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graphics matter, year the third

Now that the Centers for Disease Control and Prevention have finally updated their WISQARS system to include fatal injury data from 2008*, I am happy to announce the below update to last year’s "Graphics Matter" post, including some slight changes prompted by viewer feedback:

This year, we are just going to start over with the disclaimers, and go at it from the top.

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. 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.

3. 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. As such, the American Population numbers from 2000 to 2008 have been changed to reflect the Census’ updated estimates; however, this change did not result in an appreciable change in any of the data (<1%). How the population from 10 years ago changed over the past year, I have no idea…

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 BATFE 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).

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)).

4. Conclusions: Obviously, both the population of America and the number of firearms in America have been increasing over the past 28 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 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 28 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 last year, 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.

5. 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 2010’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.

6. 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 2008’s data change things? Again, not appreciably. The American population grew 0.92% (a bit faster than the previous year), firearm-related deaths grew 1.17% (also a bit faster than the previous year), the number of firearms in common circulation increased by 1.68% (also a bit faster than the previous year), firearm-related deaths per 100,000,000 people increased by 0.25% (ditto), firearm-related deaths per 100,000,000 firearms decreased by 0.5% (the same as last year), and the number of firearms owned per 10,000 people grew by 0.76% (a bit faster).

Basically, firearm-related deaths grew slightly faster in 2008 than the American population, which is the same as 2007, but in contrast with 2006 and 2005 where the opposite was true, and 2004 and 2003 where firearm-related deaths actually decreased slightly. Over that same period (2003-2008), the number of firearms in common circulation has been increasing between 1.3% and 1.67% a year.

… 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 28 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 + 40646. The ‘r’-value for this line is -0.37031, and the R2 value for this line is 0.13713.

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 -0.37031, 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.

Additionally, it is interesting to note that last year’s data yielded an ‘r’-value between firearm numbers and firearm-related fatalities of -0.36343. As the dataset grows, so too does the negative correlation between raw numbers of firearms and raw numbers of firearm-related fatalities.

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

As we discussed in last 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 -0.37031 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 fatality 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 + 35.07780. The ‘r’-value for this line is -0.76483, and the R2 value for this line is 0.58497.

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, 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 28 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 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 variables than I care to.

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, 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.

* – Does anyone know why the CDC had those numbers up in July of last year, but took until September to generate them this year?

** – I would have thought this form of citation would be standard for any other respectable website out there, but it would seem as though some content-stealing hacks have a hard time giving credit where credit is due. Originally the post indirectly alluded that the Brady Campaign generated my chart due to the omission of the "click here for the www.wallsofthecity.net original", which was only added after a rather heated conversation with that site’s obnoxious and paranoid owner, and still fails to link back to the appropriate page.

29 comments to graphics matter, year the third

  • […] Blog Title Home About Me Contact RSS Login << The Soldiers’ Angels engraved SIG SAUER 1911 up for auction | Home Oh, don’t bother the anti’s with all those pesky facts Why We Win Linoge, once again, does all the hard work of crunching the numbers that the anti-gun bigots like to ignore. […]

  • RKV

    Suggest number of shall issue carry states is, in and of itself, a less than useful metric since its dimensions are not the same as the values used in other curves in the graphic (population). I would suggest that number of shall issue carry states be replaced population living in shall issue carry states, or percent of US population living in same.

    Otherwise thanks for the analysis and especially for the details on R squared.

  • Maths is hard.

    Thanks for crunching those numbers!

  • […] eight-by-ten colour glossy photographs with circles and arrows and a paragraph on the back of each o… […]

  • […] For another look at the data, check out the comprehensive work done by Linoge at Walls of the City in his 3rd year of “Graphics Matter”. […]

  • Wow, you made a great job.
    If you don’t mind – i’ll place a link in my blog to this research:
    http://hyperprapor.blogspot.com/2011/09/blog-post_1172.html

  • Once again, very nice work-thank you for putting this together.

    It’s weird when looking at the last graph-it’s like the rates were steady until about 1992 or so (assuming the points along the x axis move forward one year at a time as I suppose they should based on how you arrived at the number of firearms in circulation) then something happens causing a transitory change to a new, lower steady rate. I have no idea how to analyze for that, or what that event could be, but it seems like trying for a correlation coefficient may be nearly meaningless. If I’m right and we have no more transitory changes, the slope of your line will eventually approach 0 as the later data points swamp the earlier when doing the least square fit. Of course those are also really big ifs.

