Another mass shooting in America and a very predictable gag reflex response:

The implication being that the correct laws would prevent this kind of thing and that the correct legislation is lacking. Congress should fix this thing, because congress couldn't possibly have caused this thing.

None more prestigious than The New York Times jumped on the bandwagon, virtually shoving Piers Morgan out of the way, with What Explains Mass Shootings? International Comparisons Suggest an Answer. They get it so wrong that I made a follow-up post, More Mass Shooting Madness.

Mass Shootings: Do International Comparisons Suggest an Answer?

Poking fun at Piers Morgan is hardly a challenge, so I'll spend the rest of this post poking fun at The New York Times's unfortunate article. Let's start with the first chart:

The First Chart.

Note the caption. This is cherry picking as it only reckons countries with a lot of people, and a lot of guns, and lots of mass shooters. It suppresses evidence of countries which may have a lot of guns and not that many mass shooters. This is already objectionable, since this is what the article sets out to prove. It's confirmation bias. Good thing this isn't a research paper or something posted somewhere influential where the public may be mislead, right? Like, The New York Times.

Speaking of a lot of guns and a lot of mass shooters, the graph compares raw numbers of millions of guns with raw numbers of mass shooters. You shouldn't compare raw gun numbers with raw mass shooters. Incidents are usually compared as number of incidents per 100 000, or n/100 000, as the great article on Farm Murder Blindness illustrates.

There's nothing enlightening to be gained from a graph that just plots guns versus mass shooters, except perhaps that the person who compiled this report is innumerate and didn't do more statistics than the little bit I did.

But let's take that graph as it stands. The countries on that graph with the most mass shooters? The Philippines, China, India, Russia and the USA.

• The Philippines has gun control.
• In China, for all intents and purposes, private gun ownership is completely outlawed.
• India has gun control, including banning of what I imagine people mean with assault rifles (it's a contrived media term and not a technical term that denotes a particular kind of firearm).
• Russia has gun control. You aren't even allowed to own more than 10 guns and you aren't allowed to have a handgun.

Let's assume for a second that we can take this graph seriously. It inadvertently shows that the countries with the most mass shooters have the most mass shooters despite gun control and banning assault rifles and doing background checks. To reiterate, this graph isn't useful to show us anything at all. It is entirely bunk, but if it did show us something, that's what it would also show - completely the opposite of the claims about the graph!

The only variable that can explain the high rate of mass shootings in America is its astronomical number of guns

As Dr Peterson says, any social scientist worth their salt would do a multivariate analysis, because there are many variables and there isn't any one single variable that can predict things so easily. Gun control variables are especially numerous and tricky.

Also note that the graphs show mass shooters, as in perpetrators. The graphs do not show mass shootings. These are not necessarily interchangeable terms.

Does America have an astronomical number of guns?

If you want to determine this, you can't just count the guns and compare it to other regions where you just count the guns like the first graph purported to do. One way to measure this is by guns per capita.

Note that the guns listed there are presented as guns per 100 people. This is the same as n/100 000 with some arithmetic to bring it down to n/100, so at least one can make comparisons. The answer is unequivocally yes, America does have an astronomical number of guns by any measure.

Assuming that the astronomical number of guns explain the high rate of mass shooters, we would then expect other countries with an astronomical number of guns per capita to also have astronomically high rates of mass shooters. Or at least a higher rate as predicted by the higher number of guns, right?

Do countries like Serbia, Yemen, Cyprus, Saudi Arabia, Iraq, Uruguay, Norway, France, Canada and Austria, with similarly astronomically high numbers of guns, also have a high incidence of mass shooters? Because if they don't, then a claim like an astronomically high number of guns is the only variable that explains a higher rate of mass shootings cannot be based on evidence.

The Second Chart and How It Mysteriously Switched Metrics

The Second Chart. Better. Much better.

Note that the metrics here are different. It's guns per 100 people versus mass shooters per 100 million people. This is much better, since raw numbers are often skewed by well, other raw numbers. It seems to be the same data set, so conveniently countries with a lot of guns and no mass shooters or not enough mass shooters have been pruned, but at least we've got some sane metrics here.

Worldwide, Mr. Lankford found, a country’s rate of gun ownership correlated with the odds it would experience a mass shooting.

It's a mystery how Mr Lankford could have reached this finding from the presented evidence. He cautions us that Yemen is an outlier. Fair enough, let's ignore the troublesome Yemen since we already cherry picked data left right and centre. Let's look at the rest of the graph.

Presumably, Afghanistan is not an outlier then? So how did Afghanistan end up being third on the list of mass shooters per 100 million people when it doesn't have an astronomically high number of guns like Yemen and the USA? In fact, there are fewer guns there than in France, Canada and Iraq, all of which have lower rates of mass shooters? If we do ignore that ghastly outlier Yemen, then Afghanistan is second on the list of mass shooters and still way behind on the list of countries with an astronomical number of guns - and this is guns per capita, not raw numbers.

Correlation, causation and consternation

Here's a fun little exercise for the reader. Ever wondered what correlation looks like?

Correlation in scatter plots. The bottom right one should look familiar. Please help Mr Lankford to connect the dots.

Leaving day one of Statistics 101 out of this, where one learns that correlation does not imply causation, at the very least, a correlation needs to be established between two variables before a claim like the only variable that can explain the high rate of mass shootings in America is its astronomical number of guns can end up in The New York Times.

Your homework is to look at the second graph above, and see if you can spot which one it resembles in the correlation scatter plots here.