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 important detail 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.

chart

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, 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, 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:

 

UrbanRuralGunDeaths
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, part two, 2018 edition

The first version of this post (on this site, at least) provides the full explanation of how and why this series exists, but the same two disclaimers from the first part of this year’s edition apply to this one as well:  “more guns = more ‘gun violence'” is not my hypothesis, and I am not setting out to prove causation.

As with last year’s update, I am using the usual sources:  the FBI’s Uniform Crime Report for 2015, the Centers for Disease Control, the Small Arms Survey of 2003, the BATFE’s Firearms Commerce in the United States, and Radical Gun Nuttery.

So, have the “gun control” extremists’ pipe dream of “more guns = more ‘gun violence'” finally come true?

PopulationFirearmsCrimes2018

You probably already know the answer.

The rate of average firearm ownership in America and the rate of crimes committed with firearms correlates with a coefficient of -0.734, indicating a strong, negative correlation between the two.

The raw number of firearms in America and the raw number of crimes committed with firearms correlates with a coefficient of -0.40019, indicating a negative correlation between the two.

In other words, the hypothesis of “more guns = more ‘gun violence’ remains false.  Still.

(Feel free to check my work (*.xlsx file).)

(Important note:  It has come to my attention that comparing, for example, this year’s correlation numbers to last year’s correlation numbers will be inherently flawed, on account of both the FBI and the CDC going back and updating/correcting/etc. information up to five years in the past.  The most-recent “graphics matter” post will have the most-recent information from both sources, but the previous years’ information from last year’s posts may have been updated/changed.  I do not know how, for example, the CDC managed to misrecord the US population from four years ago, but it is a little annoying.)

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.

PopulationFirearmsDeaths2018

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, part two, 2017 edition

Last year’s edition of this post adequately explained the methods and reasons behind this post, so feel free to skim it if you need a refresher.  The sources remain the same:

So, with another year of data under our belt, does my answer to the hypothesis of “more guns = more ‘gun violence’” change?

PopulationFirearmsCrime2017

Nope.

The short answer is that the rate of firearm ownership correlates with the rate of crimes committed with a firearm with a coefficient of -0.57582, showing a negative correlation between the two.

Likewise, the raw number of firearms in private hands correlates to the raw number of crimes committed with a firearm with a coefficient of -0.44568, also indicating a negative correlation between these two data sets.

In a shock to no one, the hypothesis of “more guns = more ‘gun violence'” still cannot be true.

As always, please feel free to check my work (*.xlsx file).

 

florida concealed weapon or firearm license holders are more law-abiding than average

First, allow me to present the pretty picture for today’s post:

FloridaCWFL

You might have to take my word for it, but there really is a bar to go with “CWFLs Revoked and not Reinstated”.  The “problem”, so to speak, is a matter of scale.

From 01OCT87 to 31MAR17, Florida has issued 3,518,256 Concealed Weapon or Firearm Licenses – their version of a “concealed carry permit”.  As of 31MAR17, 1,747,635 of those licenses are still active.  Likewise, as of that date, 11,916 permits had been revoked, but 1,048 of those revoked have been reinstated leaving a total “revoked but not reinstated” of 10,868.

In other words, out of the literally millions of permits that Florida has issued over the past almost-30 years, they have had a failure rate of only 0.309%.

On the other hand, in 2015, the total violent and property crime rate (since any felony alone is sufficient to get a license revoked, not just a violent crime) in Florida was 3,275.1 per 100,000 people.

Given that the total violent and property crime rate in 1988 were 8,937.6 per 100,000 people, it is entirely reasonable to state that Florida Concealed Weapon or Firearm License holders are at least 10 times less likely to break a serious law than “average” Floridians.  

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.

AmericanPopulationFirearmsDeaths2017

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.)