Just the numbers.
keywords: Guns, Violence, Correlation
In light of the recent news and discussion of guns and gun control I spent some time analyzing the data regarding gun ownership and homicide world wide in more than 170 countries. I report various statistics regarding the relationship between gun ownership rates, homicide rates, and homicide due to gun rates.
The Data
These charts are based on data from two sources:
- A blog at the UK’s Guardian regarding gun ownership rates by country, as well as gun related homicide rates, and
- A wikipedia entry that reports overall homicide rates by country.
I combined these two datasets in order to assess the relationship between gun ownership and overall homicide rates. There is a lot of missing data, so for some plots not all countries are represented.
If you are interested to crunch the numbers yourself, the data is here: gun-stats-raw
Chart 1: Gun ownership versus homicide rate: scatter & correlation
In this chart each data point represents one country. The X location is determined by the gun ownership rate of the country. The Y location is determined by the homicide rate per 100,000 people. The US leads the world in guns per 100 people at 88.8. The US is the dot at the furthest right.
The red trend line was determined using linear regression. The correlation is -0.17. This indicates that higher gun ownership rates are correlated with lower homicide rates. However this value is not an especially strong correlation.
X = gun ownership / 100 people. Y = homicide rate / 100,000.
Chart 2: Gun ownership versus homicide by gun rate: scatter & correlation
In this chart each data point represents one country. The X location is determined by the gun ownership rate of the country. The Y location is determined by the percentage of all homicides caused by guns. The US leads the world in guns per 100 people at 88.8. The US is the dot at the furthest right.
The red trend line was determined using linear regression. The correlation is 0.10. This indicates that higher gun ownership rates are correlated with a higher proportion of homicides by gun. However this value is not an especially strong correlation.
X = gun ownership / 100 people. Y = % of homicides by gun.
Chart 3: Gun ownership versus homicide rate: Separate plots
In this chart the countries are sorted left to right by gun ownership rates (further right means more guns per 100 people). The US leads the world in guns per 100 people at 88.8. The US is at the furthest right.
The red line indicates guns / 100 people. The blue line indicates homicides per 100,000 people. If increased gun ownership were correlated with increased homicide rates we should see the blue line increase as we go right. We do not see that.
X = world wide rank in terms of gun ownership rate (more guns to the right). Y for red line = number of guns/100 people. Y for blue line = homicides/100,000 people.
Chart 4: Homicide rate versus gun ownership: Separate plots
In this chart the countries are sorted left to right by homicide rates (further right means more homicides per 100,000 people).
The red line indicates guns / 100 people. The blue line indicates homicides per 100,000 people. The US is the big spike in the red line in the middle. The US is about in the middle with regard to overall homicide rates.
If increased gun ownership were correlated with increased homicide rates we should see the red line increase as we go right. We do not see that. In fact it seems to decrease somewhat as we move to the right.
X = world wide ranking according to homicide rate (more homicides to the right). Y for red line = number of guns/100 people, Y for blue line = homicides/100,000 people.
Chart 5: Gun ownership versus homicides due to guns: Separate plots
In this chart the countries are sorted left to right by gun ownership rates (further right means more guns per 100 people).
The red line indicates guns / 100 people. The blue line indicates the % of homicides due to guns. The US is the furthest right.
If increased gun ownership rates were correlated with increased homicides due to guns we should see the blue line increase as we go right. We do not see that. Overall, the relationship seems random. Perhaps there is some correlation at the very right side. Maybe these are the developed countries? We’ll check that out in the next chart.
X = world wide ranking according to gun ownership rate. Y for red line = guns/100 people, Y for blue line = % of homicides that were caused by guns.
Chart 6: Gun ownership versus homicide rates in developed countries
In this chart we focus on 45 developed countries (list of developed countries at end of post). The countries are sorted left to right by gun ownership rates (further right means more guns per 100 people).
