## August 11, 2006

### Latitude Centrality and Brilliance in Europe

I have often made the point that one should not consider only the average values when discussing the achievement of different populations.

I was looking at the TIMSS international mathematics report, and I was struck once again by the great differences in the shapes of mathematical ability distributions in different countries. In the 8th grade report, for example, the standard deviation of mathematical ability ranged from 60 in Tunisia, to 107 in South Africa, no doubt to the multi-racial character of the last country.

I entered the data from European countries into a spreadsheet to do some more analyses. The countries were (N=19): Belgium, Bulgaria, England, Estonia, Hungary, Italy, Latvia, Lithuania, FYRO Macedonia, Moldova, Netherlands, Norway, Romania, Russian Federation, Scotland, Serbia, Slovak Republic, Slovenia, Sweden

I mainly wanted to check whether my previous observation was accurate, that "A third observation is that there is a significant geographic structuring of the standard deviation of IQ." As before, I used the latitude of capital cities to represent the different countries.

The analysis of the mathematical achievement in this sample revealed (as before) that more southern countries have a higher standard deviation of achievement than more northern ones. This time, the R-squared value was 51.8%. As before, latitude did not predict the average achievement (R-squared value of 2.9%).

Next, I concentrated on the performance of top achievers, i.e., those who belong to the top 5% of the distribution (95% percentile). I regressed the 95% percentile on both latitude and a derivative "latitude peripherality" which was defined as |latitude-mean(latitude)|. Latitude peripherality is high for countries that are in the northern and southern extremes of latitude, and is low for more centrally placed ones.

It turns out that latitude does not predict the performance of the most brilliant students, belonging to the top-5% (R-squared is 3.2%). On the other hand, latitude peripherality does, and is negatively correlated with it (R-squared of 29.3%).

So, it seems that the countries of the middle latitude zone produce more geniuses per capita (at least 8th grade ones) than the more northern and southern regions in Europe [1]. Topping the achievement chart are the Hungarians, those notorious aliens.

[1] It should be noted however, that with the exception of Italy and some Slavic countries of the Balkans, Mediterranean Europe was not represented in this sample.

UPDATE (14 AUG): Using the PISA data that someone posted on the comments, it turns out that latitude explains 10% of the variance in the percentage of students who have a proficiency score above 668 in mathematics. Latitude peripherality explains 23% of the variance. Thus, the PISA results also indicate that latitude centrality, i.e., intermediate north-south geographical position in Europe is associated with top performance in Europe. All European countries in the PISA dataset were used except for the small states of Luxemburg and Liechtenstein.