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graphics matter, year the second

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]

28 comments to graphics matter, year the second

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  • Dixie

    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.

    As a “sanity test,” you could pick two similarly sized cities in the same area– one with and one without gun control– and compare gun deaths. It still would not prove that more guns = less crime (that the data forces you to reject A does not cause B to be true), but it would show that (pound-for-pound) it’s safer to live in a gun-rich environment.

  • Now if you can just correlate this with Global Warming, you can probably get an NSF grant.

    Very nice job, and the transparency of your work is something to be wished for in climate science.

  • @Dixie – Unfortunately, it would be nearly impossible to find cities to meet those requirements… Richmond and D.C. are sufficiently different to not be comparable, Chicago has nothing nearby that is of similar population density / political corruption, etc. etc. Still, to systemically prove that “more guns = fewer deaths”, you would also have to account for pretty much every other variable out there that could influence the increase or decrease of firearm-related deaths throughout history, and that is something I am just not willing to sit down and do… if it is even possible :).

    @Borepatch – Sadly (at least in terms of getting globull warming grant money), none of my graphs appear to have the prerequisite “hockey stick” at the end of them… Perhaps if I follow the same statistical methodologies of the folks IPCC and just throw out numbers that I do not like, I might be able to work things out the right way… ;)

    Thanks, though – like I said, the conclusions and routes I took to make them are all about as valid as the data they are based on, but anyone who can point me to better sources is more than welcome to do so.

  • FYI seems that MikeB and Jade feel pretty threatened by your hard work (good job)

    Jade attempts to refute your graph by claiming that all these new guns are going to people like me who already own lots of guns, so while the number of guns in private hands has gone up, the number of hands those guns are in has stayed the same.

    Of course one HUGE way to refute this (and I respond to that here because my comment will both be published, and fall on intelligent ears) is this story:
    http://www.boston.com/news/local/massachusetts/articles/2009/12/20/gun_permits_surge_in_state/

    If the Massachusetts permits are on the rise (And Still are. The wife and I got turned away from the range today because the club was having its monthly safety class. I knew something was up before the clubhouse was even in sight as EVERY parking spot in the lot was taken.) that means new gun owners are on the rise, given that you can’t buy a gun without a Mass permit, and Massholes get their permit either to buy their first gun, or so they can own their guns as they move into the state. Given that the state population is actually shrinking, the former is vastly more likely than the latter.

    And of course there’s the tremendous amount of data on new woman shooters. They were a pitifully small demographic several years ago, but now they are quickly approaching the 50% mark. If there were so few woman shooters back in the 90s, and so many today, I’d say that would point strongly to MORE hands to hold the guns entering the private market.

    Just thought I’d shoot that little flare across your bow, as i know you don’t venture into the puss-filled parts of the cortex.

  • Dixie

    Linoge- Yeah, I know. After I commented, I actually tried a first pass to see if I could find two close fit cities that matched my parameters. The only options would be to 1) find two smaller cities or 2) pick a big city and somehow divide it in half and remove gun control in one half. But then everybody would rush to the free half, and our experiment would be all buggered. (chuckle)

    Weer’d- I can refute it even more simply– safety equipment. I’ve had a time finding more earmuffs and glasses. Experienced shooters don’t buy new equipment all at once… newbies do. (I think Breda brought this up once, I’m not sure.)

  • @Dixie – GREAT point, Dixie. Just anecdotally I’ve seen people buying their first gun at the shop, and I can tell by how they first buy the gun, then with the paperwork and the sale all under wraps, then they start looking at ammo, hearing and eye protection, and CLEANING KITS!

    I wear out bore brushes every few years, and I run out of cleaning solution and oil, but how often does one need a new kit? (OK Mine is getting kinda beat-to-shit, I could probably stand a new one).

  • Originally Posted By Weer’d Beard
    Jade attempts to refute your graph by claiming that all these new guns are going to people like me who already own lots of guns, so while the number of guns in private hands has gone up, the number of hands those guns are in has stayed the same.

    Thanks for the heads-up – I have pretty much sworn off Sparky’s webpage as being a complete and utter waste of time, so I am very rarely exposed to their rampant idiocy any more. I do note that neither of the spineless cowards had the nerve to actually come over here and voice their objections, though… Funny, that.

    As for his assertion, it does not matter – their claim has always been that as the number of firearms increase, so, too, will the number of firearm-related crimes and deaths. JG is engaging in nothing more than his typical goal-post relocation, as he always does when confronted with realities that demolish his arguments.

    Regardless, even looking past the self-inflicted narrowness of their particular gument, as you say, the news reports are positively crammed with new people getting their handgun carry permits, new people taking firearm-safety classes, and new people showing up at gun shows. The “old timers” are undoubtedly stocking up, but there are a lot of new folks joining the crowd and tasting freedom.

    Of course, that is all remarkably inconvenient to the likes of JG and Sparky, so of course it is downplayed, minimized, and generally ignored. “Intellectual honesty”, at its worst.

    [Update] *giggle* Ok, that was worth the waste of five minutes… Their entire “argument”, if you want to call it that, basically boils down to “I do not like it so it cannot be true”, and “it is too long, I cannot understand it, so I did not read it, and it must not be true”. Wow. Just. Plain. Wow. Then again[/Update]

    @Dixie – Oh, if you want to actually engage in the experimentation, we are going to be a here a few years, and first you would have to find a city willing ;). But, even now, no good sampling population exists.

