I have previously argued that the problem with averages, as summary statistics, is they 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.
This morning I found another example of this problem with averages in my email inbox. The “Daily Bulletin” published by the newsadvocacy outlet, The Trace, contained the following summary of a research article:
23 states with “stand your ground” laws saw 8% to 11% increases in monthly rates of gun homicide over 16 years. Proponents of the laws that remove a person’s duty to retreat before using deadly force say they make the public safer by deterring would-be attackers, but a new study led by Michelle Degli Esposti of Oxford University and three colleagues found the laws actually correlate to more homicides overall, as well as more gun homicides specifically. The study compared 23 U.S. states that enacted SYG laws between 2000 and 2016, and 18 that did not have them in the same period (excluding the nine remaining states because they could not accurately be sorted into either group with sufficient data). They found large regional differences, with many SYG states in the South — including Alabama, Florida, Georgia, and Missouri — seeing increases in violent deaths rise by as much as 33.5 perfect, while similar laws in Arizona, Indiana, Michigan, Nevada, Oklahoma, Texas, and West Virginia were not associated with any difference. “These findings suggest that adoption of SYG laws across the U.S. was associated with increases in violent deaths, deaths that could potentially have been avoided,” the authors wrote.
The Trace Daily Bulletin, 23 February 2022
Even in this short summary, we see this problem quite glaringly. On the one hand:
[A] new study . . . found [Stand Your Ground] laws actually correlate to more homicides overall, as well as more gun homicides specifically.
On the other hand:
They found large regional differences, with many SYG states in the South — including Alabama, Florida, Georgia, and Missouri — seeing increases in violent deaths rise by as much as 33.5 perfect, while similar laws in Arizona, Indiana, Michigan, Nevada, Oklahoma, Texas, and West Virginia were not associated with any difference.
So, Stand Your Ground laws “correlate to more homicides” (including with firearms) nationally, but of 11 states mentioned, SYG laws in 7 “were not associated with any difference” in the homicide rate.
Even ignoring the “correlation is not causation” argument, if a casual factor only has an effect in 4 of 11 cases, it would not seem to be an independent causal factor in the outcome of interest. What else is going on in those 4 cases that are acting in concert with that causal factor that is not happening in the other 7 cases?
NOTE: I have not yet read the article and I make no claim about the accuracy of the research, one way or the other. My concern is how the findings are being spun by The Trace. If The Trace is accurately conveying the authors’ conclusion, then the authors, too, are thinking too simplistically about their findings.