
De-Obfuscating the Statistics of Mass Shootings - FigBug
http://www.charlespetzold.com/blog/2015/07/De-Obfuscating-the-Statistics-of-Mass-Shootings.html
======
aftbit
Interest groups lying with statistics is a specific example of confirmation
bias. It's sadly so prevalent that I generally assume that any statistics I
find are intended to lead me in a particular direction.

I am skeptical of the final implication of the blog entry, that improved gun-
safety legislation would solve this issue. For someone taking such a strong
approach to statistics, it's a shame that they focus on only one facet of such
a complicated situation. American culture, mental health treatments, social
programs, and gun laws are all different from most other countries on their
list - it seems disingenuous to mention only the last.

~~~
kromem
Your comment is actually a perfect example of why I have issues with using per
capita as the basis of the analysis.

I adjusted the OCED numbers to be on a per-gun basis as opposed to a per
capita basis and non US OCED countries combined were more likely to have
rampage shootings per gun than the US.

There are not issues in the US with social programs, mental health, etc as
compared with other countries when looking at mass shootings. The only number
that plays any significance is the number of guns per capita to influence the
number of shootings per capita.

If other countries had as many guns per person as the US, the data indicates
they'd proportionally have the same amount of shootings per person or more.

~~~
jcromartie
In the USA, people who own guns are likely to own more than one gun. They may
be hunters or collectors. Per-gun is fairly meaningless.

~~~
jcranmer
I recently read statistics that the number of households owning guns has
decreased from 50% to ~30% since 1977, while the number of guns increased over
that time period.

~~~
hga
I did some back of the envelope checks on those statistics, and they would
require us gun owners to have arsenals worth $100,000 or so.

Note that one's willingness to tell an anonymous voice on a phone that one
owns guns changes with the political climate towards guns.

~~~
mikeash
How do you get $100,000? If 30% of households own guns, that's about 37
million gun-owning households. If there are 300 million guns, that's about 8
guns per gun-owning household. If that's $100,000, that means a gun is worth
on average $12,500. I'm hardly an expert on guns but that seems about an order
of magnitude too high from what I do know.

~~~
hga
This was in reference to a statistic about who's buying newly manufactured
"assault weapons", particularly the mass quantities of AR-15 pattern rifles
and the like that have been selling like hot cakes since the 2008 election.

It insisted that only us "gun nuts", not e.g. the large number of households
that only have one or two guns for self-protection, were buying almost all of
these new guns; to review and improve my estimate we'd have to find that
particular statistic/study.

~~~
mikeash
I see. Is there some context in the gun world that I'm missing out on? Since
the comment you replied to said nothing about AR-15s or indeed anything beyond
the number of gun-owning households and number of guns overall changing over
the years.

------
Spooky23
This brings up more questions than answers in my mind. Do we care about mass
killings, or whatever is qualified as a "rampage shooting"?

For example, Mexico has 1 "rampage shooting" in the data referenced in the
article. Yet you have cartels killing dozens of people on a regular basis. The
question in my mind is that if we don't have lots of "rampage shootings" in
countries with lots of access to weapons, why does the US have so many? Why
aren't developing countries with ubiquitous AK-47s experiencing this
phenomenon?

~~~
dsmithatx
And if you included all the killings in Chicago during the same period, it
would probably make most of Mexico looks like Disney Land.

~~~
GVIrish
Sure you could find a city in Mexico that would look like Disneyland next to
Chicago. But compare Chicago to Ciudad Juarez and the murder rates are about
the same (457 in 2014 in Chicago, 424 in 2014 in Juarez). And a few years ago
(2010) Ciudad Juarez was the murder capital of the world with over 3000
murders.

Mexico as a country still has about twice as many murders per year as the
United States while having less than one-third the population. Mexico has FAR
stricter gun laws btw.

~~~
hga
_Mexico has FAR stricter gun laws btw._

Mexico has exactly _one_ legal gun store for the entire civilian population.
Ownership of guns in "military" calibers (previously adapted by a country's
military) are illegal, once reason .38 Super was developed for the M1911. The
whole country probably makes NYC look like a legal gun-owners' paradise (less
than 60,000 each for handgun and long gun ownership permits for 8 million
residents).

