Analysen baserer sig på detaljerede data på individniveau, indhentet fra Danmarks Statistik. Dette inkluderer oplysninger om de karakterer, hver
enkelt folkeskoleelev har opnået ved afgangseksamen i 9. klasse i perioden fra 2007 til 2009. Undersøgelsen er afgrænset til at omfatte resultater fra prøverne i de bundne eksaminer med ekstern censur ud fra en vurdering af, at karaktererne i disse eksamensprøver i højere grad kan sammenlignes end de, hvor eksterne bedømmere ikke har medvirket.

Følgende prøvekarakterer er dermed inddraget i undersøgelsen:
• Dansk læsning
• Mundtlig dansk
• Dansk orden
• Dansk retskrivning
• Dansk skriftlig fremstilling
• Mundtlig engelsk
• Mundtlig fysik/kemi
• Matematiske færdigheder (skriftlig)
• Matematisk problemløsning (skriftlig)

The analysis is based on detailed individual-level data which is retrieved from Statistics Denmark. This includes information about the grades every public school student has received at the final exams in the 9th grade in the period 2007 to 2009.
The analysis is restricted to the results from the mandatory exams with external censorship because these were judged to be easier to compare than those where external censors did not take part.

The following exam grades are thus included in the study:
- Danish reading
- Verbal Danish
- Danish order
- Danish spelling
- Danish writing
- Verbal English
- Verbal physics/chemistry
- Mathematical proficiency (written)
- Mathematical problem solving (written)

De karakterer, som der ses på, er karakterer i de såkaldt bundne prøvefag ved folkeskolens afgangsprøve. Det drejer sig om:

Dansk, mundtlig
Dansk, læsning
Dansk, retskrivning
Dansk, skriftlig
Matematik, matematiske færdigheder
Matematik, matematisk problemløsning
Engelsk, mundtlig
Fysik/kemi, praktisk/mundtlig

Karakterer i alle de ovenstående fag er lagt sammen ved udregningen af de samlede gennemsnit for alle bundne prøvefag. I de fleste tilfælde er de seneste fem skoleår lagt sammen, så det er muligt at se på alle herkomstgrupper og underopdele nogle af grupperne på enkelte oprindelseslande. Dansk, orden har i nogle af årene også været et bundet prøvefag, men det er ekskluderet i alle beregninger. Elever i specialklasser og privatister (elever som ikke har mulighed for at aflægge prøve på en skole fx på grund af hjemmeundervisning) er heller ikke medtaget.

The grades we look at here are grades from the so-called mandatory exam classes at the public school's final exams. It concerns:

Danish, verbal
Danish, reading
Danish, spelling
Danish, written
Mathematics, proficiency
Mathematics, problem solving
English, verbal
Physics/Chemistry, practical/verbal

Grades in the above mentioned classes are summed in the calculation of the overall average for all mandatory exam classes. In most cases the five years [where data are from] are treated as one, so as to make it possible to examine all origin groups and further divide some of the groups into single origin countries. Danish, order has in some of the years also been a mandatory exam class, but it is excluded from all calculations. Students in special education classes and privatists (students who don't have the option to take the exam at a school e.g. because of home education) are not included either.

What's up with footnote (3)?

Would you mind rerunning the correlations with native Danes excluded and letting me know if the results are similar. Immigrants (i.e., 1st and 2nd gen) often systematically perform differently than natives (i.e., a true immigrant effect), so there can be a immigrant x origin effect. I have found one before.

• Removed the analysis of restriction of range. This was technically flawed and not very informative due to very small samples.
• Proofreading by a native
• Analysis of combined GPA scores, new section
• Analysis of data without Denmark, as requested by Fuerst /w scatterplots.
• More data tables with Spearman's cors and discrepancy scores

Emil,

I have only a few minor criticisms and observations:

1. You should add a paragraph that would summarize the excellent points you made about immigrant overrepresentation in special education classes and communal youth schools. Truancy is another factor that might make IQ differences seem smaller than they really are.

A problem with interpreting the results is that it only concerns normal schools. Special education schools are thus excluded, and they are disproportionately attended by lower GI students. Thus one would expect immigrants to be over-represented in special education classes and this would have the effect of reducing the GPA gap found in the normal schools. Immigrants are in fact over-represented in some forms of special education schools, especially the second generation (see the appendix for details). However, here we are assuming that there is no under-diagnostization of special educational needs among immigrant students. Such under-diagnostization is likely because social workers would try to avoid over-representation of immigrant students in schools for the retarded. It is also expected because a higher proportion of students below the cut-off (usually IQ 75) from a lower GI population would be socially normal because they are part of the left tail of their distribution as opposed to having a major genetic defect such as Down's Syndrome which makes it very plain that one has special educational needs.\cite{jensen1969much} It is currently unknown how large these biases are for the Danish data, so some caution is advised.

