### Statistical Literacy Matters

12.12.129:43 AM ET

# Guns Don't Make You Safer, Ctd.

Further to my posts below about guns and safety:

Twitter follower @reedfrich forwards another study debunking the claim of "2.5 million defensive gun uses per year."

The estimate of 2.5 million self-defense gun uses per year leads to many other absurd conclusions. For example, the number of respondents who claim to have used a gun against rape and robbery suggests that victims of these attempted crimes are more likely to use a gun against the offender than the attackers are to use a gun against the victim - even though the criminal chooses the time and place for the attack, most citizens do not own guns, and very few carry guns.

David Hemenway, the author of this debunking, traces the overstatement of defensive gun uses to an inherent statistical problem: with very rare events (like defensive gun use), seemingly small sampling errors can lead to very large overstatements of incidence.

Say that survey findings are a 1% overestimate of the true incidence. If the true incidence were 40%, estimating it at 41% might not be a problem. But if the true incidence were .2%, measuring it as 1.2% would be six times higher than the true rate, and if the true incidence were .1%, measuring it at 1.1% would be a teen fold overestimate.

How might this work in practice? Hemenway offers a funny example.

In May 1994, ABC News and The Washington Post conducted a national random-digit-dial telephone survey of over 1,500 adults. One question asked: "Have you yourself ever seen anything that you believe was a spacecraft from another planet?" Ten percent of respondents answered in the affirmative. These 150 individuals were then asked, "Have you personally ever been in contact with aliens from another planet or not?" and 6% answered "Yes."

Extrapolating to the U.S. population as a whole, we might conclude that 20 million Americans have seen an alien spacecraft, and 1.2 million have been in actual contact with beings from other planets.

I wouldn't want to suggest that defensive gun use against real dangers (i.e, not carrying a shotgun to investigate raccoons rooting through the trash) is quite so rare as contact with extra-terrestrials. But it's rare enough that conscientious people should think very hard about exposing themselves, their children, and their loved ones to the large and amply documented dangers of a weapon in the house.