------
grkvlt
Isn't the fact that Norway appears near the top of this list only due to a
single incident with a large number of victims, i.e.
[https://en.wikipedia.org/wiki/2011_Norway_attacks](https://en.wikipedia.org/wiki/2011_Norway_attacks)
which skews the statistics. This is what he means when discussing small-N
statistics being meaningless.

------
geggam
I would be interested in seeing the data correlating SSRI drugs to mass
shootings statistically analysed so neatly

~~~
innguest
I've been panning these comments with Ctrl+F for "SSRI" and you're the first
one.

You and I would be interested in seeing that data, and you and I will never
see that data. ;)

Also the media never ever mentions most of those shooter kids were on those
hardcore FDA drugs.

What's the point? We know the gun was responsible for the killings. /s

~~~
hga
Seriously, we _do_ believe these shooting are correlated with just plain
mental illness. Which are largely "treated" with "those hardcore FDA drugs"
(which SSRIs, due to the low side effect profile, really aren't), so therefore
I'm not surprised there seems to be a correlation between the two. However,
after a fair degree of study, and discussion with one of my psychiatrists a
dozen or so year ago, I don't think there's causation, just correlation. Or at
least he didn't believe the "antidepressants give you enough energy to be
violent" thesis based on all three generations of them.

~~~
norea-armozel
I can say that sadly I'm one of those people that don't do well on SSRIs (at
least the withdraw from them). I literally wanted to stab my own mother and
sister when I was coming off of SSRIs (Zoloft). I literally felt so angry at
everyone and everything. So, I'll never go on SSRIs ever again.

------
caf
I believe the statistical lesson here is widely applicable, and may well be of
use if data analysis - particularly of rare events - is part of your job.

~~~
praptak
This statistical lesson is actually a textbook error, similar to taking a
p=0.05 test on multiple subjects separately.

What makes this interesting is the political context.

~~~
caf
Certainly, but I have seen _many_ people tasked with analysing data in a work
context who have never picked up a stats textbook.

------
phantarch
Sherlock (or Doyle) says it best. "It is a capital mistake to theorize before
one has data. Insensibly one begins to twist facts to suit theories, instead
of theories to suit facts."

Petzold does a really good job of debunking the original claim that the US is
not statistically significant when it comes to the number of mass shootings.
However, all of the effort he goes through only points to one conclusion: the
number of shootings we have in the US isn't statistically random. All this
means is that there's something causing the rate of shootings to be higher
here than is expected by random influences. It doesn't point to what that
cause is.

It's odd to see how statistics are abused by interest groups/media. Intuition
is usually a pretty good yardstick for the validity of a statistic, insofar as
knowing what kinds of conclusions should be able to be drawn from what kinds
of data. If you've got a bunch of data about who likes what flavor of ice
cream, it's not likely that data says anything about /why/ each person likes
what they like. In the same way, it doesn't matter if you say that the US is
normal when it comes to number of shootings or to say that it's abnormal as
Petzold does, when you try to say /why/ this is the case, you better be
drawing direct conclusions from your data.

~~~
avn2109
Speaking of validity, it's not immediately obvious to me that each citizen of
an OECD country constitutes a valid Bernoulli trial. Applying a uniform
empirical prior of shooting rampage probability across the entire population
strikes me as questionable. Presumably the results would be roughly convergent
if he had done this with an inhomogeneous Poisson or something, but it seems a
little handwavy to just fire off a binomial and call it good.

------
awptimus
This article demonstrates the danger of thinking statistics is logic - you can
only use statistics with the analytical framework firmly set up...not as a
replacement.

The United States is just that - United. States. 38 mass shootings, however
defined, means there is /less than one per State/. Guess what? That makes
Finland's two /much/ higher. That's...statistically significant!

Explaining how completely incapable frequentist statistics are at describing
anything at a low sample size doesn't mean that something succumbs to "random
fluctuation." There is nothing random about a person deciding to take arms and
shoot lots of people. Not only that, this data is based on a full population
sample - it's not a survey of 5,000 people extrapolating to the whole
population - it IS the full population.

And he removed the idea that the original chart was designed show - lack of
data that shows compelling evidence that more restrictive gun laws prevent
either mass shooting incidents or mass shooting deaths.

