June 13, 2003
Correlation between IQ Variability and Math Olympiad Performance
IQ data is from Buj (1981). Math Olympiad Scores are from here. A couple of caveats: (i) IQ scores are about twenty years older than Math Olympiad Scores, (ii) Yugoslavia and Czechoslovakia of 1981 are different from today, and Great Britain in 1981 study is presumably slightly different from UK of Math Olympiad results.
With all that said, the correlation between the standard deviation of IQ as reported by Buj (1981) and Math Olympiad scores is is 0.44 (significant at the 0.05 level). A higher standard deviation may mean overrepresentation at the tails of the IQ distribution, assuming similar distribution shapes. This result is compatible with that interpretation.
A few more results. Correlation between mean IQ and Math Olympiad scores is a non-significant -0.02. Correlation between population size and scores is 0.44 as well [presumably larger populations have greater pools of very smart individuals to pick from when forming a team].
Correlation between longitude and Math Olympiad performance is 0.51 (significant at the 0.02 level) with Eastern Europeans outperforming Western Europeans. Correlation between latitude and Math Olympiad performance is an insignificant 0.001.
Interestingly, the five ex-communist nations have a mean score of 132.2 while the remainder have a mean score of 68.25.
Correlation between GDP per capita (from CIA World Factbook 2002) and Math Olympiad performance is -0.54. Competitors from poorer countries tend to do better.
And a few more correlations. Mean IQ and GDP per capita are not significantly correlated (-0.02). However the Standard Deviation of IQ and GDP per capita are significantly correlated (-0.63) at the 0.01 level. It looks like as I predicted, homogeneity (in this case in IQ) seems to promote affluence (because of reduced friction and dissonance?), while heterogeneity seems to promote superior performance. This result still needs to be further investigated, but the data so far seems not to contradict it.
Buj, V., 1981, Average IQ values in various European countries, Personality and Individual Differences, 2, 168-169
Posted by Dienekes at June 13, 2003 11:43 PM | PermaLinkYour analysis is rather shaky.
Since you have a number of variables that may jointly affect the math score, a multiple regression analysis would be more appropriate than what you did.
So using Excel, let's fit a model:
math score = a1*x1 + a2*x2 + a3*x3 + a4*x4
where
x1 = mean iq
x2 = s.d. iq
x3 = population
x4 = binary variable (formerly communist? no=0 yes=1)
and a1...a4 are numerical coefficients to be computed.
The 4 variables together account for R^2 = 77% (adjusted R^2 = 71%) of the variability in the data.
When the independent variables (x1...x4) are scaled to have mean=0 and SD=1, the regression coefficients turn out to be:
a1 = -9.841445377
a2 = -6.662297785
a3 = 28.70288097
a4 = 35.13536156
The individual p-values for each variable are:
p X1 = 0.094051511
p X2 = 0.320882318
p X3 = 0.000242646
p X4 = 0.000029612
So you can see that when we control for population and former communist status, the mean and standard deviation of the IQ are not significant at the .05 level. Population and communism, on the other hand, are highly significant and positively related to the European countries' math scores.
You should try alternate models with different sets of variables and see which model(s) have the best predictive value (one good criterion is to shoot for a high adjusted R^2).
Posted by: Bruno at June 16, 2003 05:41 AMPlease send me your excel worksheet if you don't mind.
Posted by: Dienekes at June 16, 2003 03:09 PMThanks for good info
Posted by: Overweight at June 21, 2004 07:46 AM