Sunday, May 22, 2011

Random charts

Source: The Geography of Hate. An article in The Atlantic looks at the distribution of hate groups across the U.S. and says: "... America's racist groups concentrate in certain regions -- and their presence correlates with religion, McCain votes, and poverty..."

Damning? Well... not so much! The following table provides a 'qualitative description of the strength' of the coefficient of correlation. From this we see that the touted 0.35 correlation with religion is a "weak positive", as are those of 'higher poverty rates' (+0.39) and a 'larger blue-collar working class workforce' (+0.41). The correlation with McCain votes is stronger at 0.52, but this still barely makes it into the "moderate positive" range.

Mathematically, the coefficient of determination is actually a better measure to use when comparing the magnitude of the relationship between two measures. Using the numbers quoted in the article, the coefficients of determination between hate groups and religion and McCain voting are 0.1225 and 0.2704 respectively. In other words, only approximately 12.25% of the variation in the hate group variable can be explained by variation in the religion variable; and 27.04% by the variation in the McCain vote variable....

The article took pains to note that "... correlation does not imply causation ..." and that "...we are simply looking at associations between variables...". However, by not providing qualitative context for the numeric correlation coefficient values, and by focusing on the correlation coefficient rather than the coefficient of determination, this exposition is not the most ingenuous or scrupulous...

Correlation Coefficient
Correlation: Interpretations
Pearson’s Correlation Coefficient

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