No, the PISA SD is 100 within a population. An individual with a PISA score of 700 has an equivalent IQ of 130.

The reporting scales that were developed for each of reading, mathematics and science in PISA 2000 were linear transformations of the natural logit metrics that result from the scaling as described above. The transformations were chosen so that the mean and standard deviation of the PISA 2000 scores was 500 and 100 respectively, for the equally weighted 27 OECD countries that participated in PISA 2000 that had acceptable response rates (Wu and Adams, 2002).

A few comments:

The wording in this paper is sometimes abrupt, excessive, or simply wrong. Here are a few examples:

"We obtained data from Denmark for the largest 71 immigrants by country of origin." - replace "immigrants" with "immigrant groups" or "the 71 largest sources of immigrants by ..." You might want to mention that some of these groups are heterogeneous. The term "Ugandan" probably includes not only indigenous Africans but also people of South Asian origin.

"Yugoslavia's IQ" - the state of Yugoslavia has not existed for some time. You should write "the former Yugoslavia"

"they immigrated too late to the country and so have not taken advantage of the tax-funded education system." - Why not simply say: "and so have not attended Danish schools". Schools are tax-funded in most countries. Why insist on that point?

"Perhaps some immigrant groups are criminal" - Wouldn't it be more correct to say that some immigrant groups have a high incidence of criminality?

"Islam", "Islam", "Islam", etc. etc. etc. As I pointed out in a previous comment, most Muslims in Western Europe are only nominally so. This is particularly true among the young men who contribute the most to the high crime rates we hear about. I knew a young Moroccan man who would brag about the people he had beaten up ("You see that blood on my jacket? It's not mine!"). He had no interest at all in religion and was probably more influenced by African American hip hop than anything else. Insofar as "Islam" plays a role in all this, it is simply as an identity tag and not as a belief system.

If we look at immigrants to Denmark, they fall into three groups:

1. Other Europeans.

2. People from North Africa, the Middle East, Afghanistan, and Pakistan, i.e., the Muslim world.

3. East Asia, Southeast Asia, and non-Muslim South Asia.

On the face of it, religion (i.e., Islam) is the main difference between group 2 and groups 1 and 3. I would argue that there is another difference. Groups 1 and 3 have lived in societies where the State has exercised an effective monopoly over the use of violence, with the result that people have much higher thresholds for expression of personal violence. Group 2 corresponds to societies where the state has never monopolized the use of violence and where every adult male is expected to use violence as a legitimate means of resolving personal disputes. Thresholds for the expression of personal violence are thus correspondingly lower.

I don't expect to convince you. All I'm saying is that you shouldn't prejudge things by positing "Islam" as a causal factor when it probably isn't.

I said it before but I like the tables when they look like the one you have in table 13. The numbers appearing in your correlation matrix are just too small and I must zoom in constantly. And worse, they don't fit the text. That it, the numbers in your tables are too small compared to the text.

The first thing I find very shocking is that you have not explained what the highest values in your educational variables are. Worse outcome or better outcome ? Because anyone looking at your table 1, with basic school correlating negatively with GDP and IQ, everyone will not interpret it correctly. If that variable measures the % of people who had only basic schooling, it's obvious that the expected correlation will be negative. You must precise it below the table 1. Or change the name of your variable in "percentage having only basic school". For example.

For your Islam variable, I look at your .sav file, and hopefully, it's not a dichotomy variable. Otherwise, i would have questioned the relevance of that data.

"The corollary of this is that the known correlates of g are also retained such as average education levels."

This sentence is not clear to me.

"All four predictors performed similarly for this variable which is surprising given that height seems to have no conceptual relevance to education."

It's curious because I think it has relevance. Height is correlated with education because it correlates with physical health, SES, and perhaps IQ (if I remember well).

Also, when you use PC2EdAtt, you should probably precise that whatever the correlation may look like, none of these correlations make sense because the PC2 does not make sense, and you admitted it. In fact, there is no necessity to correlate that PC2 if it is not interpretable, if there is no theoretical basis for PC2.

"IQs (NIQ) did not predict income after age 60,"

That's wrong. The r was 0.225. Not impressive maybe, but not small either.

For tables 6 & 7, I know that early income is PC2, but perhaps you should precise it in your text, and make sure everyone understand it. For example the sentence may look like "The second was interpretable as an early income and we label it as such, e.g., in table 7.". And for that same reason, you also expect negative r between use of social benefit and height. And it's exactly what you have in table 8 and 10.

"Perhaps some immigrant groups high relatively high crime rates but also have relatively high average incomes"

There is surely one word or more that is missing here.

When you jump from table 9 to 10. It's too abrupt. You simply write that the correlations are shown below. But you don't discuss the output. I think it's recommended to do this. For example, height is negatively correlated with Islam and social benefit. Why this pattern ? for example, you can say (but it's my interpretation, not necessarily yours) that taller people have higher SES levels, and because social benefits correlate negatively with GDP and IQ, this pattern was also expected. Why Islam has a negative sign for height, well, I don't know.

Concerning table 11, I want to make sure about something. Can you reverse the numbers in "long-tert-edu" and "income" ? And then, re-do the PC? If everything is right, the PCs with and without "long-tert-edu" reversed should be correlated at 100%.

To be honest I recommend you to reverse the variables of income and long-tert-edu or the others. Usually, in PC analysis, all the loadings must be positive. In your situation, you have signs in every direction, and it's truly confusing. It's even more complicated to interpret PC2, PC3, and PC4. I'm pretty sure most practioners will not like your table 11. And, for example, I don't like it.

"We tested whether predictors could be combined to improve the prediction of the general socioeconomic factor with multiple regression."

To be honest, I don't like R². The practice of squaring correlation is really so wrong. I don't think it's needed for your analyses. It really adds nothing, just more confusion for people who trust the R². If any predictors add something, the best way to look at it is through its beta coefficient (standardized and/or unstandardized). The r² is difficult to interpret, especially for the individual predictors. That does not even tell you how much they change when more independent var are added in the model.

"Islam was an very good predictor"

There is an error with that word.

"was due to Islamic countries have low IQs"

Must be "having".

Concerning your series of plot, I'm not sure everyone will understand what you do. You have not introduced the method of the regression's predicted value and what you attempt to show here in the different plots.

"If anything Islam is a better predictor within the sample of European countries of origin although this was due to two countries Bosnia Herzegovina and Macedonia."

Ok, but that simply means your correlation depends only on these two countries. Remove them, and perhaps the correlation will fall. At 1rst shot I don't see any clear trend for european countries. However, I'm not sure that the removal of the MENAPs is the correct thing to do. As Templer said in Can't see the forest because of the trees, "To omit the Black-African countries in considering the geographical distribution of HIV/AIDS is like omitting the Northwestern European countries in a study of Nobel laureates." So you'll surely remove some relevant information belonging to these countries, and some variances as well.

"We have shown that how well an immigrant group"

I'm not very good in english but i'm sure this sentence is wrong. The word "that" can be removed.

By the way... the introduction seems a little bit short, no ? Perhaps I would suggest a little description about what you attempt to show, what you expect to find in your series of correlations/regressions. I feel the readers may be at loss otherwise.