The red line indicates guns / 100 people. The blue line indicates the homicides per 100,000. The US is the furthest right.
If increased gun ownership rates were correlated with increased homicides we should see the blue line increase as we go right. We do not see that.
X = rank among developed nations according to gun ownership rating (more guns to the right). Y for red line = guns/100 people. Y for blue line = homicides/100,000 people.
Commentary
Based on these data, I conclude:
- Increased gun ownership rates are slightly negatively correlated with homicide rates worldwide. This means that more guns is correlated with fewer homicides.
- Gun ownership rates are slightly positively correlated with the rate of homicides due to guns. This means that of all the homicides in a country, a higher proportion of them are gun related when there are more guns per person.
- Increased gun ownership rates are not correlated with homicide rates in developed nations.
There are other studies, including these by Harvard that seem to be somewhat in conflict with the data I charted above. I think, actually, that it is possible for my results, and Harvard’s to be correct. Here’s why: Access to guns is probably a factor in overall homicide rates. However, social factors like poverty and culture play a much more significant role. In a worldwide study these factors overwhelm the data, so the gun ownership/homicide relationship is not apparent (even seems random or unrelated). If you can control for poverty and culture (e.g., a US only study) I believe you may find correlations. I think this is why the Harvard studies show some relationship.
Also, this paper asserts that the measures of gun ownership used by some of the Harvard authors is not accurate.
Developed Countries
| Singapore |
| Japan |
| Romania |
| Lithuania |
| South Korea |
| Poland |
| Austria |
| Netherlands |
| India |
| Taiwan |
| Hungary |
| United Kingdom |
| Bulgaria |
| Ukraine |
| Belarus |
| Israel |
| Slovakia |
| Portugal |
| Ireland |
| Albania |
| Estonia |
| Spain |
| Italy |
| Denmark |
| Argentina |
| Turkey |
| South Africa |
| Luxembourg |
| Czech Republic |
| Belgium |
| Latvia |
| Qatar |
| Greece |
| New Zealand |
| Macedonia |
| Iceland |
| Germany |
| Australia |
| Canada |
| France |
| Norway |
| Sweden |
| Finland |
| Switzerland |
| United States |
the augmented trader 
Alexander Stohr
December 16, 2012
#27 – South Africa is so much different from other developed countries.
Rob
December 16, 2012
Well done Tucker. It would be interesting to see countries with mandatory military service and gun ownership/ homicide rates.
Alexander Stohr
December 16, 2012
If you can access data on facebook, then please give that diagram a visit:
Tucker Balch
December 19, 2012
The data in that diagram is not correct. Or at least it is not the data reported in the Guardian article.
Alexander Stohr
December 20, 2012
these are the numbers from the guardian in an x-y plot with logarithmic scale and labels on the dots. for not going into fractions the per-head count base dividers were changed.
as you seemingly have the data as well it should not be much fuzz for you to do the same.
James Mayfield
December 16, 2012
It’s interesting to compare these stats with the ones at (which seems to be a version of Alexander Stohr’s chart restricted to Western countries, and not on a log scale). It suggests that there are significant factors outside of gun ownership that need to be controlled for before we draw strong conclusions.
David D
December 19, 2012
Looking at the raw data, it seems evident that you left out an important factor from your work: the countries where there are the highest number of gun related deaths per capita are in unstable/3rd world regions with little to no law enforcement. How can you compare that to industrialized nations?
I think if you were to redo this with ONLY industrialized nations in the mix, you would see that the US is out in front by a large margin.
This is an apples and oranges comparison as it is right now…
Tucker Balch
December 19, 2012
The data for industrialized countries is at the end.
David D
December 19, 2012
But what are you using as the criteria for industrialized/developed countries? If you use the most common method, which the Human Development Index, then your formula doesn’t hold up. In fact, looking at another crime stat that was released, the US is only behind South Africa, Columbia, and Thailand in gun related murders, and those countries are far from developed.
