LOS ANGELES — A study set for publication in the December issue of Pediatrics confirms what some of Hollywood’s sharpest critics have suspected: The level of gun violence in the top-selling PG-13 movies has been rising, and it now exceeds that in the most popular R-rated films.

Violent encounters with guns occur, on average, more than twice an hour in the best sellers in both ratings categories, according to researchers, who worked with support from the Annenberg Public Policy Center at the University of Pennsylvania and the Robert Wood Johnson Foundation.

In all, the researchers examined 945 movies, counting the appearances of overall violence in each five-minute segment of a sampling of films that ranked among the top 30 at the domestic box office from 1950 to 2012. Perhaps not surprisingly, the results — reported by Brad J. Bushman of Ohio State University, and Patrick E. Jamieson, Ilana Weitz and Daniel Romer of the Annenberg center — showed that violence in American films had more than doubled in that time.