    By the by, check out Home Depot or Lowes for your hearing protection needs – most newbies, and current shooters, for that matter, do not think to go there.

  • Dixie

    (OK Mine is getting kinda beat-to-shit, I could probably stand a new one).

    Heh. I had to upgrade mine… new pair got “lent” to a newbie, old pair has been used around the tractors too much (oil, grass and gunpowder don’t mix well), so I went and sprung for a set of electronic muffs.

    … and first you would have to find a city willing…

    Think I convince half of Chi-town to play around? (chuckle)

    By the by, check out Home Depot or Lowes for your hearing protection needs – most newbies, and current shooters, for that matter, do not think to go there.

    My newest pair came from a sporting goods store in a bad spot. They’ve closed a few times, always re-opening under new management. Great prices, great staff, great selection… impossible to get into or out of the parking lot.

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  • Gotta love stores that alternate between “grand opening” sales and “going out of business” sales!

  • Yu-Ain Gonnano

    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.

    Actually, statistically speaking, you’ve proven that both are false. And it’s not because the beta[ Y = beta*X ] is negative.

    The residuals (that is, the difference between the actuals and the models predictions) do not follow a Normal(0,sigma^2) distribution therefor the model Y = beta*X is invalid for all values of beta both positive *and* negative. The structure itself is inadequate.

    And as you can see from the plots of the actuals and the model results a quadratic or 3rd power relationship doesn’t change this (very little in this world follows higher than 3rd order polynomials) therefore there must be something else which accounts for the variation.

    Once you account for that something else the beta for firearms may indeed by positive but that due to the effeects of the other variables the whole relationship is negative. Or it could be even more greatly negative and some other factor is causing it to be higher than it otherwise would be.

    So what you’ve actually proven is that it’s just not that simple.

  • Coincidentally, I am quite satisfied with that outcome as well. But, then again, I am not one of those folks throwing out “if A then B” arguments, in either direction, for a system as complicated as American (or any country’s) society ;).

    But, then, that is the reason I always hated my statistics classes – if I wanted to, was a little more dishonest, and a little more creative, I could probably tweak those numbers into falling out along a normal distribution, and if I was good enough at doing that, I could run with it and few would be the wiser.

    But, regardless, it is quite true that the system is not that simple… which still prove the null hypothesis :).

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  • Yu-Ain Gonnano

    But, then, that is the reason I always hated my statistics classes…

    Ok, now I gotta yank your chain.

    Repeat after me: Stats don’t murder numbers, People do. :-)

    which still prove the null hypothesis

    Actually it does not prove it, it fails to reject it. It’s a technical difference, but it is one that’s important. It may be the case that more guns = more deaths, all else being constant. The problem is that all else is demonstratably *not* constant.

    For example, take the model Z = 2X + Y. Here we have defined both X and Y to be positivly related to Z. That is More X = More Z and More Y = More Z. But that is only true if you hold the other variable constant. If you allow *both* to move, all bets are off. If you increase Y by 1 and decrease X by 1 *at the same time* Z will actually decrease. Thus, by leaving out the X variable what you observe is an increase in Y and a decrease in Z. If we take this to “prove” that More Y = More Z is false, we have made an error. The statement can not be false because we defined it to be true. What is false is the structure of a model that Z is a function solely of Y.

    Which, as you said, suits the purpose as our side isn’t arguing the relationship period. More cars do equal more deaths, but you don’t hear us supporting car bans because of it.

  • Dixie

    But, then, that is the reason I always hated my statistics classes…

    I loved my stats classes. It’s just that my professor was utterly forgettable in his teaching style.

    it fails to reject it

    Which I why I forgot this term. (chuckle)

  • Originally Posted By Yu-Ain Gonnano
    Repeat after me: Stats don’t murder numbers, People do. :-)

    Yes, but my stats class taught me all the different ways that people can murder numbers, and that is why I hated them – ignorance is bliss, and all that.

    Originally Posted By Yu-Ain Gonnano
    Actually it does not prove it, it fails to reject it. It’s a technical difference, but it is one that’s important. It may be the case that more guns = more deaths, all else being constant. The problem is that all else is demonstratably *not* constant.

    *sigh* And that is the other reason I hate statistics – there are four right answers to every question, and some of them are more-right than others. You are, of course, quite correct, and it does still work out for us.

    Messily, but it works.

  • [...] Better late then never to the party I guess! Or is it fashionably late?? Anyhow more solid data on more guns DO NOT equal more deaths! [...]

  • Yu-Ain Gonnano

    You sound like my dad. He wants things to either be right or be wrong. It just bugs him that the best statistics can say is “Yeah, we’ll be wrong occasionally, but we’ll be right often enough that we’re OK with it.”

    It annoys him to no end. :-)

    It’s also why I reject arguments of the type “Does having a gun actually make you safer or more risky”. It’s not a questions of statistics, 1 in a million odds don’t mean a thing if that one is you.

  • Hm. Methinks your father and I would get along just fine ;). Still, numbers are occasionally fun to fool around with, and sometimes yield useful results like these. It surely would be nice if people stopped fielding the same, tired, over-simplified bulldren, though…

  • Dixie

    It’s not a questions of statistics, 1 in a million odds don’t mean a thing if that one is you.

    My doctor put it in a different way: “Statistically, this medicine has a very low percentage of major side effects. However, when we reduce the sample size to one, those numbers are useless.”

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