fixed points in data

For far too long now, whenever someone shares my “graphics matter” series of posts, someone pipes up with a response that can be summarized as:

“We don’t know how many firearms there are in America, so we cannot draw any correlation or causation conclusions between firearms and the people they kill.”

It is time I address this notion.

The first phrase of the sentence is actually correct.  Not only are firearms a durable good – meaning that firearms produced before the Revolutionary War could still be used today so long as they were properly maintained – but national registration of non-NFA-regulated firearms is outlawed by the Firearm Owners Protection Act.

As well it should be – the government simply has no business knowing what I own.

“But that means the second phrase of the sentence has to be correct, right?”

Well, no.

The entire point of the “graphics matter” series is to examine the correlation of the number of firearms in America with the number of firearm-related fatalities or crimes in America, as well as the per-population rate of the same.  The fun thing about correlating two data sets is that you do not need to know their starting points.

“Wait, what?”

It is one of the fundamental aspects of correlation, really. “Positive correlation” means that “as data set A increases, data set B also increases”. “Negative correlation” means that “as data set A increases, data set B also decreases”.

(An important distinction I want to make before moving on is that this does not mean A’s increase causes B’s increase, or vice versa, or anything of the sort.  The world is full of correlations that have no causal relationship with one another.)

The reason the definitions are significant is this – you are looking at the rate of change. The “slope”, for those of you who remember… what was that, high school algebra?

But rate of change – slope – is determined between two points, and is completely independent of Y-intercept, or any starting point. As long as point 1 is separate from point 2 by the expected difference, it doesn’t actually matter what the individual values are.

In other words, the slope between the X/Y data points of 1/100 and 2/200, and the slope between the X/Y data points of 1/0 and 2/100 are exactly the same, despite the values being different.

It is kind of whacky to think about, but in most-basic terms, 2x+10 has the same slope as 2x+100, but entirely different values, and both correlate against 4x in exactly the same way (they both have a correlation value of 1 with respect to 4x).

In fact, since this is a graphically-related site, let us look at an example.

Here we have a plot of 2X + 10, 2X + 100, 4X, and X raised to the power of 1.5 over time.

As I mentioned above, both 2X + 10 and 2X + 100 correlate to 4X with a coefficient of 1, meaning that as the first two equations increase, the third equation also increases, and the ratio of the increases is always the same.  This makes sense – all three are straight lines, meaning their slope is constant along their lengths, so comparisons between those slopes will always be equal.

However, both of the first two equations correlate with X^1.5 with a coefficient of 0.99052.  Why?  Well, the slope of the fourth equation changes over time, since it involves a power.  The first two equations do not have the pronounced curve of the fourth, so their growth does not mirror the fourth’s growth, no matter how different that growth might be (as when comparing the first two equations with the third).  However, all three equations are increasing over time, hence their very strong correlation (coefficients can range from 1 to -1).

But the point – that I am perhaps belaboring – is that the first two equations have the exact same correlation with any other equation or line you care to throw on the chart with them.

Why does this matter?

We really do not have any idea how many firearms are in America.  We never will.  I use the 2003 Small Arms Survey as the basis for my “graphics matter” series because it was the most-current when I started the post series, and changing reference points midway through is generally bad.

But I literally could have started in 1981 with the (atrociously flawed) assumption that there were no firearms in America, and the math would still work out exactly the same.

“Uh… why?”

We will never know how many firearms there are in America at any given time, but we do have a very accurate accounting of how many firearms are produced and imported into the country every year.  The BATFE’s Firearms Commerce in the United States Annual Statistical Update provides us that data back to 1986, and then the Shooting Industry News covers the remainder.  How can this be so accurate?  National registries may be outlawed, but all new firearms commercially produced must be uniquely serialized, and must be declared to the BATFE at the end of the year.  The penalties for “fudging” numbers are… severe.

We have the yearly production data.  Which means we have the rate of change – the slope.

Likewise, we have a… noticeably less-accurate, but still-considered-reliable accounting of the American population and the number of Americans who were killed by other people using firearms at the CDC WISQARS Fatal Injury Report.  I refer to this as “less-accurate”, because I have personally witnessed the CDC correcting data five years past; while I would prefer accurate data over leaving the inaccurate data, it annoys me that, for example, they got the American population wrong by 300,000 residents in one year.

Having to go back and update my data aside, we have the yearly numbers of firearm-related fatalities, which means we can calculate the rate of change.

In other words, I – or you – can compare the two-year-paired slopes for each of those data sets, or the average slope as a whole, or any other combination, and it simply does not matter where the firearms data started.  Only the differences between each year’s data matters, and we have those differences tallied by “authoritative” sources.

