbalanced by the millions of talented East Asians, Indians, and other intelligent and highly motivated people who still want to make America their home. Thanks to that the world’s biggest immigrant nation only loses 1.3 IQ points due to all the newcomers.

So is there any truth to (1) the raw PISA data has decreased; (2) does it really correspond to an "IQ" (let's say raw IQ score) decrease; and (3) does it really imply anything about the effects of immigration?

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    I'm confused about how this means anything. It doesn't seem surprising that the average scores go down if the test gets taken by a bunch of displaced people who don't speak the local language. It doesn't mean the smart people who were there already there aren't still smart, and it doesn't mean the children of the displaced people won't be just as smart as others in their area, given that they will get access to all the options of their new country; things their parents didn't have. – Erik Jul 22 '18 at 8:24
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    For all the pretentious teens here claiming IQ cannot possibly change, it can, does, and is constantly improving. The median within any given population at one time will be 100, but you can compare changes in the reasoning abilities and raw scores that produce those medians between populations. The fact that the median within various races can be set as 100 doesn't mean those races can't be compared with one another; the question is about race as a construct and, here, about actual causes... – lly Jul 22 '18 at 11:45
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    The other thing that makes no sense here is that, if it really were true countries "weren't sending their best", i.e. their thickos were leaving them for other nations, that would drag their own averages up. I don't see much green on that map. – J.G. Jul 22 '18 at 13:58
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    Interestingly, the largest variation is the improvement in Qatar and the UAE, which have a larger percentage of immigration than Europe or the USA. Fake as it could be, that study seems to prove the opposite of what it's claiming. – Pere Jul 22 '18 at 22:27
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    The article assumes that IQ is a useful, culture-independent and accurate measure of intelligence, which it isn't. – dont_shog_me_bro Jul 23 '18 at 9:03

The PISA results are available online.

The OECD also published a summary paper which described what PISA is:

[T]he OECD Programme for International Student Assessment, PISA, [is] the world’s premier yardstick for evaluating the quality, equity and efficiency of school systems.

It does not measure IQ and does not claim to be comparable to IQ.

The summary also provides a table with data about the "Difference in science performance between immigrant and non-immigrant students, after accounting for ESCS and language" (page 8 of the PDF). It is true that immigrant children performed worse in science in many countries (some exceptions are Australia, Hungary, New Zealand, the US, or Israel).

The difference is generally reduced in second-generation immigrants (see eg this report by the EU commission, page 21; or this PDF from the OECD, page 2f).

The OECD explains some of these differences in the chapter Immigrant background, student performance and students' attitudes towards science of the 2015 PISA results; None of their explanations are related to the IQ of immigrants:

PISA results show that the performance of immigrant students is also strongly related to the characteristics of education systems in host countries [...]

the findings suggest that these differences are also related to the capacity of school systems in host countries to nurture the talents of students with different cultural backgrounds

According to the report, other explanations may include the language spoken at home, concentration of immigrant students in schools, or differences in access to educational resources.

Regarding the claim of dropping PISA scores:

In the majority of countries with comparable data, students’ performance in science remained essentially unchanged since 2006.

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    So you intend to disprove the assumption that IQ is affected by immigration by ignoring performance in subjects (When ignoring the three core subjects - science, reading, and math) that are supposed to correlate with IQ scores? I think the argument would be a lot better when only focusing on Pisa being not an assessment of the pupils, but the schools – dualed Jul 22 '18 at 14:12
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    @dualed I didn't really want to get into the IQ/immigrant issue too much as it's imho too broad here and not very useful in general (unless you measure a persons - or at least a non-white persons - worth by IQ). I could have stopped after "PISA doesn't measure IQ" because it's enough to contradict the image in OP, but the rest of the answer provides some more information that is somewhat relevant. I updated the answer though to remove that paragraph as it seems less relevant, and added more information on the OECDs reasoning for the differences. – tim Jul 22 '18 at 15:04
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    A persons measured IQ depends on their genes, their education/training, and influences like trauma, self confidence etc. I would expect someone escaping from Syria to do less well on an IQ test than someone having a good, stable upbringing in a first world country. But the next generation, the difference is gone. – gnasher729 Jul 22 '18 at 20:29
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    If nothing else, working in a language you are not quite fluent in will make understanding the questions harder, and impact results in the core subjects. Unless the PISA tests are set up to eliminate that bias (either by offering the tests in native language - which is not exactly possible for "reading" - or by segregating results from fluent/non-fluent pupils - which is probably illegal) then you would obviously get a drop in average score as the number of pupils who have been learning the language for less than a year goes up... – Chronocidal Jul 23 '18 at 6:27
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    @UKMonkey in theory yes, in practice, practicing doing a bunch of IQ tests beforehand will substantially raise/inflate your score, so there's clearly some learning going on. – mbrig Jul 23 '18 at 14:15

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