An unusual study done in 49 remote Hutterite farming colonies in western Canada has provided the surest proof yet that giving flu shots to schoolchildren protects a whole community from the disease.

Although previous studies have demonstrated what scientists call “herd immunity,” none have been so incontrovertible, because they were done in less isolated places with more sources of flu passing through. Also, only one other study, done 42 years ago, immunized over 80 percent of a community’s children, as this one did. Success repeated in many separate communities with very high vaccination rates implies that the shots themselves — rather than luck, viral mutations, hand-washing or any other factor — were the crucial protective element.

The study, done by scientists from several Canadian universities and St. Jude’s Children’s Research Hospital in Tennessee, was paid for by the governments of Canada and the United States. It was published online Tuesday by The Journal of the American Medical Association.

“This is quite a definitive study, and it took a Herculean effort,” said Dr. Carolyn B. Bridges, an expert in influenza epidemiology at the Centers for Disease Control and Prevention. “My hat’s off to them.”