He should step away from the statistics - it's a loaded gun and he's not
trained to use the weapon properly.

------
kromem
It's disingenuous to compare shootings purely by a per-capita basis. It should
be per-capita among gun owners.

The data as shown indicates the US has a cultural mass shooting phenomenon,
but it's simply not accurate. The US just has more guns, and mass shootings
happen at extremely rare rates among gun owners everywhere.

This approach would be like comparing drunk driving fatalities in Los Angeles
vs Venice, Italy.

Edit: I was curious and just ran the numbers with the full OCED countries. The
US had 0.136 rampage shootings per gun (compared to 0.120 rampage shootings
per capita), and non-US countries had 0.177 rampage shootings per-gun
(compared to 0.246 rampage shootings per capita). I used the author's numbers
and the Wikipedia page data for guns/100 residents.

~~~
girvo
> It's disingenuous to compare shootings purely by a per-capita basis. It
> should be per-capita among gun owners.

First off, I don't live in the US and I don't have a horse in this race.

You may have a point. However, wouldn't the fact that having a large number of
gun owners directly correlating to mass-shooting fatalities still come down to
the same conclusion: that guns should be regulated further? Or do you think
that if the analysis was done it'd show something different to what the
analysis in the original article shows?

~~~
bmelton
> First off, I don't live in the US and I don't have a horse in this race.

Not living in the US presumably subjects you to position bias. Those who live
in countries where gun rights are strong tend to favor gun rights. Those who
live in countries where gun control is strong tend to favor gun control. This
is true of most things, as the moral compasses of most are drawn from what is
currently normative to their existing environment. This is true of most places
in which socio-political biases are codified into law, whether regarding
religion, gay rights, whatever; Change in these areas tends to come slowly if
at all.

> guns should be regulated further

Perhaps they should, perhaps they shouldn't. I have my bias, as I'm sure does
everyone engaged in the discussion, but, at the end of the day, the document
of the highest possible authority suggests that the citizenry should have
access to guns, and the only way to overturn that is by ratifying that
document. Thankfully, the document itself offers prescriptive measures for
such ratification, but at the end of the day, without a strong enough amount
of support throughout the nation and states for such a measure to pass.

At present, such support does not exist, so our politicians play different
games on what does or does not constitute "infringement".

In the past, the argument was that it wasn't infringing if the person who
wanted to exercise gun rights wasn't a member of a militia. We can prove
historically and grammatically that this isn't true, but it took the Supreme
Court's agreement for the legislature to accept it.

Then, the argument was that sure, it's an individual right and not limited to
those in the militia, but hey, the second amendment says you can keep and bear
arms, but it doesn't say where, so instead, the government insists that the
right is only applicable to within the home. Have as many guns as you like,
and carry them anywhere you want, as long as it's inside your home.

It took Chicago v. McDonald getting that one overturned in 2012 by the Supreme
Court.

So, legally speaking, we know that the right to keep and bear arms is an
individual right, disconnected from membership in a militia, and it extends
outside the home. To those who favor gun rights, the matter might settled, but
to those who favor gun control, it's a challenge to come up with a new rule
that doesn't directly contradict those recently affirmed rules by the Supreme
Court.

In D.C., the argument is currently that the right to keep and bear arms is
only available to those with a heightened need... but what other right in our
Constitution merits such a high bar to exercise? Would it be okay to restrict
voting only to those harmed by the current administration? Would it be okay to
limit speech only to those who can show that they have been victimized?