The stat is here: http://www.nationmaster.com/graph/cri_mur_wit_fir-crime-murders-with-firearms
Tucker Balch
December 19, 2012
Your citation uses a different metric, namely “gun-related deaths” which is not the same as overall homicide rate.
David D
December 19, 2012
Also, if you look at the list on wikipedia, which you used as a source for you article, it shows the US as #10 in gun related deaths, behind only undeveloped nations. So again, the US is #1 among developed countries.
Tucker Balch
December 19, 2012
Again “gun-related deaths” which is not the same as homicides.
Alexander Stohr
December 19, 2012
USA: 10.000
Mexico: 2.500
does that tell you anything?
Tucker Balch
December 19, 2012
I’m not sure what number you are citing, but keep in mind that the US has a substantially larger population. If your number is about homicides, I would say that this indicates a very much elevated rate for Mexico.
David D
December 19, 2012
If you’re referring to the number of deaths, it seems to back up my point…
Brdrker
December 20, 2012
One question/critique: Your measurement (unless I misread) is taking the total number of guns in the society and then dividing by the population size to get firearms/100 people. Since many individuals own multiple firearms, have you considered re-doing the data with firearm ownership/100 people. The number would be smaller and maybe the effect not as drastic but I suspect your analysis would still hold.
Tucker Balch
December 20, 2012
I don’t have data for firearm ownership/100 people.
Brdrker
December 20, 2012
Not sure how valid this is but here this is:
http://www.statisticbrain.com/gun-ownership-statistics-demographics/
Brdrker
December 20, 2012
Nevermind… I just realized you needed gun ownership for each country and the link I’ve provided doesn’t help you at all.
Jason
December 22, 2012
Maybe this… http://www.smallarmssurvey.org/fileadmin/docs/A-Yearbook/2007/en/full/Small-Arms-Survey-2007-Chapter-02-EN.pdf
lol
December 22, 2012
You’re using linear regression to model an obviously highly non-linear relationship (seriously, just look at your plots), it makes no sense to draw any conclusions from the tiny correlations you’re finding.
The comparison between gun ownership and homicides is misleading because there are clearly many other factors that affect homicide rates that you’re not controlling for. It would make much more sense to analyze guns/person vs gun deaths/person or similar.
Tucker Balch
December 23, 2012
The point of my article is that there is very little discernible relationship between gun ownership rates and homicides. I agree that there are clearly many other more significant factors that affect homicide rates. Again, thats the point.
Richard
December 23, 2012
How about if you include gdp per capita?
George Fournier
December 23, 2012
Very provocative statistics. It would be interesting to examine the homicide perpetrator rates among various types of groups of gun owners such as retired military, off duty or retired police officers, concealed weapons licensees, firearm hunters (as opposed to bow hunters) and gun collectors, and compare these rates to the population as a whole.
Raj
December 30, 2012
I won’t argue with a conclusion that says that the rate of gun ownership is not correlated to the homicide rate overall. But what needs to be studied is the correlation between the ownership of military style assault weapons and the number of people killed in mass murders.
unklee
December 30, 2012
Interesting, I did exactly the same thing, got pretty much the same graph, with a slight negative correlation between gun ownership and gun homicides. And I got the same coefficient of correlation, r = 0.1.
But did you know that the important statistic is r^2, which indicates the amount of the relationship between the two variables explained by the correlation? In this case, r^2 = 0.01, or 1%. This means that the correlation is indistinguishable from zero, and is worthless.
You have not proved there is a negative relationship, but that there is no relationship worldwide!
This means that other factors determine the rate of gun homicide. I also tried graphing gun homicide against wealth inequality (measured as the ratio of the 90% percentile to the 10th percentile). This showed an r^2 = 0.3, which is significant though still only one part of the picture. Countries where there is wealth inequality (worst in south & central America and AFrica, and worst among OECD countries in the US) are more likely to have higher gun homicide rates. It would be interesting to find other important factors.
