Steve Penny, president of USA Gymnastics, the sport’s governing body, says the study doesn’t accurately reflect gymnastics in an organized setting because it counts things like injuries on school playgrounds and mishaps during a backyard cartwheel. “I think most people view gymnastics as a very healthy thing for young girls,” he said.

At gymnastics centers, business is booming in the wake of the Olympics. At the California Sports Center in San Jose, enrollment jumped 33 percent in August. The owner, Dave Peterson, said parents should look for programs that help children develop skills that will enable them to compete all the way up to college if they choose.

Once children reach a skill level that allows for competition, he said, they train just two hours for three days a week. Over time, the program increases to about 21 hours a week. He added that the athlete-to-coach ratio should be about 6 to 1 in preschool and about 8 to 1 for older athletes.

In the absence of firm data about the best age to start competitive sports, the solution may not be to discourage young athletes from working out too much, but instead to encourage them to try out more sports. The journal Pediatrics reported last year that young athletes who participated in a variety of sports had fewer injuries and continued longer than those who specialized before puberty.

For young athletes determined to specialize, doctors recommend breaks from training at least one to two days a week, and long breaks every two to three months to allow the athlete to do another activity or at least cross-train to exercise different muscle groups.

Ms. Miller, the gymnast, says her sport can give children coordination, flexibility and strength that will help them in other sports. And she adds that the focus shouldn’t be on competition.

“The biggest factor is how excited they are to be there,” she said. “Are they enjoying it and having fun?”