At the request of John Hardin, last year’s chart comparing the number of firearms to the number of firearm-related deaths in America has been updated to take into account 2007’s numbers:
For the newcomers to the party, the same set of disclaimers applies as last time, with some updates and changes for the new year’s data:
1. Fitting it all together: I had to fiddle with orders of magnitude to get all of the lines visible within the same general range, so ups-and-downs did not get minimized. This does not affect the accuracy of the data, it just moves lines around such that you can show them all on the same graph (so you can see the trending of various lines easier). Both the “American Population” line and the “Number of Firearms” line must be multiplied by 10,000 to give their “real” numbers. Additionally, the both forms of the “Rate of Firearm-Related Deaths” are presented in “X per 100,000,000”. Again, this change does not affect the accuracy of the information presented (especially since I kept all the digits of each relevant data point, despite moving those numbers’ decimal points around). The important thing on this graph is trending, not specific numbers (although once you multiply by the appropriate order of magnitude, the numbers are still correct).
The “Number of Firearm-Related Death” line was not adjusted at all – its numbers are its numbers. However, be advised: this category includes “all Intents” of any fatal injury in which the “cause or mechanism” was a firearm, according to WISQARS – “all intents” includes “unintentional”, “suicide”, “homicide”, “legal intervention”, and “undetermined intent”. This is done, with malice aforethought, to intentionally skew the numbers in favor of those who would support the “more guns = more deaths” hypothesis.
2. Where the numbers come from: The “American Population” and “Number of Firearm-Related Deaths” information came from WISQARS.
The “Number of Firearms” was a little more tricky, though… I used the lower end of the range hypothesized in the Small Arms Survey of 2003 as my 2003 datapoint (as denoted by the large dot on that line). For any years after 2003, I added the BATFE Annual Firearms Manufacturers and Export Report numbers. For the years between 2002 and 1997, I successively subtractved the data from the same BATFE report. For the years between 1996 and 1981, I successively subtracted the data from the Shooting Industry Magazine’s U.S. Firearm Industry Report (Extended).
If I had used the information from the 1997 study (192 million firearms in 1994), the number of firearms in America would be reduced by approximately 13 million each year. If I had used the upper range of the Small Arms Survey, the number of firearms in America would increase by approximately 38 million each year. I consider my choice to be a gracious compromise. However, the “Number of Firearms” data is only as accurate as its base assumptions, and I have no way of verifying if any of the three numbers available are accurate, or any more accurate than any others.
The two “Rate” lines were calculated internally to the spreadsheet that generated this graph (however, the “Rate of Firearm Related Deaths per 100,000,000 People” correlates perfectly to a similar statistic generated by WISQARS (once you factor in that their rate is per 100,000 individuals)).
3. Conclusions: Obviously, both the population of America and the number of firearms in America have been increasing over the past 26 years. Additionally, the number of firearms has been, very slightly, increasing faster than the population.
On the other hand, firearm-related deaths have declined, despite a significant bump in the early 1990s. Those deaths have very slowly started increasing again in the past five years, but at a rate roughly commensurate with the population’s.
And on the third hand, the rate of firearm deaths in relation to both population and number of firearms has been steadily decreasing (with a few bumps, here and there) over the course of the 26 years graphed.
This post graphically demonstrates that the hypothesis that more firearms result in more firearm-related deaths is historically and demonstrably false. However, proving “more guns = more deaths” false does not necessarily prove “more guns = fewer deaths” true.
4. Verification: Unlike anti-rights advocates, I have used facts and figures to make my point. Additionally unlike anti-rights advocates, I will make those facts and figures, as well as my methods, publicly available (last year’s spreadsheet is available here). Feel free to download the spreadsheet (I promise it is clean) and take a look at the numbers for yourselves. If I did something wrong, please correct me. If you can find better counts of the number of firearms in America (or anything else), please provide them. I know that the facts are the only things that matter, again, unlike the anti-rights advocates, and anything that can give us a better look at those facts is something we should pursue.
So how did 2007’s data change things? Not appreciably. The American population grew 0.8%, firearm-related deaths grew 1.1%, the number of firearms in common circulation increased by 1.6%, firearm-related deaths per 100,000,000 people increased by 0.2%, firearm-related deaths per 100,000,000 firearms decreased by 0.5%, and firearm ownership per 10,000 people grew by 0.7%.
Basically, firearm-related deaths grew slightly faster in 2007 than the American population, which is in contrast with 2006 and 2005 where the opposite was true, and 2004 and 2003 where firearm-related deaths actually decreasedslightly. Over that same period (2003-2007), the number of firearms in common circulation has been increasing between 1.3% and 1.6% a year.
… Which brings me to the next product of my bored mind. We are all familiar with the phrase, “Correlation does not equate to causation,” but a lot of people forget about the rest of it, “… but causation requres correlation.” So, given that the hypothesis of “more guns = more deaths” is demonstrably false over the past 26 years here in America, is there any correlation at all between those two events?
