And now for something completely different:
https://www.quantamagazine.org/dona...n-the-data-of-life-and-the-universe-20180411/
It turns out the stats dominating the gun control debate have been so strikingly bad they have been used to promote major improvements in how statistics are treated in the first place. Here's Donald Richards illustrating the value of a new measure of correlation he helped invent, the "distance correlation", by retailing how it improves on an example of the common public misuse of gun violence statistics:
https://www.quantamagazine.org/dona...n-the-data-of-life-and-the-universe-20180411/
It turns out the stats dominating the gun control debate have been so strikingly bad they have been used to promote major improvements in how statistics are treated in the first place. Here's Donald Richards illustrating the value of a new measure of correlation he helped invent, the "distance correlation", by retailing how it improves on an example of the common public misuse of gun violence statistics:
- - I guarantee you that the bulk of applications of the Pearson correlation coefficient are invalid - -
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You wrote a paper last year giving examples where distance correlation improves on Pearson’s method. Talk about the case of homicide rates and state guns laws.
This was prompted by an opinion piece in The Washington Post in 2015, by Eugene Volokh, a professor of law at UCLA. The title of the article is “Zero Correlation Between State Homicide Rate and State Gun Laws.” What he did was — you know, my eyes bugged out; I couldn’t believe it — he found some data on the states’ Brady scores, which are ratings based on the toughness of their gun laws, and he plotted the Brady scores on an x-y plot against the homicide rates in each of these states. And if you look at the plot, it looks like there’s no pattern. He used Excel or something to fit a straight line to this data set, and he calculated the Pearson correlation coefficient for this data set, and it came out to be nearly zero. And he said, “Aha, zero correlation between state homicide rate and state gun laws.”
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But should you even fit a linear regression line to this data set? If you look at the rest of the data, you don’t see any linearity to the relationship, and it’s easy to understand why: There are bunches of points that correspond to geographic and culturally similar regions. If you break up the states by region, then you see reasonably linear relationships starting to show up in the scatter plots. And then in each case, you find that the higher the Brady score, the lower the homicide rate.
Distance correlation does an even better job without having to split things up, right?
Exactly. My wife and I did these calculations in the fall of ’15, when we saw the opinion piece. - -