Tucker Balch
January 1, 2013
Yes, I know about r^2. My point is that the two variables are not related. If you re-read my post you’ll see that I’m not asserting any relationship. Or at leas that was my intent.
unklee
January 1, 2013
Sorry, I misunderstood you. You said “This indicates that higher gun ownership rates are correlated with lower homicide rates. However this value is not an especially strong correlation.” Having done exactly the same thing as you, I felt the first statement here was misleading by saying there was a correlation when I think the r^2 is so low that there is no correlation. Anyway, if we’re both on the same page, then that’s cool. Thanks.
Tucker Balch
January 1, 2013
Yeah, OK. I agree the text sounds stronger than I meant it. I’ll tone it down a bit.
Poingly
January 6, 2013
There are a few potential problems with the data used as well.
(1) It should be noted that the numbers are gun numbers, not percentage of gun owners. There is a huge difference there. One private citizen in a country who owned a million guns could skew the numbers, as this would essentially be the same as a country with an equal sized population where one million citizens each own one gun.
(2) I can’t see to find any indication as to whether these numbers are legal guns, illegal guns, or both.
(3) It only includes civilian guns, does the homicide rate only include civilian homicides?
AD
January 10, 2013
Interesting analysis. Is there data on “mass shootings” that could be analyzed as well? It seems like some of the public policy recommendations (i.e. assault weapons ban) that are being considered are aimed at minimizing that specific type of scenario.
mmbowden60
January 16, 2013
It would be interesting to see how results are affected when the US is removed from the data set. The US is an outlier in terms of gun ownership. Does that skew the results?
Dale Ruff
April 6, 2013
This analysis is a red herring. The strong correlation, among peer (such as developed) nations is between strict gun laws and low gun (and other) homicide rates. Germany and Switzerland have many guns but very strict gun laws…so they have 90% fewer gun homicides per capita than the US. The UK and Japan, with very few guns and strict laws have 99% fewer per capita gun homcides.
It is not guns per se which increase gun deaths but the absence of strict laws and limits.
Of 34 of 35 advanced nations, all have much lower gun homicide rates (and murder rates overall) than the US. The difference is strict gun laws, strictly enforced.
Therefore, this article picks the wrong variable in locating effective reduction of gun violence.
In this way, it distorts the solution to gun violence, which is strict laws without loopholes on a national level, including gun registration. The US has 90% more guns and 90% more gun homcides than the other advanced nations. Our gun violence record is that of a 3d world nation torn with civil strife, because of lack of adequate and universal gun laws.
The article, focusing on guns rather than gun regulation, obscures this truth. As such, it is part of the problem.
Dale Ruff
April 6, 2013
South Africa, Russia, and Brazil, cherrypicked as having high gun violence rates, are in no way peer nations of the US, such as true peers like Canada, the UK, Germany, France, Italy, Spain, Australia.
Russia is ranked 46th in terms of GDP per capita, Brazil is 75th, and South Africa is 79th. Russia is poorer than Trinidad; Brazil and South Africa are poorer than poor countries like Botswana and Costa Rica. This is comparing apples to oranges, a logical fallacy.
Peer nations would be the top 35 or so including Europe, Israel, Japan, et al, all with much higher levels of income and development than the nations chosen by the author. With similar
subterfuge, you can argue that the wealthy nation with the worst homicide rate has totally banned firearms. That would be Luxembourg, the world’s richest nation per capita, which had 2 gun homicides last year, a nation with fewer people than McAllen, Tx. That too is apples and oranges, tho a well-known study uses it (and Russia) to prove that gun bans are correlated with the highest gun homicide rates.
But if you look at Germany, Italy, France, Austria, the rest of Europe, New Zealand, Australia, Canada, Israel, and the top 35 advanced nations, you find that all have 90-99% fewer gun murders per capita. This is not cherry picking: this is taking all other developed nations (in the top 35) and looking at the data.
