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"walls of the city" logo conceptualized by Oleg Volk and executed by Linoge. Logo is © "walls of the city".

graphics matter, year the fourth

[Please consider this updated version of this post, which has integrated firearm importation data as well as production numbers.]

Thanks to the newest preliminary FBI stats on crime coming out recently (the past pattern was replicated again: crime is down overall), I was reminded that I needed to check up on the Centers for Disease Control and Prevention and see if they had updated their WISQARS system to include fatal injury data from 2009; lo and behold they had, so it is time to update last year’s Graphics Matter post:

image

We will follow with the pattern from last year and lead with the disclaimers first:

1. Intellectual property: While all of this data is publicly available from the sources listed below, it takes time and effort for me to collate it all together and present it in a (barely) understandable format. All of the images in this post are my original works and copyrighted by me. If you want to use any of these images, you are more than welcome to do so; however, I must formally request that you link back to this specific page and give full credit to me, the originator, when doing so.

2. Feedback: If you have any questions, comments, or concerns about the graphs, my methodologies, my sources, my conclusions, or anything else, please post them here. I cannot and will not troll the internet checking the comments sections of all the webpages that link to this page trying to figure out what people think of this work. If you do not post it here, I will assume your concerns just are not important enough to express to me directly, and proceed accordingly. 

3. 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 divided 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. Giving those people every benefit of the doubt makes it all the more priceless when their hypothesis is shown to be erroneous.

4. Where the numbers come from: The "American Population" and "Number of Firearm-Related Deaths" information came from WISQARS. Be advised: the CDC pulls their population numbers from the United States Census Bureau, who has a nasty habit of repeatedly going back and revising previous years’ estimates, so the historical numbers on these charts may periodically change.

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 data point (as denoted by the large dot on that line). For any years after 2003, I added the Bureau of Alcohol, Tobacco, Firearms, and Explosives’ Annual Firearms Manufacturers and Export Report numbers. For the years between 2002 and 1997, I successively subtracted 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)… which apparently does not exist any more. They still have a U.S. Firearms Industry Today article, but those numbers only go back to 1990; I have an email in to the Shooting Industry Magazine to see about making that missing decade of data public again.

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 – there has been no authoritative, comprehensive inventory of every civilian-owned firearm in America, and there never should be.

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)).

5. Conclusions: Obviously, both the population of America and the number of firearms in America have been increasing over the past 29 years. Additionally, the number of firearms has been slightly increasing faster than the population. Of note, 2009 experienced the single biggest increase in firearm production of all the years on the chart recorded thus far; over 5.5 million firearms were produced in the United States that year.

On the other hand, firearm-related deaths have declined, despite a significant bump in the early 1990s. Those deaths were very slowly increasing again in the past six years, but at a rate roughly commensurate with the population’s, and that increase stopped in 2009, which instead experienced a decrease in deaths.

And on the gripping 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 29 years graphed.

This post graphically shows that the hypothesis that more firearms result in more firearm-related deaths is historically and demonstrably false. However, showing "more guns = more deaths" to be false does not prove "more guns = fewer deaths" true. In truth, as Yu-Ain Gonnano accurately observed previously, all this chart does is fails to reject the null hypothesis, which means there is more to the story than "gun control" extremists would have you believe with their "more guns = more deaths" oversimplification.

6. Verification: Unlike "gun control" extremists, I have used facts and figures to make my point. Additionally unlike "gun control" extremists, I will make those facts and figures, as well as my methods, publicly available (last year’s spreadsheet is available here). You will note that that particular spreadsheet also contains the data for my "more guns = more ‘gun violence’" Graphics Matter post, which will be updated as soon as the FBI finalizes 2011′s numbers. 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 "gun control" extremists, and anything that can give us a better look at those facts is something we should pursue.

And unlike those extremists, I certainly do not mind being corrected – the graph you see before you is the product of four years’ worth of feedback from you, the readers, and can always be improved in some fashion I am sure I have not thought of yet.

7. Controlling for variables: In short, I did not. Countless "gun control" extremists have fielded the argument that more guns invariably lead to more firearm-related fatalities. Their argument never progresses past that point, so this post makes no attempt to do either, and instead focuses on the core hypothesis contained within it. Obviously, the firearm-related fatality numbers in America are influenced by far more things than simply the number of firearms present, but I lack the wherewithal and data to adequately address all of those various factors, nor is it really necessary to adequately make my point. It is precisely due to that omission and simplification of the situation that trying to misappropriate this chart to claim that the Brady Bill is responsible for the sharp decline in firearm-related fatalities is a failing argument before it is even expressed; rather than try to convince yourself it works, I would suggest 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.