Anyway, I'm obviously ranting, and there's certainly more of my bias in this
post than I intended, so I should shut up. The point, that I'm sure I made
poorly, is that the law here says that we can have firearms, and that not even
the elected legislature has the power to overturn that without ratifying the
Constitution... unless they can come up with something legally clever, or wait
until there exists a more favorable court to their cause.

~~~
hga
Nits:

 _In the past, the argument was that it wasn 't infringing if the person who
wanted to exercise gun rights wasn't a member of a militia. We can prove
historically and grammatically that this isn't true, but it took the Supreme
Court's agreement for the legislature to accept it._

I don't see any legislators changing their mind about this, or any laws being
passed based on it, although I might have forgotten some state ones. Except
for:

 _Then, the argument was that sure, it 's an individual right and not limited
to those in the militia, but hey, the second amendment says you can keep and
bear arms, but it doesn't say where, so instead, the government insists that
the right is only applicable to within the home. Have as many guns as you
like, and carry them anywhere you want, as long as it's inside your home.

It took Chicago v. McDonald getting that one overturned in 2012 by the Supreme
Court._

Errr, _McDonald v. Chicago_ just applied _Heller_ to the states and
specifically Chicago, and further Federal court action, not appealed to the
Supreme Courts, enforced a shall issue concealed carry regime on the state ...
which I'll note for a blue state is much better balanced between the big
cities and "downstate" for it.

Not counting California and Hawaii, where this is still being litigated,
_every_ other Federal judicial challenge to a restrictive concealed carry
regime has failed, and the Supremes have then denied cert, despite the circuit
split. As it stands in the Federal courts, we now have a right to keep arms in
our homes, and to bear them there (that was actually an issue litigate in
_Heller_ and is elsewhere one, based on so called "safe storage" laws), but
not outside our homes.

~~~
bmelton
"I don't see any legislators changing their mind about this"

That's more to rebut the perennial tide of "Well, if you read the second
amendment it clearly states that it belongs to a well regulated militia"
argument that invariably crops up in lesser discussions on the subject.

"Errr, McDonald v. Chicago just applied Heller to the states and specifically
Chicago"

Correct. I crossed it with Moore v. Madigan. It's late, and they're in the
same jurisdiction, which I don't live in. Apologies for the error.

"Not counting California and Hawaii, where this is still being litigated,
every other Federal judicial challenge to a restrictive concealed carry regime
has failed"

And D.C., as Pena v. Lindley is being reheard en banc, and the new panel has
stayed their previous injunction on enforcing "good and substantial"...
otherwise, yes, agreed.

------
nabla9
Intresting note:

Nordic countries (Finland, Norway) and Swizerland rank very high in gun
ownership among OECD countries. [http://www.nationmaster.com/country-
info/stats/Crime/Gun-own...](http://www.nationmaster.com/country-
info/stats/Crime/Gun-ownership/Guns-per-100-residents/2007)

~~~
tomwilde
Switzerland is biased because of the militan army approach. Every able-bodied
Swiss male has an assault rifle at home, without any bullets, however.

~~~
at-fates-hands
>> Switzerland is biased because of the militan army approach. Every able-
bodied Swiss male has an assault rifle at home, without any bullets, however.

This was exactly the purpose of the text in the second amendment when they
talk about having a "well regulated militia":

 _The phrase “well-regulated” was in common use long before 1789, and remained
so for a century thereafter. It referred to the property of something being in
proper working order. Something that was well-regulated was calibrated
correctly, functioning as expected. Establishing government oversight of the
people’s arms was not only not the intent in using the phrase in the 2nd
amendment, it was precisely to render the government powerless to do so that
the founders wrote it._

source: [http://bearingarms.com/well-regulated/](http://bearingarms.com/well-
regulated/)

Essentially this meant every citizen should be properly armed should they be
called into duty for defending the country. Sure, a lot has changed since
then, but most gun owners I know still take this wording very seriously and
believe it is their duty to defend against government tyranny.

~~~
rayiner
> Essentially this meant every citizen should be properly armed should they be
> called into duty for defending the country. Sure, a lot has changed since
> then, but most gun owners I know still take this wording very seriously and
> believe it is their duty to defend against government tyranny.

I don't see how you get from point A ("well-regulated" means keeping in proper
working order) to point B (the purpose of the militia was to defend against
_government_ tyranny).

One of the motivating purposes of the Constitutional Convention was to respond
to the failure of the state militias to put down armed rebellions _against the
government_. Whether or not the second amendment guarantees the right to own
personal firearms, the idea that the framers intended those firearms be used
against the government is ludicrous. The most reasonable conclusion from the
primary materials is that those well-regulated militias exist to put down
those who would take up arms against the government!