Feel free to play with the situation yourself; I have uploaded the spreadsheet for the above graphic, and you can fiddle with the numbers to see how things change.

We genuinely have no idea how many firearms there are in America, and that is fine.  We do know how many have been produced a year for the past ~35 years, and the only correlation between the change in firearms in America and the change in firearm-related fatalities is negative-to-non-existent, for both raw numbers and per-American rates.  Thus, “more guns = more deaths” cannot be true.

graphics matter, 2019 edition

Honestly?  I’m tired of writing these posts.  Because reality does not change.

No matter the “gun control” extremists’ beliefs, inanimate objects cannot control a human being’s behavior.

To believe otherwise is pure fetishism.

But people continue to believe otherwise, so here we are.

As always, check out the original version of this post for the series’ explanation.  And, as always, “more guns = more deaths” is not my hypothesis, nor does this series of posts mean to prove that “more guns = fewer deaths”.

Instead, this series of posts exclusively exists to disprove the notion that more firearms automatically means more fatalities, as the aforementioned “gun control” extremists incessantly, erroneously declare.

My sources include:

– the CDC WISQARS Fatal Injrury Report
– the BATFE Firearms Commerce in the United States Annual Statistical Update 2018
– the Small Arms Survey of 2003
– Radical Gun Nuttery
– my data spreadsheet

And, once again, as every time previous, the hypothesis of “more guns = more deaths” falls flat on its face.

Now, it’s absolutely worth noting that the firearm-related fatalities are almost as high as their peak back in the early ’90s… but the US population has grown massively since then, meaning the rate of firearm-related fatalities is actually down since then.

Relatedly – pun intended – the correlation between the raw number of firearms in the United States and the raw number of firearm-related fatalities in the United States is -0.03268.

That is to say, there is precisely no correlation.

Which means there cannot be causation.

And that is a complicated way of saying, “the number of firearms in America is not driving the number of firearm-related deaths in America.”

Which brings us to rates, and any sociologist knows that rates are much more valuable than raw numbers.

Well, the correlation between the rate of firearm ownership – that is to say, the number of firearms in America divided by the American population – and the rate of firearm-related fatalities is -0.34575.

In other words, there is a noticeable, negative correlation.

Which, again, means there cannot be causation.

Look, I get it.

Kind of.

It is literally an article of faith among some people that “guns are bad”.

But the data simply does not back that prejudice up.  And, frankly, it is kind of disappointing that modern people are still bitterly clinging to the notion that inanimate lumps of metal can affect conscious, cognizant humans’ minds.

But here we are.

graphics matter, demographics edition

By and large, I am generally disinclined to believe Pew’s / Gallup’s / [insert polling agency here]’s reporting of firearm ownership rates in America.  First and foremost, there are some pretty significant flaws in modern polling methods.  Second and perhaps more importantly, based on my entirely-anecdotal-but-decades-long experience with the firearm-owning public, the probability of an average firearm owner answering truthfully when a random stranger calls them on the phone or knocks on their door asking if they own firearm is… vanishingly small.

However, exclusively for the sake of discussion, I am willing to accept a small part of this 2017 Pew Research Center report on the demographics of firearm ownership.  If you read through it, you will see that people who live in rural areas are approximately 2.4x more likely to own a firearm than people who live in urban areas (46% of rural residents reported owning a firearm, versus 19% of urban residents).

Given that we are talking about rates, Pew has already normalized for the substantial population differences between the two areas, so if the “gun control” extremists’ hypothesis of “more guns = more ‘gun deaths'” were true (we already know it is not, but bear with me here), one would expect rural areas to have a strictly higher rate of firearm-related fatalities, and probably close to 2.4x higher, right?

Unsurprisingly, that hypothesis continues to fail:

 

Please note that that the firearm ownership rate is per 100 people, while the “gun death” rate is per 1,000,000 individuals.  This is necessary to have both numbers significantly visible on the chart.  

 

Naturally, the firearm-related fatality rates come from the CDC’s WISQARS system, by way of their new “Metro / Non-Metro Indicator”.

Naturally, there will be some differences as to how WISQARS counts “urban” incidents as compared to Pew’s methods, but even accounting for those slight variations… well, the chart speaks for itself, as I always endeavor to accomplish.

You know, if they were not so busy trying to paint hundreds of millions of peaceful Americans as children-hating mass-murderers who deserve to have their Constitutionally-protected rights unjustly stripped from them, I would almost feel bad for the “gun control” extremists.  They just cannot seem to catch a break when it comes to the facts of the debate.

 

graphics matter, 2018 edition

Before I provide you this year’s update on the data, it has come to my attention that I need to clarify a few things.