So how did 2009′s data change things? Due to the increased output of firearm manufacturers in the United States that year, there were some fairly noticeable changes. The American population grew 0.87% (a bit slower than the previous year), firearm-related deaths actually decreased 0.78% (breaking a four-year trend), the number of firearms in common circulation increased by 2.12% (significantly faster than the previous year), firearm-related deaths per 100,000,000 people decreased by 1.63% (a departure from the previous year’s number), firearm-related deaths per 100,000,000 firearms decreased by 2.88% (a significant swing due to the increased production), and the number of firearms owned per 10,000 people grew by 1.27% (ditto).

Basically, 2009 provides us a nice little microcosm to demonstrate the full failure of the "more guns = more deaths" myth. That year’s significantly increased firearm production – spurred, no doubt, by the significantly increased firearm demand preceding and following the 2008 elections – increased the total number of firearms in America by over 2% – the biggest number I have seen thus far in this exercise. On the other hand, firearm-related deaths actually dropped by almost a full percentage point, breaking with a trend that was steadily pointing upwards. Even allowing for the possibility of a "lag" being implied in the "gun control" extremist’s myth, firearm production had been "spooling up" since 2003, and there has never been a single year when firearm production was negligible, which completely destroys any chance of their drawing a causal relationship.

… Which brings us to the second half of these posts. 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 requires correlation." So, given that the hypothesis of "more guns = more deaths" is demonstrably false over the past 29 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 = -0.3929X + 41037. The ‘r’-value for this line is -0.41533, and the R2 value for this line is 0.17250.

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 -0.41533, the number of firearms in civilian circulation and the number of firearm-related deaths are 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.

Additionally, it is interesting to note that last year’s data yielded an ‘r’-value between firearm numbers and firearm-related fatalities of -0.37031. As the dataset grows, so too does the negative correlation between raw numbers of firearms and raw numbers of firearm-related fatalities; in other words, the truth just keeps helping us and damaging the arguments of those who would deprive us of our rights.

To give you a pretty picture of what we are talking about:

image

As we discussed in a previous year’s post, there are no other equations that match the current distribution with any better degree of fit and do not suffer from some radical departures later on in the graph, so we will just move right along.

Is -0.41533 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. At this point, though, I am willing to say that the negative correlation between raw firearm and firearm-related death numbers is not "weak", for whatever that may be worth. But wait… all of this conveniently overlooks the impact of population growth on all fatality numbers. What happens if we look at rates, rather than raw numbers?

Assuming the number of firearms per 10,000 people in common circulation describes the X-axis of a graph, and assuming the number of firearm-related fatalities per 100,000,000 people describes the Y-axis of a graph (I changed the orders of magnitude on these scales a little from last year to simplify copy-pasting the data from one sheet to the next – this does not really change anything, since we are still looking at the rate of change, not the actual numbers), the equation necessary to describe the closest-fit line is: Y = -2.9145X + 35053. The ‘r’-value for this line is -0.77863, and the R2 value for this line is 0.60627.

image

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 almost doubles, is still quite negative, and is arguably strongly negative. Interesting, that.

Equally interesting is that the rates experienced the same increase in negative correlation, based on the additional data, as the raw numbers. It would seem as though every time I crunch the numbers, the outlook just gets more and more bleak for the myth that "more guns = more deaths".

*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 29 years of documented 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 or even consistently increasing. However, again, since there seems to be some confusion on the concept, proving "more guns = more deaths" to be false does not 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, and require controlling for far more influences than I care to.

2. When comparing raw numbers, there is a negative correlation between the number of firearms in America and the number of firearm-related fatalities, and that correlation seems to become more negative with additional data.

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, and that correlation seems to become more negative with additional data.

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, please see Disclaimer 1 above.

However, while all of these pretty pictures do a fairly handy job of demolishing a childish argument far too repeatedly parroted by "gun control" extremists, none of it really matters – our rights are not subject to any statistics anyone can dredge or dream up. Or, to put it another way:

Where the hell do you get off thinking you can tell me I can’t own a gun? I don’t care if every other gun owner on the planet went out and murdered somebody last night. I didn’t. So piss off.