~~~
hga
Errr, how about Thomas Jefferson in 1789, after the Revolutionary War just to
be clear? From Wikiquote:

 _God forbid we should ever be twenty years without such a rebellion. The
people cannot be all, and always, well informed. The part which is wrong will
be discontented, in proportion to the importance of the facts they
misconceive. If they remain quiet under such misconceptions, it is lethargy,
the forerunner of death to the public liberty. … What country before ever
existed a century and half without a rebellion? And what country can preserve
its liberties if their rulers are not warned from time to time that their
people preserve the spirit of resistance? Let them take arms. The remedy is to
set them right as to facts, pardon and pacify them. What signify a few lives
lost in a century or two? The tree of liberty must be refreshed from time to
time with the blood of patriots and tyrants. It is its natural manure._

But he was most certainly a firebrand, and you do have a point about
motivations for our current Constitution if this book is to be believed:
[http://www.upenn.edu/pennpress/book/13777.html](http://www.upenn.edu/pennpress/book/13777.html)
(it's new (2003) and sounds revisionist, but that doesn't mean it's incorrect,
just that as with anything historically political like it it has to be
checked, see e.g. _Arming America_ ).

~~~
rayiner
Thomas Jefferson was a lot of things, but one of the things he wasn't was at
the Constitutional Convention. His writings evidence strains of thought that
existed at the time of the founding, but to the extent that you can divine
some sort of "intent" on the part of the 40 people who signed the
Constitution, his writings do not clarify that intent.

------
smoyer
I'm to the right of president Obama, own guns (yes plural) and yet agree with
him whole-heartedly. We, as a nation, need to figure out how to stop this
violence. Please don't paint all conservatives with the radical right-wing
brush.

As an aside, I don't think Finland is celebrating in the streets with shouts
of "we're number one".

------
jamesfe
You know what Twain says - there are lies, damned lies, and statistics.

([https://en.wikipedia.org/wiki/Lies,_damned_lies,_and_statist...](https://en.wikipedia.org/wiki/Lies,_damned_lies,_and_statistics))

------
adamtj
Intentionally or not, the author has cherry-picked the data in a way that
completely undermines the article. The conclusion that "lives are at stake" is
obviously true and supported by the data, but the implication that the US has
too many guns is not. An analysis is only as accurate as the data. Here, the
missing data makes it painfully obvious that, while we should whatever we can
to reduce gun violence, we cannot morally accomplish it by disarming US
citizens.

If you merely look back to about 1939, you would find numbers for Poland alone
that dwarf any statistics for the US, even ignoring differences in population!
Poland isn't the only such example. Around that time, certain groups of people
suffered from numerous horrific shootings, decimating their populations,
despite those groups having been recently disarmed almost entirely. Of course,
I'm being sarcastic. These people suffered at the hands of their own
governments _because_ they were disarmed, not despite it. There are some still
alive who remember.

An honest assesment of history, even very recent history, makes it clear that
America's current level of gun violence is a mere rounding error next to the
real threat: descent into tyranny. We're lucky that we live in such a
relatively peaceful time, but let us not delude ourselves. No human will ever
live without the threat of tyranny. No government of the people or by the
people will ever, by it's own internal guidance, remain civilized
indefinitely. We must never surrender the tools needed to provide the most
drastic of course corrections for a government gone astray.

We are fortunate that by keeping and maintaining arms, we make it _more_
likely that we will never have to use them. Armed violence is always the
absolute last resort, but if we give up our last resort, we give up all the
other ones too. Speech, for example, is of little use against a tyrant with
absolute power. But speech from the mouths of well-practiced riflemen, with
their weapons close at hand? Those words cannot be safely ignored by anyone.

It is for this reason that the right to keep and bear arms is not unique to
just the United States. Rather, it is a fundamental and irrevokable human
right. The Constitution of the United States does not and cannot _grant_ this
right -- though it does explicitly _recognize_ it, lest we forget.

Yes, gun violence is awful, and we should work hard to reduce it. But let us
not forget that is is the price we pay for a civilized society, and it is a
small price compared to the alternatives. I grow tired of articles that
completely miss this point.

------
sudioStudio64
Petzold is awesome. His blog has several articles he's written about his
political views. I'm glad that someone with that kind of notoriety isn't
afraid to write about politics.

~~~
kyberias
I'm sorry, what notoriety?

~~~
CodeCube
He's known, amongst certain people in the industry -
[https://en.wikipedia.org/wiki/Charles_Petzold](https://en.wikipedia.org/wiki/Charles_Petzold)

------
cronjobber
The reason we care about mass shootings is because people die. Petzold drops
the one variable we _care_ about and calls it de-obfuscation? Neat.

