army1987 comments on Rationality Quotes September 2011 - Less Wrong

7 Post author: dvasya 02 September 2011 07:38AM

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Comment author: gwern 03 February 2013 01:41:12AM *  5 points [-]

"Exponential correlation of IQ and the wealth of nations", Dickerson 2006:

Plots of mean IQ and per capita real Gross Domestic Product for groups of 81 and 185 nations, as collected by Lynn and Vanhanen, are best fitted by an exponential function of the form: GDP = a * 10^b*(IQ), where a and b are empirical constants. Exponential fitting yields markedly higher correlation coefficients than either linear or quadratic. The implication of exponential fitting is that a given increment in IQ, anywhere along the IQ scale, results in a given percentage in GDP, rather than a given dollar increase as linear fitting would predict. As a rough rule of thumb, an increase of 10 points in mean IQ results in a doubling of the per capita GDP.

....In their book, IQ and the Wealth of Nations, Lynn and Vanhanen (2002) present a table listing for 81 nations the measured mean IQ and the per capita real Gross Domestic Product as of 1998 (their Table 7.7). They subsequently extend this to all 185 nations, using estimated IQs for the 104 new entries based chiefly on IQ values for immediate neighbors (their Table 8.9). In both cases they observe a significant correlation between IQ and GDP, with linear correlation factors R^2 = 0.537 for the 81-nation group and 0.389 for 185 nations. McDaniel and Whetzel have extended the examination of correlations to quadratic fitting in a paper that demonstrates the robustness of these correlations to minor variations in individual IQ values (McDaniel & Whetzel, in press). But an even stronger correlation is found if the fitting is exponential rather than linear or quadratic.

Comment author: [deleted] 03 February 2013 08:42:30AM *  3 points [-]

It peeves me when scatterplots of GDP per capita versus something else use a linear scale -- do they actually think the difference between $30k and $20k is anywhere near as important as that between $11k and $1k? And yet hardly anybody uses logarithmic scales.

Likewise, the fit looks a lot less scary if you write it as ln(GDP) = A + B*IQ.

Comment author: gwern 09 February 2013 08:43:05PM *  0 points [-]

Yes, Dickerson does point out that his exponential fit is a linear relationship on a log scale. For example, he does show a log-scale in figure 3 (pg3), fitting the most reliable 83 nation-points on a plot of log(GDP) against mean IQ in which the exponential fit looks exactly like you would expect. (Is it per capita? As far as I can tell, he always means per capita GDP even if he writes just 'GDP'.) Figure 4 does the same thing but expands the dataset to 185 nations. The latter plot should probably be ignored given that the expansion comes from basically guessing:

In their book, IQ and the Wealth of Nations, Lynn and Vanhanen (2002) present a table listing for 81 nations the measured mean IQ and the per capita real Gross Domestic Product as of 1998 (their Table 7.7). They subsequently extend this to all 185 nations, using estimated IQs for the 104 new entries based chiefly on IQ values for immediate neighbors (their Table 8.9).

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