So, please, feel free to use these charts and this data to address the specious arguments of "gun control" extremists, but make sure never to buy into the basic premise that if, one day, the statistics were to turn against us, it would be "appropriate" to abridge our rights. It would not be, no matter how much other people might want it to.

16 comments to graphics matter, year the fourth

  • [...] has this year’s “Graphics Matter” post up. This year there’s an interesting trend visible in the newly available data for [...]

  • [...] Linoge has released the latest “Graphics Matter” post, showing once again that the anti-rights cultists are full of crap. [...]

  • [...] Once again, Linoge has compiled the data and distilled it into graphic form. No surprise, it continues to demonstrate how the anti’s claim of “more guns = more death” is absolutely false.  He puts a lot of work into putting these things together.  Go check it out. [...]

  • Ken Rhanek

    Thank you for doing all the work to put this together.

  • [...] The 2009 data is in and it looks like, yet again, the more guns = more gun deaths claim is still wrong. [...]

  • Old Windways

    Well done once again. Looking forward to the updated FBI numbers.

  • @ Ken Rhanek: At this point, it is glorified copy-pasting, if even that, but you are welcome all the same :).

    @ Old Windways: Well, given that the FBI is reporting decreased crime stats across the board, I can already hint that the data is going to be much the same ;).

  • Wow very nice work. If you don’t mind I’m going to direct my listeners to your site tomorrow.

  • [...] But Linoge has yet another update of his Graphics Matter [...]

  • If I had known this is what you could do with math growing up I would have studied math more.

  • @ Ryan: Would I mind some more traffic? Nah, I could probably survive that ;).

    Thanks!

    @ Terriligunn: Heh, I let Excel do most of the hard crunching; my math education merely showed me that this kind of thing was possible :).

  • Tam

    Thank you for all your work on this, Linoge!

  • TS

    Linoge, it looks to me like you made an oversight when I see your data for total number of firearms. Did you include imports? I see you added 5.5 million for 2009 which is the total number of manufactured firearms in the USA. Exports need to be subtracted from this number as well (which are small) but adding imports is huge. According to the ATF 3.6 million firearms were imported into the US in 2009. These numbers are going to look a lot worse for them. I compiled a little table back when the antis were trying to say that gun sales are down. I came up with these numbers from the ATF which is total manufactured guns, minus exports, plus imports:

    1998 – 4,509,105
    1999 – 4,731,796
    2000 – 4,781,532
    2001 – 4,190,476
    2002 – 4,845,376
    2003 – 4,632,994
    2004 – 4,869,964
    2005 – 5,153,487
    2006 – 5,715,325
    2007 – 6,461,824
    2008 – 6,676,095
    2009 – 8,968,180
    2010 – 7,820,445

    Joan’s answer to these frightful numbers is to conclude that they must be sitting in a warehouse somewhere, because gun manufacturers are willing to collectively collude to waste billions of dollars just to fool Josh Horwitz.

    To be fair, I think some estimation needs to be derived for attrition. Some guns get lost, some guns get destroyed, some guns get used in crimes and then destroyed by police, and some guns get “bought-back” and melted down to get “guns off the street”. I can’t see how this number could possibly be on the same scale of new guns entering the pool, but we could throw them a bone with a worst case estimate.

    By the way, I found that import data from this report:

    http://www.atf.gov/publications/firearms/121611-firearms-commerce-2011.pdf

  • TS

    Oh, we also need to subtract the number of guns that the ATF smuggles to Mexico each year. Those aren’t counted in the export stats.

  • @ Evyl Robot Michael: Thank you kindly!

    @ Tam: You are most welcome :).

    @ TS: Ahah! Howard Nemerov and I had a conversation about how imports would affect these numbers, but neither of us managed to dig up a consistent, verifiable number of imports for the years under consideration. I will have to take a look at that PDF and update things accordingly.

    Regarding exports, though, I am pretty sure the charts I am looking at for production numbers considers “in house” consumption and exportation to be two separate pools, and counts them separately – at least that is how the data sounded to me. Of course, I could subtract those numbers from the total, and they would more than account for losses due to wear-and-tear/criminal use/etc.

    I want to know what the six handguns imported from Canada in 2010 were, though… ;)