Given that the chart of firearm-related deaths is not monotonic, we cannot solve for Spearman’s rank correlation coefficients, so we are stuck with the Pearson correlation coefficient, which allows us to solve for linear correlation between two data sets. As you can see on the spreadsheet, I solved for linear correlation by hand, and then by using Excel’s onboard linear regression tools, with the same results.
Assuming the number of firearms in common circulation describes the X-axis of a graph, and assuming the number of firearm-related fatalities describes the Y-axis of a graph, the equation necessary to describe the closest-fit line is: Y = -0.00004X + 40852. The ‘r’-value for this line is -0.36343, and the R2 value for this line is 0.13208.
What does that mean? ‘r’-values can range from -1 to +1, with +1 meaning that all data points lie perfectly on a line, with Y increasing as X increases, and -1 means the same with Y decreasing and X increasing. 0, logically enough, means no correlation at all. Based on an ‘r’-value of -0.36343, the number of firearms in civilian circulation and the number of firearm-related deaths are weakly correlated, but in a negative fashion – as the number of firearms increases, the number of firearm-related fatalities generally decreases, though not in anything even approximating a “direct” fashion.
However, in order to again separate ourselves from those anti-rights advocates who abuse statistics on a regular basis, it is necessary to be honest about this linear regression, and point out that the graph we are attempting to analyze is far from linear:
Which, of course, begs the question of whether or not there is an equation that can better describe the line we are seeing displayed above, with a better ‘r’-value? I am not sure, but after tinkering around a little with Excel’s trendline abilities, I did find an equation that had a much better R2, meaning that its “goodness of fit” is significantly better: y = -3E-42x6 + 4E-33x5 – 2E-24x4 + 5E-16x3 – 7E-08x2 + 5.3301x – 2E+08
For those keeping up at home, that is, indeed, a sixth-order polynomial, but its R2 value is 0.9232. Great, right? Yeah… until you ask it to project out a little into the future:
That meteoric drop on the right just keeps going if the graph goes farther out, reaching positively absurd negative depths in very short order, leading one to believe that this is not actually a better representation of what little correlation there might exist between firearms and firearm-related deaths.
So is -0.36343 a significant correlation? Well, it seems to depend on who you ask, and whether or not you are interested in doing some complicated math, but, regardless, it is still a negative correlation. But wait… all of this conveniently overlooks the impact of population growth on all crime numbers. What happens if we look at rates, rather than raw numbers?
Assuming the number of firearms per 100,000 people in common circulation describes the X-axis of a graph, and assuming the number of firearm-related fatalities per 100,000 people describes the Y-axis of a graph, the equation necessary to describe the closest-fit line is: Y = -0.00029X + 34.97729. The ‘r’-value for this line is -0.75124, and the R2 value for this line is 0.56436.
Well, would you look at that? If you pay attention to rates as opposed to raw numbers, the linear correlation between firearm ownership and firearm-related deaths over doubles, and is still quite negative. Interesting, that. (For those interested, some higher-order polynomial functions do, indeed, match the curve significantly better, but have the same kind of problems when asked to predict future performance as before.)
*Wipes forehead* Whew. So after all this nonsense, where do we stand?
1. The hypothesis of “more guns = more deaths” is demonstrably false over the past 26 years of American history. The number of firearms in civilian circulation have been steadily increasing over that time period, and the number of firearm-related fatalities has not been equivalently increasing. However, again, since there seems to be some confusion on the concept, proving “more guns = more deaths” to be false does not necessarily prove “more guns = fewer deaths” to be true. Doing so would require accounting for far more variables than I did, and involve far more interesting math than I employed.
2. When comparing raw numbers, there is a weak, negative correlation between the number of firearms in America, and the number of firearm-related fatalities.
3. When comparing rates, there is a strong, negative correlation between the number of firearms per person in America and the number of firearm-related fatalities per person.
Is that not interesting?
As before, all of the above data is freely available on the spreadsheet, and you are more than welcome to check my calculations, perform some figuring of your own, and use the numbers for whatever you see fit. However, if you decide to use the above graphics, I would sincerely appreciate an appropriate link back to this page, and proper attribution to go with it.
… Now watch this post get absolutely no attention, what with it being Friday evening and all.
[1230 12JUN10 Update] To clear up some potentially intentional confusion, the dataset “Rate of Firearm Ownership per 10,000 People” has been renamed to “Number of Firearms per 10,000 People”. All graphs and text should be updated to reflect this change. [/Update]
[1750 12JUN10 Update] For those folks out there who plan on using this chart to try and claim that the Brady Bill is responsible for the sharp decline in firearm-related fatalities, or are otherwise concerned about someone doing that, you might want to check out this set of four posts done by fellow pro-rights weblogger Reputo. He takes a look at all of the significant elements at play that could describe that somewhat precipitous increase, then decrease, in crime in the 80s and 90s, and does so in a significantly more-understandable, less-confusing way. [/Update]