People who buy organic food are usually convinced it’s better for their health, and they’re willing to pay dearly for it. But until now, evidence of the benefits of eating organic has been lacking.

Now a new French study that followed 70,000 adults, most of them women, for five years has reported that the most frequent consumers of organic food had 25 percent fewer cancers over all t han those who never ate organic. Those who ate the most organic fruits, vegetables, dairy products, meat and other foods had a particularly steep drop in the incidence of lymphomas, and a significant reduction in postmenopausal breast cancers.

The magnitude of protection surprised the study authors. “We did expect to find a reduction, but the extent of the reduction is quite important,” said Julia Baudry, the study’s lead author and a researcher with the Center of Research in Epidemiology and Statistics Sorbonne Paris Cité of the French National Institute of Health and Medical Research. She noted the study does not prove an organic diet causes a reduction in cancers, but strongly suggests “that an organic-based diet could contribute to reducing cancer risk."

The study, published Monday in JAMA Internal Medicine, was paid for entirely by public and government funds.