On the occasion of my 5th blog-iversary recently, I listed my 10 most popular blog posts ever. To my surprise, my 9th most popular blog post ever was published just 2 months ago, which means it got strong immediate readership. It was my second take on what I have called “The Problem with Averages in Understanding Guns, Violence, and Crime.”
The heart of the problem is that averages, as summary statistics, can obscure significant underlying differences in the data producing the averages. Two very different distributions of data can result in the same average. Imagine a city that has two neighborhoods and a city-level average of 100 homicides per year. That average is the same whether those homicides are distributed evenly between the two neighborhoods or are concentrated entirely in one of the two neighborhoods. The average as a summary statistic only tells part of the story.
Although I came to this insight inductively, through my own personal experience of living in a community with tremendous social inequality (including inequalities of violence and crime), others have approached the dangers of summary statistics in a much more sophisticated manner. Among these sophisticated thinkers are the statistician Francis Anscombe who in 1973 created four datasets with differing underlying data distributions but the same summary statistics (mean, standard deviation, and correlation).
Anscombe’s Quartet has recently been updated in a very clever way by two researchers at Autodesk (with an assist to Alberto Cairo). They show even more dynamically than Anscombe how different underlying distributions of data can yield the same summary statistics (h/t to Dan Hirschman at scatterplot).
To bring this back to guns, violence, and crime, over 2 years ago (April 10, 2015) I observed:
The problem with averages is that there is no “United States of America” when it comes to guns, violence, and crime, but many Americas. Some of these Americas – like my neighborhood in Winston-Salem – are more like our first world counterparts in the OECD, and some of them are more like the third world politically, economically, and socially.
I recently came across a graphic published by Richard Florida on The Atlantic magazine’s CityLab website in 2013 which makes my point in a visually compelling way by comparing the firearm homicide rates in various U.S. cities to those in comparable countries. For example, Phoenix’s homicide rate of 10.6 is like Mexico’s rate of 10, Buffalo is like Panama, Boston like Nicaragua, Atlanta like South Africa, Portland like Chile, and so on. Really fascinating and instructive.
Of course, what is missing here is the flip side of the coin. Those parts of the United States whose lower firearms homicide rates resemble those of European countries. Maybe someone who is better at data visualization than I am will undertake to create this second map?