    As a refinement to the number of firearms-any way to estimate the number of firearms destroyed or otherwise taken from circulation (buy-ups by cities, evidence lockers, KABOOMS, end of useful life etc) every year? It’s probably very small in proportion to the number of guns in circulation (perhaps as high as 100k/year).

  • […] yet again they do not support the premises behind gun control. 1. The hypothesis of “more guns = more deaths” is demonstrably false over the past 28 […]

  • Chad

    Thanks. While I agree with your final assessment (my rights don’t live and die at the whim of statistics), it’s nice to see that the numbers don’t contradict what we all believe.

  • […] Linoge at Walls of the City has a series of easy to read graphics demonstrating what I have been preaching for 43 years. Fewer guns result in more crime, and more guns result in less crime. […]

  • Braden Lynch

    I wonder what the overall homicide rate looks like in comparison to the firearms-related deaths. That might be an interesting addition to the graphs.

  • Braden Lynch

    Sorry, silly me. I went to the “Raputo” links and saw information related to total deaths. My bad.

    And in Point 6 you mentioned that your interest was in disputing the gun control freaks on the idea that less guns = less gun deaths.

    Thanks for GREAT job in slicing and dicing this data.

  • Graphics Matter • Where Angels Fear To Tread

    […] »   Graphics MatterBy Patrick, on September 15th, 2011 | Skip to commentsLinoge has released his 3rd year num­ber crunch with graph­ics explod­ing every­where. If you want to debunk some pro-​criminal argu­ments, […]

  • @ RKV: Again, that metric is mostly there is a trending observation, and less of a raw-number exercise. The problem with listing the state population is that is not necessarily indicative of the number of people who actually carry in the state, and hard numbers for those counts are annoyingly difficult to find. If, however, you can find an accurate tally of all 38 states’ carriers, that would be a useful inclusion, but given the growth of Constitutional carry, it is becoming increasingly impossible… which is a good thing ;).

    @ That Guy: Math is hard, but I want to stress that this math is not. All of those numbers are from public sources that anyone can find and access using relatively simple Google searches, and the statistical number-crunching is accomplished by a single, solitary Excel function (“=CORREL”, which solves for the r-value). Using nothing more than that and basic division, you could generate this entire sequence of charts for yourself.

    Which just goes to show how heinous the lie of “more guns = more deaths” really is – the information is out there, it is not hard to find, and yet people continue to perpetuate the myth. Sad.

    @ Alexander: Not a problem, please do!

    @ LC Scotty: So the last two graphs do not have years anywhere on their axes – instead, it is number of firearm-related deaths vs. number of firearms, and rate of firearm-related deaths vs. rate of firearm ownership. As for what causes that bubble, I would assume it has to do with the crime surge of the 90’s, but without looking into it deeper, I am not sure.

    As for what the future holds, dunno… the correlations seem to be getting stronger (but still negative) as time rolls on, but, in reality, 28 is a relatively small number of datapoints. And given that we are not controlling for all of the other countless variables that affect crime rates, you are right, trying to demonstrate solid correlation is almost pointless… but that is also not the point of this exercise ;).

    Not sure about firearms lost per year… I assume police departments keep records of how many they destroy, but given that the anti-rights cultists are not crowing the numbers every year as you would assume them to, I guess they are not public knowledge.

    @ Chad: The inviobility of rights is the key point… the statistics to support our case are just icing on the proverbial cake :).

    @ Braden Lynch: So the second half of this exercise (published when the FBI finalize 2010’s numbers) addresses firearm-related crime in total (last year’s is here), but, yeah, Reputo did an outstanding job in his series.

  • […] reciprocal-nessErin Palette on a little reciprocal-nessbluesun on a little reciprocal-nessLinoge on graphics matter, year the thirdLinoge on quote of the day – mike w.Ian Argent on a funny thing happened yesterdayLinoge on […]

  • Linoge, If I understand how you determined # of firearms-2003 is really the only hard data point. For years after 2003, you’ve added a number from an annually released ATF report and for years earlier you subtracted the same number from the same report. Doesn’t that imply that the x axis also shows increasing time?