Tucker Balch
April 7, 2013
Dale, please feel free to download the spreadsheet and conduct your own analysis using your preferred list of developed countries.
Brdrker
April 7, 2013
FBI violent crime statistics:
http://www.fbi.gov/about-us/cjis/ucr/crime-in-the-u.s/2011/crime-in-the-u.s.-2011/tables/table-1
Of interest to note is that since 1992 (the start of this chart) our overall violent crime rate in the US has dropped approximately 50% (757.7 => 386.3 which is per 100,000). You can also drill down to see where the crime happens. It shows a majority of violent crime happens in big cities (not a shock, this, as there is a concentration of people in cities) but you can also see the neighborhoods where it happens (which brings up socio-economic factors as a pre-cursor to violent crime). Now, compare this against this:
http://www.homeoffice.gov.uk/publications/science-research-statistics/research-statistics/crime-research/hosb0812/hosb0812?view=Binary
Look at Table 2a. The number of interest is 762,515. That’s the total number of violent crimes in England/Wales. Population of England/Wales was, at this time, around 56,000,000. 757,515/56,000,000*100,000 = 1353.7.
Now compare: Our violent crime rate per 100,000 is now 386.3. England/Wales violent crime rate is 1352.7. England’s violent crime rate is about 3.5x the violent crime rate of the U.S. England does have a lower murder rate than the U.S., maybe, in part, attributable to the firearm laws but less firearms doesn’t mean less violent crime. It’s a much more complicated problem than getting rid of firearms.
Bernd
April 29, 2013
Your article pretty much misses the point. What you observe is simply the correlation between gun ownership and high living standards. In many countries, the average income does not allow you to buy a gun, even if you wanted to. Of course, poor countries also tend to have very high homicide rates, so on a global scale it is hardly surprising that there is a negative correlation between gun ownership and homicides. On the other hand, when we’re talking about gun control (in the US or elsewhere), we’re talking about HIGHLY DEVELOPED COUNTRIES. If you restrict you data to, say, the 30 countries with the highest Human Development Index, you will find a positive correlation: http://postimg.org/image/tuzd8w72p/
Jacob Clements
April 29, 2013
This includes about 50 countries! Ten of which are very unstable countries! We need to compare murder rates of countries and the gun rates, that will give you the information.
logischdede
May 3, 2013
http://news.yahoo.com/5-old-boy-shoots-2-old-sister-ky-161229579.html
according to the words in the article its an accident if a gun for a pre-school age child is still loaded whilst its in reach for him.
David Platts
May 25, 2013
The IMF recognizes 27 developed nations (population in excess of 100,000) that overlap with CIA data. I think the data is too wide in your range to have valuable comparative analysis and reduces the ability to obtain any usefulness from the work. I have worked on the 27 developed nations in total murder, firearm murder and firearm death rates per 100,000. The data correlates quite well and the U.S. in the sole outlier. I have examined the most recent data I could find on developed European nations with the IMF/CIA overlap. I added the U.S. to this examination. I used the data on total reported crime Eurostat and examined the data from the FBI and converted the data into total reported crime per 100,000. 3 had no provided information: Austria, Ireland and Spain. A total of 13 European nations were examined. Of the 14 nations, including the U.S, the highest total reported crime rate per 100,000 was Sweden. The U.S. was eighth on the list. The reason I did not use violent crime is that each nation has identifiers different from each other on violent crimes. Total crimes seemed to provide ample data to provide a basis in the belief that more firearms equate to less crime. The U.S. was 8th on this list and 3 or the 4 lowest crime nations had low firearm ownership. By the way, I used firearm ownership from a multiple resources obtained from the University of Sydney. No correlation could be found for the premise of low crime versus high firearm ownership. Absolutely none!
