The set of players posthumously tested by Dr. McKee is far from a random sample of N.F.L. retirees. “There’s a tremendous selection bias,” she has cautioned, noting that many families have donated brains specifically because the former player showed symptoms of C.T.E.

But 110 positives remain significant scientific evidence of an N.F.L. player’s risk of developing C.T.E., which can be diagnosed only after death. About 1,300 former players have died since the B.U. group began examining brains. So even if every one of the other 1,200 players had tested negative — which even the heartiest skeptics would agree could not possibly be the case — the minimum C.T.E. prevalence would be close to 9 percent, vastly higher than in the general population.

Playing tackle football under the age of 12 exposes children to repetitive head impacts that may double their risk of developing behavioral problems and triple their chances of suffering depression later in life, according to a study published Tuesday in Nature magazine’s journal, Translational Psychiatry.

The research, conducted by Boston University’s Chronic Traumatic Encephalopathy Center, provides the most powerful evidence to date that playing contact football before age 12 may cause brain changes throughout life.

“This study adds to growing research suggesting that incurring repeated head impacts through tackle football before the age of 12 can lead to a greater risk for short- and long-term neurological consequences,” said Michael Alosco, the study’s lead author, a post-doctoral fellow at Boston University School of Medicine.

The consequences include behavioral and mood impairments such as depression and apathy, the study suggests. The research was supported by a variety of sources, including the National Institutes of Health and a grant from the Concussion Legacy Foundation.

The study follows previous findings that brain damage can result from repetitive head impacts, regardless of whether the blows cause concussions.

“Parents have a really hard decision to make, and they can’t say the science is there yet to make an easy decision based on just one study,’’ said Robert Stern, one of the study’s senior authors “At the same time, there is growing research on the effect of football on the brain, and we can’t ignore it.’’

The study stopped short of recommending policy or rule changes for youth football, stating that additional research is necessary. But Stern, a professor of neurology, neurosurgery, and anatomy and neurobiology at BU, as well as director of clinical research for the school’s CTE center, said, “I’m at a point where I feel comfortable saying that, based on logic and common sense and the growing totality of the research, I don’t think kids should be playing tackle football.’’

The paper’s authors said they believe they are the first to study both former amateur and professional players and discover a link between children under 12 playing football and clinical dysfunction. They said the outcomes were similar regardless of how many years the participants played football or the number of concussions they reported.

They also found that the younger the players were when they began playing tackle football, the greater risk they faced of developing problems later in life.

Researchers examined 214 former football players who did not play any other organized contact sports, including 103 who played football only through college and 43 who played only through high school. The 68 others played in the National Football League. Their average age was 51.

The findings follow a BU study in 2015 that focused only on former NFL players. In that study, those who began participating in tackle football before age 12 were found to have worse memory and mental flexibility than those who waited to play until they were at least 12.

Neurologists say the brain undergoes a stage of peak maturation between the ages of 9 and 12 -- a period when children who play tackle football experience a median of 252 head impacts per season, according to a separate survey.

The broader study published Tuesday comes as parents seem increasingly concerned about whether to permit their young children to play tackle football. In a national survey completed in August by the UMass Lowell Center for Public Opinion, 53 percent of adults said they believe playing football is not safe for children before they reach high school.

According to the Sports & Fitness Industry Association, 1.23 million children between the ages of 6-12 played tackle football in 2015.

Dr. Robert Cantu, who helped author the new BU study, has long cautioned against children playing football before age 14 because their brains are not fully developed. Cantu, a neurosurgeon who teaches at BU, has studied head injuries in sports for decades and is the co-founder and medical director of the Concussion Legacy Foundation, as well as an adviser to the NFL.

Notable among the NFL stars whose parents have shared Cantu’s health concerns is Patriots quarterback Tom Brady, who was not permitted to play tackle football until high school.

Numerous Pro Football Hall of Famers, including Terry Bradshaw, Troy Aikman, and Brett Favre, also have said they would be reluctant to let their young children play tackle football if they had kids that age.

Medical experts supported by the NFL and youth football organizations have disputed research linking brain damage to the head impacts absorbed by children who play tackle football. A 2016 study published by the American Journal of Sports Medicine found no association between playing football before high school and neurological or behavioral problems

The 2016 study argued that BU’s findings in 2015 were limited by a variety of factors, including a small sample size.

In the BU paper published Tuesday, the authors asserted that they had addressed all the concerns raised about their previous research. They said they continued “to find a robust relationship between [playing football before age 12] and long-term clinical dysfunction.”

The major youth football organizations have taken numerous steps to improve safety since the damage caused by head blows in football began commanding national headlines and driving down participation among children nearly a decade ago.

Dr. Julian Bailes, an early researcher of CTE and the current medical director for Pop Warner football, has decried what he has described as the “near-hysteria’’ over head injuries in sports.

Bailes, speaking to reporters in 2015, cited the rule changes in youth football aimed at making the game safer.

“With the changes that have occurred to reduce or eliminate head contact in practice and to eliminate open-field, direct-head hits, I think that football is safe as long as the players and their parents understand the risk and the pros and cons, the benefits and potential risks of participating,’’ Bailes said.

None of the studies addressed the possible of risks of children developing CTE, a neurodegenerative disease that can only be diagnosed postmortem and has been found in the brains of many deceased football players.

Stern praised the health and social benefits of children participating in active team sports, including flag football. Stern said the BU center will continue participating in a $16 million, long-term study, funded by the NIH and National Institute of Neurological Disorders and Stroke, aimed at better understanding the clinical implications of head impacts in football and finding a way to diagnose CTE in the living.

Aaron Hernandez, the former New England Patriots tight end who committed suicide in April while serving a life sentence for murder, was found to have a severe form of C.T.E., the degenerative brain disease linked to repeated head trauma that has been found in more than 100 former N.F.L. players.

Researchers who examined the brain determined it was “the most severe case they had ever seen in someone of Aaron’s age,” said a lawyer for Hernandez in announcing the result at a news conference on Thursday. Hernandez was 27.