    So in 2003 there were X firearms. In 2004, ATF says A firearms were released into the wild, so the point for 2004 is X+A. In 2005, ATF says B firearms were released into the wild, so the number for 2005 is X+A+B etc…

    I realize that earlier than 96 you switched the source of firearms #s, but the principle still holds.

    Or am I completely confused?

  • JohnS

    Nice post – I’ve done similar things with population/# of guns. Yours is better.

    Gary Kleck published firearms ownership data he got from BATFE and other sources; the most recent I have from him is in Targeting Guns, 1997, in table 3.1 Size of the U. S. Civilian Gun Stock, 1945-1994.

    Bureau of Justice Statistics has homicide trends, including weapons use, at http://bjs.ojp.usdoj.gov/content/homicide/weapons.cfm. Different data set from CDC/WISQARS, so not directly comparable, but could push your data back a few years.

  • JohnS

    Added – Good heavens, I don’t come here often enough! I made essentially the same comment in 2009. Mea Culpa.

  • Well done Sir, and thank you for a very visible proof set that the lefties are full of ‘s**t’…

  • […] end-game is getting closer…their efforts are crashing. Linoge of course shows this in his great graphics. That overall there is MORE gun owners and private gun sales than ever before in the country, there […]

  • @ LC Scotty: You may not be confused, but I am :).

    Are you referring to the last graph, or the first one? The last graph does not mess around with dates at all, just rates, while the first one has dates along the y-axis.

    If you are talking about the first graph, the reduction in both of the firearm-related crime rates can be explained by some of the research Reputo did in the above links (in the post, point 6). In short, there was a lot going on, with the increase in police forces, the increase in prison sizes, the reduction of drug usage, the recovering economy, and countless other elements all factoring in. It does currently look like that now that whatever was going on leveled off, the firearm-related death rates are stabilizing to a fixed percentage of the population, if even that, but the question over time will be whether that rate correlates better to the people population or firearm population. In any case, as the information approaches today, it will get even more interesting, as we all recall that all crime statistics have been decreasing of late.

    You are right about how I figured firearm numbers, but, like I said, finding destroyed numbers is hard…

    @ JohnS: In reality, the specific number of firearms in the wild is completely immaterial to this graph – I could have started at 0 in 1991 and gone up to wherever it should be in 2008, and the conclusions would still be the same, because the key in this argument is the slopes – the change – rather than the actual numbers. And, like I said, I am intentionally giving the anti-rights cultists the benefit of the doubt, which further goes to show how weak their positions are :).

    @ Old NFO: Ayup. But, of course, the important thing goes beyond these basic statistics, into the realm of the inviolability of individual rights, but you already knew that ;).

  • […] bigotry? (31)online ammunition retailers – a hypothesis (24)lucky gunner – hypothesis confirmed (21)graphics matter, year the third (21)friendly note to squids* (19)save what you can, where you can (19)Bugging Out (18)yesterday, at best […]

  • Just FYI, the AWB expiration is in the wrong place in the updated graphic. It expired late 2004, not late 2005.

    Other than that, nice work.

  • bob

    I would love to see this data presented excluding non-violent firearm deaths, like suicides and accidents. The data would be even more damning to the anti-firearm side.

  • […] the City on a daily basis. While I forgot to mention it last week, I wanted to make mention of his Graphics Matter, Year the Third post which you should take some time to read, an overall awesome resource for people like me that […]

  • @ Nick Leghorn: Right you are, and thanks for pointing that out. The image will be updated momentarily.

    Also, thank you for taking the time to propertly cite your sources for your TTAG article, unlike your boss.

    @ bob: But, see, since the anti-rights cultists include that data themselves in order to pad their “gun deaths” numbers, doing the same here also weakens their arguments, because even with that padding, they still fail.

    But wait. You might like today’s post :).

  • […] the bull is so thick we need to break out the hip waders!  Linoge has been breaking out the numbers lately.  I think he likes this tradition.  What makes his numbers […]

  • […] So as previously noted the Brady score means absolutely nothing.  Linoge has examined the 2010 UCR as the pertain to firearms.  He has also detailed other firearm related data from the CDC. […]

  • […] has often said correlation does not equal causation with regards to analyzing the statistics around gun control.  For those who are still unsure what he meant by that we now have a […]