I don't think that's a valid operation. The title of the article refers to four groups of people Group A: People who lived in a home with handguns and were kil

I don't think that's a valid operation. The title of the article refers to four groups of people Group A: People who lived in a home with handguns and were killed by a gun. Group B: People who lived in a home with handguns and were not killed by a gun. Group C: People who lived in a home without handguns and were killed by a gun. Group D: People who lived in a home without handguns and were not killed by a gun. Original: "People in homes with handguns more likely to be killed (by guns)" sounds to me like "The fraction of people in homes with handguns that are killed by guns is higher than the fraction of people in homes without handguns that are killed by guns", that is "A/(A+B) > C/(C+D)". Modified: "People who were killed (by guns) were more likely to be in homes with handguns." sounds to me like "The fraction of people who killed by guns who lived in a home with handguns is higher than the fraction of people who killed by guns who lived in a home without handguns", that is "A/(A+C) > C/(A+C)". If, for example, you have a population with 25% of households owning guns (which describes California's population, and the study was done in California), and the risk of being killed by a gun is 12/100,000 if you live with a gun and 8/100,000 if you don't, the a sample of 1,000,000 people will have a ratio of roughly 30 : 249,970 : 60 : 749,940 in group A : B : C : D respectively. Which means for that population, the original statement is true (people in households with guns are more likely (12/100000) to be killed by guns than people in households without guns (8/100000)) but the modified statement is false (30 of the 90 people killed by guns come from a household with guns vs 60 / 90 from a household without guns). Edit: I suppose the reverse statement could also be > People who were killed by guns were more likely to be in homes with handguns than people who were not killed by guns which would be valid but to me doesn't sound like it says anything meaningfully different from > People who lived in homes with handguns were more likely to be killed by guns than people who lived in homes without handguns.