1. The hypothesis of “more guns = more deaths” is not my hypothesis, claim, or allegation.  In point of fact, it is the underlying, foundational argument of every “gun control” organization in the country, and I am simply accepting it, at face value, for the sake of examining it.
2. I am not setting out to prove any causation.  In other words, I am emphatically not making the counter-argument that “more guns = fewer deaths”.  Such a claim would require a lot more work and study than I am willing to put into these posts, unlike those aforementioned “gun control” organizations, who are more than willing to perpetuate easily-believable falsehoods in order to line their pockets and unjustly limit your rights.

With those caveats made as explicit as I can, it’s time to give y’all the update to last year’s post.  So, with another year’s data under our belt, is the hypothesis of “more guns = more deaths” accurate?

… not so much.

There was a surprising uptick in firearm-related fatalities in 2015, but over the course of the 34 years tracked, the trend remains mostly the same.

The number of firearms per capita and the number of firearm-related fatalities per capita correlate with a coefficient of -0.74808 – indicating a very strong, but negative, correlation between the two data sets.

The number of total firearms and the number of total firearm-related fatalities correlate with a coefficient of -0.17420 – indicating a significantly weaker, but still negative, correlation.

As students of statistics remember, correlation does not prove, or even indicate, causation, but correlation is a requirement for causation.  In other words, given that neither the rates nor the raw numbers are positively correlated, then the increase in firearms in the country over time cannot be causing an associated increase in firearm-related deaths.

In simpler terms, the hypothesis of “more guns = more deaths” remains false.

(The first post in this series, wherein I spell out the above caveats differently, but I thought fairly clearly, is available here.  The source Excel spreadsheet from which I generated the above graphic and numbers is available here, should anyone care to check my work.  As always, my sources are the CDC’s WISQARS Fatal Injury Reports (for firearm-related deaths and the US population), the Small Arms Survey of 2003 (for a starting point from which to calculate the number of firearms in circulation), the BATFE’s Firearms Commerce in the United States (this time the 2017 edition, and for the number of firearms produced/imported), the Shooting Industry News (for firearm production numbers before 1986), and Radical Gun Nuttery (for the number of shall-issue/Constitutional Carry states in the Union).

graphics matter, 2017 edition

“More data more better” is pretty much the rule when it comes to statistics, so I try to update the “graphics matter” series every year or so as my various sources update their data sets.  I missed a year somewhere in there, but I am happy to bring you the new, improved, examination of whether or not the hypothesis of “more guns = more ‘gun deaths'” holds true.

The results… will not surprise regular readers.

That is the chart, but what about the actual numbers?

The two pertinent rates – the number of firearms per capita versus the number of firearm-related fatalities per capita – correlate with a coefficient of -0.79744, indicating a strong, negative correlation between the two sets of data.

If you look at the raw numbers – the number of firearms, period, versus the number of firearm-related fatalities, or “gun deaths” – they correlate with a coefficient of -0.27315, which remains a negative correlation.

As always, correlation does not necessarily indicate, or even come close to proving, causality; but I am also not trying to prove causality.  However, the notion of “more guns = more ‘gun deaths'” does try to claim causality, when there is absolutely no positive correlation to support such a causal link.

Therefore, the hypothesis of “more guns = more ‘gun deaths'” still cannot be true.

(The previous version of this, along with a great deal more explanation, is available here.  The Excel spreadsheet from which I built the above graphic is available here.  My sources are the CDC’s WISQARS Fatal Injury Reports, the Small Arms Survey of 2003, the BATFE’s Firearms Commerce in the United States, the Shooting Industry News, and Radical Gun Nuttery.)

is “gun control” a “health issue”?

A very few folks have been making a lot of noise recently about how “gun control” – and specifically firearm-related deaths – is a “health issue”.

Unfortunately, the analogy falls flat on its face straight out of the gate simply because we only have some, if any, control over the current leading causes of death in America, while firearms are completely under human control.  Firearms are not a genetic marker that indicates your brain is going to start destroying itself as you get older – they only fire when a human makes them.  Unfortunately, the same cannot be said of diseases/ailments.

But if we were to ignore the lacking logical basis for such an argument, do the numbers even come close to supporting it?

Predictably, not so much.

