[A]lmost five Philadelphians were shot every day over the course of the study and about 1 of these 5 people died. . . .
[Police and Medical Examiners identified for researches cases where people were assaulted with firearms. From this sample,] Penn researchers. . . randomly selected 677 cases of Philadelphia residents who were shot in an assault from 2003 to 2006. Six percent of [the victims in] these cases were in possession of a gun (such as in a holster, pocket, waistband, or vehicle) when they were shot.
These shooting cases were matched to Philadelphia residents who acted as the study’s controls. To identify the controls, trained phone canvassers called random Philadelphians soon after a reported shooting and asked about their possession of a gun at the time of the shooting. These random Philadelphians had not been shot and had nothing to do with the shooting.
The conclusion: "[P]eople with a gun were 4.5 times more likely to be shot in an assault than those not possessing a gun." Thus, presumably, while 6% of people who were shot were in possession of guns, about 1.33% of people who were not shot were in possession of guns. Put another way, 41 of the people who were shot were in possession of guns, when random chance would have estimated that 9 would have been in possession of guns. This is surely statistically significant, although not overwhelmingly so.
Journal reference: Charles C. Branas, Therese S. Richmond, Dennis P. Culhane, Thomas R. Ten Have, and Douglas J. Wiebe. Investigating the Link Between Gun Possession and Gun Assault. American Journal of Public Health, 2009; DOI: 10.2105/AJPH.2008.143099
The study is interesting. It measures gun possession at an interesting point in time, as opposed to gun ownership, which is much more widely studied.
One thing that the study shows is that the percentage of people in possession of guns at the moment when they are assaulted with firearms is far below the gun ownership rate of about 50%. They vast majority of gun owners who are assaulted with firearms will no have one in his or her possession when he or she is shot.
One fair intepretation of the results is that people who know that they are at an elevated risk of being assaulted with guns are more likely to carry guns than members of the general public. If this theory is correct, then 32 of the 41 people who were shot while in possession of a firearm were in possession of a firearm because they anticipated that violent crime might be directed at them, rather than simply as a generalized precaution.
Another theory which is plausible is that when someone with a firearm assaults others, that people who are themselves armed are high priority targets, because they represent threats to the assailant. If you are committing an armed robbery, and you see one guy with a gun and three without a gun, you shoot the guy with the gun before he can shoot you. Moreover, an armed robber's willingness to use deadly force against the armed person may cause the unarmed people to comply with the armed robber's demands without any need to make further use of actual force.
The relative importance of these two theories matters. If the first theory is the main explanation, carrying a gun for self-defense, while often futile, might still make sense. If the second theory is the main explanation, carrying a gun for self-defense might genuinely be counterproductive, which is what the study authors suggest.