Guns don't make people safer?

That's what a new study seems to say.  A piece at Reason magazine's blog commenting on it is titled, Why Skydivers Would Be Better Off Without Parachutes. 

Eugene Volokh also critiques the study.

Essentially, the point the study fails to account for is that people who own guns may simply be in more dangerous situations. They may still be less likely to be killed than they would be if they didn't have access to guns, but still have a higher death rate than people who live in much safer situations.

I'll quote from Eugene's piece:

Let me illustrate this with a deliberately oversimplified model. Let's begin by assuming a total population of 100,000, that's divided into two groups, a 10% high-risk group and a 90% low-risk group. Let's say that the high-risk group has a 60% risk of being attacked, and as a result 40% of its members carry guns. And let's say that the low-risk group has a 5% risk of being attacked, and as a result 3% of its members carry guns. Let's also imagine a total population of 100,000 (just to make the numbers easier), and let's assume that possessing a gun has a modest protective effect for both groups — it reduces the risk of being injured when attacked from 75% to 60%.

Here's what this turns out yielding, with "A" meaning "armed subgroup" and "U" meaning the unarmed subgroup.

Group	Number of people in group	Probability of being attacked	Armed subgroup fraction	Armed subgroup number	Armed subgroup injury risk	Armed subgroup number injured	Unarmed subgroup number	Unarmed subgroup injury risk	Unarmed subgroup number injured
High-risk	10000	0.6	0.4	4000	0.36	1440	6000	0.45	2700
Low-risk	90000	0.05	0.03	2700	0.03	81	87300	0.0375	3273.75
Total	100000		0.067	6700	0.227015	1521	93300	0.064027	5973.75
Odds						0.293686			0.068407

The result: The armed subgroup has 3.5 the risk of injury compared to the unarmed subgroup, and the relative odds ratio between them is 4.29. And this is so even though in the model gun possession decreases the injury risk for both the high- and the low-risk group.

Naturally, this is just a model; the real numbers are likely very different from the ones I give here, and in fact no-one knows what the real numbers are.

Indeed, this is the same sort of problem we get with drug testing, and any number of other statistical tests.