~~~
OscarCunningham
If you care about people dying then mass shootings aren't an important issue.
(Compared to almost every other issue.)

------
ekianjo
Excellent article. I wonder what software was used for the computer simulation
in the second part. Can one do that in R relatively easily ?

~~~
CodeCube
He mentions that it's a C#/WPF program that he wrote :) The article includes a
link to download the code and play with it yourself:
[http://www.charlespetzold.com/blog/2015/07/RampageShootingSt...](http://www.charlespetzold.com/blog/2015/07/RampageShootingStatistics.zip)

------
vacri
Spree killings/mass murders/rampage shooters/whatever are all a canard anyway.
A canary in the coal mine. Add up all the spree killers in the US and they'll
not break 1% of the murders. Just like the debate over automatic weapons is a
canard, since they're very rarely used in murders.

The US has a murder problem. It's murder rate is four times that of it's
industrialised contemporaries. Most of those murders (~75%) are done with
firearms, and most of those (>75%, can't recall exactly) are done with
handguns. And by someone who knows the victim closely.

The stereotype of the inner-city gangsta gunning down a gangland enemy with an
automatic weapon is an outlier. And the same is true of the spree killer. As
long as debates on either side center on these kinds of outliers, little will
be achieved. The murder rate isn't going to be affected by open carry, since
most murders aren't of strangers. And banning automatic rifles isn't going to
do anything either, because it's handguns that do the dirty work.

The problem is that these details aren't sensationalist. Being gunned down by
a stranger on a rampage makes the news. Being killed by a crazy relative
doesn't.

~~~
bmelton
I hate to be pedantic in discussions like this one, and please know that I
certainly don't mean any offense beyond correcting a technical error that
perhaps nobody really cares about.

"Just like the debate over automatic weapons is a canard, since they're very
rarely used in murders"

There _is_ no debate surrounding automatic weapons, or, at least there isn't
one on the national stage. Automatic firearms are dramatically different from
semi-automatic firearms, and it's been a (specifically expressed) political
maneuver to confuse/conflate the two.

The number of deaths attributable to automatic firearms is effectively nil, as
they've been highly controlled since the days of Al Capone and his ilk.

When people are referring to "automatic firearms" in today's political arena,
they almost always mean to say "semi-automatic firearms", which most closely
maps to the sorts of weapon used in the Newtown and Aurora shootings.

It's a subtle, but important distinction, but as those who are trying to
conflate the terms generally intend to do so to confer additional scariness to
semi-automatic firearms that are simply not there.

~~~
roel_v
"The number of deaths attributable to automatic firearms is effectively nil,
as they've been highly controlled since the days of Al Capone and his ilk."

Well, since we're going to be pedantic, this should really say "the number of
deaths attributable to _legally owned_ automatic firearms", since there is
quite a bit of criminal violence (as in, violence to support criminal
activities, like drive bys, rip deals resulting in shootings etc) and deaths
involving automatic weapons (although it's quite hard to find statistics on
this, to my surprise). MAC 10's and Mini Uzis are rather popular for that sort
of shenanigans, because of their small size (thus easily concealable). An AR15
style weapon (which is usually the type of weapon people talk about when the
discussion is about 'assault rifles') is very impractical for such a thing, as
per your point.

~~~
LyndsySimon
> MAC 10's and Mini Uzis are rather popular for that sort of shenanigans,
> because of their small size (thus easily concealable).

Since you have provided no citation, I can only judge this statement by my own
anecdotal experience.

As someone who is closely involved with "gun culture", I'm aware of only a
handful of cases where automatic weapons were confiscated in the US - and of
no cases they were used in a murder in my adult lifetime.

~~~
hga
You might be younger than me ^_^, but in my lifetime two legally civilian
owned automatic weapons were used in crimes, both murders as I remember, one
by a policeman, though. I can't recall any illegal ones being used in murders,
but maybe some escaped my notice. Legal or illegal, they are demonstrably not
a problem; in fact, the NFA of 1934 used them as a wedge to try to severely
restrict handgun ownership, but that failed in the Congress.