2. "I chose Islam prevalence because of frequent media attention being given to this factor." Could you elaborate a bit? Do the media frequently discuss poor academic performance among the children of Muslim immigrants? Since you seem to attach a lot of importance to this variable, it wouldn't hurt to summarize what is said in the media and include a few quotes.

I chose Islam prevalence because of frequent media attention being given to this factor and because previous research has shown that it has incremental validity over cognitive measures and is a plausible environmental cause.\cite{kirkegaardfuerst2014} For instance, the conservative web-tabloid \textit{Den Korte Avis} (The Short Newspaper) criticized researchers from a public researcher institute for not taking culture into account\cite{DenKorteAvis}:

\begin{quote}
The research thus speaks only about breaking the negative social inheritance as early as possible, but does not mention the cultural inheritance and the creation of parallel societies as a substantial factor, and a focus area for combating the problems [with low performance of immigrant students in schools]. With this narrow, politically correct point of view one cannot straighten out the problems.
\end{quote}

2. In your paper, the word "data" is treated sometimes as a plural noun and sometimes as a singular noun. Most style books recommend treating it as a plural noun (the singular form would be "datum"). So you should write "The data for the year 2013/2014 are here" and "GPA data are also available ...".

Emil,

1. I rewrote the paragraph to emphasize the point that the two tendencies would cancel each other out. Feel free to accept or reject what I wrote:

This study only concerns normal schools and excludes special education schools, which have a higher proportion of lower GI students. Immigrants may thus be over-represented in such schools, thereby reducing the GPA gap in normal schools and making it seem smaller than it really is for the Danish population as a whole. Immigrants are in fact over-represented in some special education schools, especially the second generation (see the appendix for details). On the other hand, there may be under-diagnosis of special education needs among immigrant students. Such under-diagnosis would happen partly because social workers may try to avoid assigning immigrant students to schools for the retarded and partly because a higher proportion of immigrants appear behaviorally normal even in the "retarded" range (usually less than an IQ of 75). In a population with a lower mean IQ, it is less likely that a below-75 IQ would have unusual genetic or developmental causes (e.g., Down's Syndrome) that disrupt many aspects of mental functioning. Low IQ individuals would thus seem more behaviorally normal and be less likely assigned to special education classes.\cite{jensen1969much} These two tendencies—to assign immigrant children to special education schools and not to assign them—would cancel each other out. It is currently unknown how large these biases are for the Danish data, so some caution is advised.

2. Your quote would have more "punch" if it came from a mainstream newspaper. But maybe that's too much to hope for.

I am willing to approve the manuscript. Do you have enough approvals for publication?

I read the new version (v8) and I don't disagree with anything in the entire text. I re-approve. But even if I disagreed with any of the modified portions, due to reviews, I don't think I will disapprove because it means I have to discuss the matter with the reviewer(s) in question. I don't think it's reasonable to go so far (and it's very complicated for obvious reasons I don't need to tell). For such modifications (and only for this kind), then, the authors don't need my re-approval.

In fact, I only have some quibbles :

The use of GI (General Intelligence) while most authors would have written GCA (General Cognitive Abilities). They mean just the same thing. Why not using GCA ? Because using another, new term is not very practical (and in fact it's very irritating in my opinion) to use different terms for saying just the same thing. Say GCA and everyone in the field understands what you say. But say GI, and no one could answer that without asking the meaning of it.

1) The second GI should be GPA. 2) It can even if more than one variable affects GPA, since a variable that would have decreased the correlation IQ-GPA could have been masked (offset) by another variable that would have increased the correlation IQ-GPA.

And in page 6, you wrote "The GPA gaps were -1.7 and -1.3, -.50 and -.38 d respectively" while in your table 4 the gaps are 1.7, 1.3, -0.50 and -0.38.

It's overoptimistic. I don't call a difference of 0.8 "even a bit larger". There's no change. That's all.

Tables 2 & 5 : same problem as before. Predictor should be used for indepedent vars inserted into the regression equation in a regression analysis, as its definition implies. There is no "predictor" in a correlation analysis because both variables are treated the same. And at page 7, you wrote "predictor analyses". I know what is a regression analysis and a correlation analysis but I doubt anyone knows what is a predictor analysis.

In table 2 by the way, some numbers have 2 digits after comma, some have 1 digit, and another has zero digit. I think it's preferable to have all numbers with the same number of digit. Even for the zero correlation.

The way you write it is confusing because it implies that improved environment can either increase or decrease IQ. If a good environment has an effect on IQ, it's through IQ gain.

But outliers are sometimes useful. The more you have outliers, and the more likely you would have missed an important information, i.e., a confounding variable. And even a single outlier can be of some interest, sometimes, if you know/understand the reason for this behavior.

seem with an "s".