The children most at risk of attempted abduction by strangers are girls ages 10 to 14, many on their way to or from school, and they escape harm mostly through their own fast thinking or fierce resistance, according to a new national analysis.

Probing a crime that is infrequent but strikes fear in the hearts of parents as little else does, analysts from the National Center for Missing & Exploited Children found that children who encountered would-be abductors were usually alone, often in the late afternoon or early evening.

It’s a chilling thought for working parents and all those who have asked children to hold hands tightly in crowds or to phone as soon as they get home from school. It calls to mind last year’s killing of Somer Thompson, 7, snatched en route from school in Florida as she ran ahead of her siblings, and the highly publicized case of Elizabeth Smart, taken from her Utah bedroom at age 14.

The new analysis examines more than 4,200 cases of abductions that were attempted but not successful, and it shows that children were their own best protectors.

“They escaped these things not through the efforts of Good Samaritans, but through recognizing a bad situation and either getting away from it, avoiding it or screaming and kicking to draw attention,” said Ernie Allen, president of the missing children’s center.

In the vast majority of the cases examined, children escaped harm through their own actions. In 16 percent of the cases, an adult stepped in to help.

“The goal here is not to frighten, but to encourage parents to sit down with their kids, talk to them about their safety, and practice these things,” he said. “Our overall premise is, kids protect themselves with their heads, and if they are prepared and alert, and if they know what to do and how to respond, they are at far less risk.”

Allen said parents should be aware that children targeted in abduction attempts are often preteens and teenagers in middle grades. More than 70 percent were girls. Federal studies have found that teenagers are most at risk in non-family abductions.

Older children may be targeted more because they are less likely to be supervised, Allen said, and girls may be more often targeted by sexual predators.

Federal research shows successful abductions by strangers are relatively rare; an estimated 115 a year nationally involve children transported 50 miles or more and held at least overnight by a stranger in a classic kidnapping case.

An additional 21,500 stranger abductions involve other circumstances, according to Justice Department statistics. About 36,700 other abduction cases a year involve a caretaker, neighbor or someone a child knows at least casually.

The largest category is family abductions, with an estimated 204,000 incidents a year.

The national center looks at cases of attempted abduction as part of its work to provide technical assistance to police agencies nationally, helping track patterns and link cases in different cities.

Attempted abductions are hard to track, officials said, because police reports are not often written up. The center searched widely for every possible incident, using media coverage, hotline reports and contacts with police agencies.

Because of the limitations, the analysis is unscientific, but officials hope the patterns that emerge will help parents and children. The cases examined by the center included 1,127 in which a suspect was identified or arrested, with 43 percent involving repeat offenders and 19 percent involving registered sex offenders.

Most children were approached by someone in a vehicle, often offering a ride. Other offenders lured children with sweets or money or with an animal or a story about finding a lost animal. Some asked for directions.

Looking at nearly 3,500 cases, more than 30 percent of children who escaped kicked and screamed; 53 percent ran or otherwise fled. “The child should do whatever is necessary to stay out of the car because once the child is in that car it dramatically reduces the chances of escape,” Allen said.

Jack Levin, at the Brudnick Center on Violence at Northeastern University in Boston, said parents should educate children but keep in mind what he regards as the infrequency of such incidents.

“I think that one finding that is very helpful to parents is that children shouldn’t wait for an adult to intervene and save them,” he said.