Imagine for example two groups, A and B, and two numerical traits X and Y.

Group A has an average value of X(A)=10 and an average value of Y(A)=20.

Group B has an average value of X(B)=15 and an average value of Y(B)=30.

You can add more groups, maintaining the property that a higher group value for X is associated with a higher group value for Y. Indeed, you might regress X(.) on Y(.) and find a strong positive correlation between the two: high X(.) value corresponds to high Y(.) value.

**The logical error is the following: to infer that this means that**.

*individuals*with a high X value also tend to have a high Y valueTo see why this is the case, suppose that group A has three individuals a, b, c with values X(a)=5, X(b)=10, X(c)=15 and Y(a)=30, Y(b)=20, Y(c)=10. It is easy to see that these values do in fact correspond to a group average of X(A)=10 and Y(A)=20, but it is obvious that

*within the group*low X values are associated with high Y values and vice versa.

The same situation might also be the case for group B, and it would thus turn out that when it comes to

*individuals*low X values are associated with high Y values, that is

*the opposite correlation to that of the group averages*.

The lesson from this example is the following: whenever you hear that e.g., group A is "greener" than group B and group A is "smarter" than group B, therefore "greener" people are "smarter", you should ask to see the correlation between "green" and "smart" individuals and question the assumption that group-based differences have anything to do with individual difference.

**PS**: I had meant to write something on the topic for a while, but I was reminded to do so by Steve Sailer's new article on John Kerry's IQ. Steve brings up a recent hoax which he uncovered regarding supposedly "smarter" Democratic-voting versus "dumber" Republic-voting states. Liberals were eager to treat this as evidence that liberals are smarter than conservatives. As the analysis above shows, this would emphatically

*not*be the case, even if those results were correct. But, note also, that the fact that Democratic-leaning states vs. Republican-leaning states tend to have similar average IQs does

*not*prove that Democrats and Republicans tend to have similar IQs, for exactly the same reason. It is quite possible that individual-based comparisons within each state and consequently within the total US population might indicate that political orientation and intelligence are correlated.

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