However, I did find extraordinary correlation to firearm regulation and reduced firearm death, firearm murder and total murder rates. Total murder was not as a strong correlation which makes sense. Many nations share similar murder rates by means other than firearms while some, such as South Korea, Taiwan and New Zealand, had very high rates of murder other than by firearms. However, with those three, they still had very, very low firearm murder numbers compared to the U.S and provided total murder rates per 100,00 far lower than the U.S.
I examined the firearm regulations for each of the 27 nations. A number of similarities existed that fails to exist in the U.S. Registration of firearms existed in 26 of the 27 nations. The U.S. failed to provide this oversight. Background checks in all transaction covering at least criminal and mental background in ALL transactions (except in one nation in the transfer between family members) and locks/safes for firearms. The Swiss, like the U.S., has a Constitutional right to firearm ownership. However, unlike the U.S., the Swiss do have the above regulations instituted. The, required background checks must include domestic issues too.
I find this sort of strong evaluation to be more useful. No data is leading, factual data only was provided and one conclusion opens the way to the next study with conclusion.
David Platts
May 25, 2013
I really hate the Leavitt (University of Chicago) idea of examining the U.S. against itself. Brdrker is attempting to do this very thing. I examined total reported crime versus the tussle in “violent” crime that changes significantly in definition from one nation to the next. The U.S. does not include Assault 4 on the violent crime list while the U.K. does do this. The analysis of total reported crime is much more useful. From worst to best, the U.S. is 8th on this list at 7,218 per 100,000 while the U.K. is 9th, and lower, at 7,132 per 100,000. Please, before quoting data you have failed to examine go out and look for a legitimate resource. The list had France high on the violent crime list. Their total reported crime France views much as violent that the U.S. tosses aside) is at 3,717 per 100,000. Of the 14 nations of 1 million or more in population on my data analysis, Greece was the lowest at 3,493 per 100,000. I used firearm per household which averaged about 4 per family in the U.S. France is at about 1.5 per household. Greece was about 1 per household. This completely throws out the conclusion that higher firearm ownership leads to lower crime. There is absolutely no correlation. None!
I used the data resources accumulated by the University of Sydney for firearm ownership converting to a rounding for firearms per household. I used Eurostat data for total reported crime with the last available in 2009 and published in 2012. I used F.B.I data for the U.S. By the way, the U.S. data has dropped to 6,590 per 100,000 which means, if Europe were to be unchanged (unlikely), the U.S would exchange places with the U.K. and be 9th on my list with only 5 nations with better total reported crime rates than the U.S. Still, if this improbable result were to happen, the same conclusion would occur. No correlation exists between high firearm ownership and low crime rates among these 14 IMF/CIA overlap developed nations.
Further, the idea of the U.S. improving over a 20 year period without using comparative data to similar nations is analogous to a failing student continuing to move up a few points while maintaining failing grades at each test. A failure is a failure whether it be 1994 or 2012. The U.S. firearm death rate (10.2 per 100,000), firearm murder rate: 2.75 and total murder rate: 4.7. 2nd worst developed (IMF/CIA overlap): Canada: 4.74, Israel: 0.94 and Finland: 2.2. These are the second worst in each category. If we examine the cumulative rate, the data for the U.S. looks worse for each nation. If the 26 nations listed on the overlap were averaged on the three applicable rates using the most recent available data, the percentage the U.S. is higher is as follows: Firearm death – 569%, Total Murder Rate – 274% and Firearm Murder Rate – 1168%. I cheated a little here. Taiwan does ban firearms now. I do have data taking 6 nations out with low firearm ownership rates (<.5 per family). The data changes but not by that much. For example, Firearm Murder Rate by percentage is 1046% higher for the U.S.
Mona Albano
April 11, 2014
Look inside a country over time to compare gun ownership and homicide & suicide under similar conditions of culture. The availability of guns has a greater influence on suicide than on murder, although both show positive correlation because it simply makes them too easy on impulse.
thefirefli
June 18, 2015
Reblogged this on and commented:
A very logical, statistic based analysis.