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Please begin with an informative title:

Like many of you, I've been watching closely the debate on gun control and the general discussion of the role guns play in our society. Inevitably in these debates, the role of 'defensive gun use' (DGU) is promoted as a net positive of gun ownership. In fact, specific studies were used in the Supreme Court decision Columbia vs. Heller, striking down the DC handgun ban, reinforcing the right to self-defense.

So, what number are we talking about? 2.5 million. That's the often quoted number of annual DGU, usually presented as is, without qualifications or error bars leading one to believe that this is an indication of lives saved, injuries avoided, or at the very least violent crimes prevented due to the presence of a gun by the potential victim.

This is a huge number. An unbelievably huge number. And yes, I find it unbelievable. Follow me below the squiggly as I attempt to sort out the various studies, claims, counter-studies and counter claims.

Intro

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First, let's start with a disclaimer. I am not a statistician. Therefore, it's entirely possible that I will make a fundamental mistake regarding the stats in the studies, so any corrections by those in the know or with the skills will be appreciated.

With that said, this will mostly be an examination of work by others and an attempt to figure out whether any of the numbers make sense, and whether they can or should be used to inform policy.

The studies I will refer to are the following:

Kleck 95

Hemenway 97

Kleck 97

Cook 98

I'll try to summarize the main arguments of each study as best as possible, but for more details, the links are provided above.

The 2.5 million DGU number comes from Kleck 95, and it is based on 56 positive responses (weighted to 66) from a pool of 5000 surveyed. The DGU number comes from taking 66/5000 and multiplying by the number of adults in the US at the time (~200 million). Two common critiques to this methodology come from a consideration of 'false positives', and using 'external validation' to compare against other crime statistics.

First, the issue with false positives. This would be a survey responder identifying a DGU when none had occurred. Both Hemenway and Cook point out that when you have such a low probability event as DGU, even small false positives can utterly swamp the measurement of 'true positive' activity. For example, a 1% false positive rate would result in 50 (0.01 * 5000) of those 56 positive responses, a full 90%!

As an example, Hemenway cited a survey where a full 6% of responders claimed to have interacted with aliens. Cook took a somewhat more serious approach and noted that for even illegal, socially negative behaviors, false positives can range from 1% (false claim of meth use) up to 10% (false claim of marijuana use), so positing levels ~1% are quite within the realm of plausibility. Also, false positives can come from a variety of sources, misclassification (the responder doesn't understand the question properly), misremembering, or just plain making something up.

Kleck responded to this criticism by noting that nobody had a true measurement of the false positive rate (including him), and the 19 question survey would weed out false positives. This position is somewhat weak as DGU is often seen as a heroic, socially positive activity, especially by gun owners, and additionally Cook found that ~1/3 of the positive respondents had inconsistencies in their answers to the 19 survey questions. In the end, all Kleck was left with was argument via incredulity that there would be any significant false positive rate, despite the fact that levels on the order of 1% seem almost unavoidable given the results from surveys in general. If true, not only would it significantly reduce the 'total' DGU rate, but the incredibly low number of actual true positives would generate such large error bars that any extrapolation to the general public would be worthless.

The second factor, 'external validation' is following up on the natural instinct of "2.5 million DGUs each year? That can't be right, that's a huge number!" Indeed, that's 2 times higher than the total violent crime rate of ~1.2 million annually (including estimates of unreported crime).

How can that be? How can crime involving DGU be higher than the total crime rate? Not only that, if you assume crime affects non-DGU victims at roughly the same rate, that would imply significantly more than 2.5 million non-DGU victims.

Kleck's response is twofold, that the incidences he's measuring may not reflect typical crimes (e.g. trespassing or other non-violent crime or threat), and DGU incidences may be significantly under-reported because of illegal gun use, or other illegal activities. So, what the heck is he actually measuring?

I mean, when we're talking about trying to assess the positive social utility of DGU, scaring kids off your property by flashing a shotgun doesn't automatically go in the 'plus' category in my mind. Indeed, if you look at Table 3 in Kleck 95, you find that almost 50% of the DGU he measured involved no actual threat posed to the defender. WTF?

In fact, the primary theme that Kleck 97 uses to answer Hemenway's objections is that there is vast under-reporting of DGU because they are usually used illegally and/or in conjunction with illegal activity on the part of the defender.

Huh? I mean, maybe that's the missing piece that makes all the numbers start to make sense. The DGU measured by Kleck 95, that 2.5 million number that gets thrown around, is not lawful DGU. It's not homeowners lawfully protecting their property or lives, it's criminals using DGU to protect themselves during criminal activity. No other explanation is consistent with the much more precise estimates of crime stats of burglary, rape, robbery, and assault, and even then the 2.5 million number strains credibility.

But, maybe it would all make sense then, the fact that we don't see thousands of DGUs trumpeted by the NRA daily (2.5 million / 365 = 7000), the fact that many if not most of us personally don't know anyone successfully using a gun to protect themselves (for me, 40 years * 2.5 million/ year = 100 million DGUs during my life).

This lack of DGU visibility when we have 30 visible murders each and every day really only makes sense when the DGUs Kleck is counting have little to do with self-defense or personal safety. Or, more likely, his number is complete nonsense, and the ~100k annual DGU estimated by the National Crime Victimization survey (surveying 59000 households) is far closer to reality.

For a similar analysis, see also: http://scienceblogs.com/...

Extended (Optional)

Originally posted to Ozy on Wed Jan 30, 2013 at 03:40 PM PST.

Also republished by Shut Down the NRA, Repeal or Amend the Second Amendment (RASA), Community Spotlight, and Firearms Law and Policy.

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