Correlation of gun deaths to gun numbers world wide

Just over a week ago I got into a discussion with someone on Facebook (no names, no pack drill) about gun control in the USA, or lack of it. My interlocutor was an obviously intelligent bloke and claimed his argument was objective and emotion-free, based on mathematics. To this end he produced a graph demonstrating that there was no correlation between gun murders (homicides) and gun ownership across the 50 states of America. After the debate I found another graph that disputes his findings, but that’s not what my argument is about.

In truth, I think he was just as emotive about this issue as me, perhaps more so, but believed he could take refuge in the safe haven of statistical analysis. In fact, he made the extraordinary statement (from my perspective) that violence in the US is ‘cultural ….but there's no evidence it has anything to do with guns’. In other words, he acknowledges that America is a violent country but it has ‘nothing to do with guns’, because there is no correlation between gun ownership and homicides between states. The point I want to make is that one can make an illogical non-syllogism if one can back it up with statistics. He effectively argued that yes, there are a lot of gun-related deaths in America (over 10 per 100k of people; arguably the highest in the developed world) and America has a lot of guns (9 for every 10 people; the absolute highest apparently) but there is no connection between the 2 stats.

So I pulled out an old psychology text book on statistics and did some analysis of my own. There is a well-worn formula called the Pearson Correlation that exploits standard deviation of both sets of data and delivers a figure between -1 and +1 that is easy to interpret. 1 is obviously a perfect correlation and 0 is no correlation, with -1 an inverse correlation.

Using data on Wikipedia I did a correlation for all 74 countries that Wiki lists for total firearm-related death rate (the list of gun numbers is considerably longer). The Pearson Correlation was -0.07, which is marginally negative and seems to support my Facebook antagonist. But a handful of countries have huge death rates in the 30s and 40s per 100k, which wipes out any correlation that the majority may reveal.

So if one removes all African countries, all Central and South American countries, Caribbean countries and all Middle Eastern countries (except Israel) we are left with all of Europe (both West and East, where we have figures) and most of Asia (except Philippines; refer below) and North America; 46 countries out of the 74. Now we get a Pearson’s Correlation of 0.83 which is quite high. However, if one adds just one anomalous country like the Philippines, which has a gun death rate of 9.5 (almost the same as US) but with gun ownership less than 5 per 100 people (20% of US gun ownership) the correlation drops to 0.6, a considerable difference made by one country out of 47. On the other hand, if one drops the US from the list, the correlation also drops to 0.67, so it’s a significant weighty statistic in its own right.

If one just takes England, Ireland, Canada, Australia, New Zealand and United States (countries most culturally similar to the US) one gets a Pearson’s Correlation of 0.95 (almost exact). But taking US out of this smaller list of 6 English-speaking countries the correlation only drops to 0.86, which suggests that the US is not an anomaly in the same way that the Philippines is.

So much for statistics. Mass shootings that grab global media headlines, apparently make up only 1% of gun-related deaths in the US (according to my Facebook opponent) therefore from a statistical point of view they shouldn’t influence the debate at all, but that’s just nonsense. The point is that they should be 0% as they tend to be in other developed countries. The obvious question to ask is what is the difference between the US and the other handful of similar countries (like England, Canada, Australia and New Zealand) that provide the strongest correlation? I would suggest it’s gun control. If the US has the largest number of guns per people of anywhere in the world and the highest gun-death rate in the Western world, then it’s screaming out for gun control.

I argued on Facebook that gun-deaths in America drive up gun ownership, indicated by the fact that there is a spike in gun purchases following mass shootings. America appears to have the most liberal gun laws in the developed world – a legacy of the NRA, one of the strongest political lobbies in America. It’s unlikely that Obama will be able to do any more than previous administrations, despite his history-challenging rhetoric. Every tragic shooting reopens this debate, but nothing changes, and every incident only reinforces the belief held by many Americans that they need to be armed.