According to the Centers for Disease Control, 2,626,418 people died in 2014.  The ten leading causes for those deaths were:

• Heart disease: 614,348
• Cancer: 591,699
• Chronic lower respiratory diseases: 147,101
• Accidents (unintentional injuries): 136,053
• Stroke (cerebrovascular diseases): 133,103
• Alzheimer’s disease: 93,541
• Diabetes: 76,488
• Influenza and Pneumonia: 55,227
• Nephritis, nephrotic syndrome and nephrosis: 48,146
• Intentional self-harm (suicide): 42,773

A keen-eyed observer will note that “firearms” occurred nowhere on that list.  However, an argument could be made that “accidents” and “suicides” both include some firearm-related deaths, so let us take a page from our own playbook – the square root of 2,262,418 is approximately 1621, and that is the x and y dimension of the following graphic at full size (click to enlarge):

Firearm-related accidents – perhaps the most accurate analog to diseases – are represented by the smallest greenish square inside the slightly larger one, and only account for 586 of the total deaths according to the CDC’s WISQARS system.  Even if one were to focus exclusively on firearm-related suicides – since “suicide” as a whole does make the top 10 – those are only 21,334 out of the total 42,773 deaths in that category; almost exactly half.  Suicide is most certainly a mental health issue, but even if you were to wave a magic wand and disappear all firearms, countries that have already gone down that path show us that suicides will still find a way.  Perhaps, in those cases, time should be better spent determining why people suicide, rather than abridging millions of Americans’ rights in a vain attempt to control how people end their lives?

Regardless, as we already know, firearm-related fatality rates are already dropping across the board, including accidents, without doctors’ unnecessary involvement in the politics of the situation.  I would suggest that their time is better spent focusing on the other diseases and afflictions in which they are subject matter experts, rather than sticking their noses into topics they know very little about, especially since some of those diseases individually account for an order of magnitude more deaths than people misusing firearms.

graphics matter

One of the favorite myths of “gun control” advocates is that as the number of firearms in Americans’ hands increases, so too does the number of firearm-related deaths increase.  Superficially, this seems to make sense, and thus it is an appealing fiction to buy into.

Fortunately, the actual data proves the hypothesis to be false.

To begin with, I should clarify that we will be considering the rates of firearm ownership and rates of firearm-related fatalities, since raw numbers are affected by population growth or decline.  Thankfully, the United States population is fairly well documented, and we will be using the Centers for Disease Control‘s information.

Additionally, causes of death are also well documented, also by the CDC.  Their WISQARS Fatal Injury Reports are updated on a yearly basis, and their data set spans from 1981 to 2012, so that will be our consideration window.

Unfortunately (from the analytical standpoint), the first part of the equation – the number of firearms in private Americans’ hands – is nowhere near as accurately recorded.  Obviously I am quite sanguine with the federal government having no idea who owns what firearms or in what numbers, but it does make statistical examinations a little more challenging.  However, the Small Arms Survey of 2003 is perhaps an authoritative estimate on private ownership of arms in various nations, and they calculate the lower bound of US firearm numbers in 2003 as approximately 238,000,000.  The Small Arms Survey organization is decidedly against the “proliferation of small arms”, by their own words, so we have every reason to believe they inflate their numbers for greater impact, but we can accept that as a starting point.

From that starting point, we will add, or subtract, the firearm production figures provided by the Bureau of Alcohol, Tobacco, Firearms and Explosives‘ Firearms Commerce in the United States document, at least as far back as 1986 (the earliest publication of that document).  Before then, we will rely on the Shooting Industry News.

Finally, while it does not factor into the “does ‘more firearms’ mean ‘more firearm-related deaths?” question, the number of “shall-issue” and “Constitutional carry” states is also included in the data, with the tallying done by Radical Gun Nuttery (their *.gif documenting the march of our rights across the nation is quite handy).

So, with all this data at our fingertips, does “more firearms = more firearm-related deaths” hold true?

In short, no.

For those who want more than pretty pictures, when one considers the rates – i.e. the number of firearms or firearm-related fatalities per 10,000 people – the rate of firearm ownership correlates to the rate of firearm-related fatalities with a coefficient of -0.80155, indicating a strong, negative correlation between the two data sets.

Even when you look at the raw numbers, the number of firearms in America correlated to the number of firearm-related fatalities – i.e. “gun deaths” – with a coefficient of –0.36471, which still indicates a negative correlation between those two data sets.

At this point, it is important to clarify that correlation does not indicate, nor prove, causality… but I am not attempting to prove causality here.  However, by stating that “more guns causes more ‘gun deaths'”, the anti-rights community is attempting to claim causality, and one that would outright require positive correlation.

No such positive correlation exists.

As such, the hypothesis of “more guns = more ‘gun deaths'” cannot be true.

Feel free to spread this information as far as you like, and if you are so inclined, I welcome people checking my work (*.xlsx file).  Unlike anti-firearms organizations, I make no attempt at hiding my raw data, or the ways it was crunched.

(As a further aside, it would not matter if the hypothesis could be true – the overwhelming majority of firearm-owning Americans have broken no laws nor harmed anyone, and, as such, no one has any standing to unjustly deprive them of property or rights.)