Public-health experts have long expected that kids who eat more carrots and apples are less likely to eat a lot of candy and fries, but new research is calling that into question.

Preschoolers from low-income neighborhoods in Columbus who ate fruits and vegetables and drank milk many times every day were just as likely to eat foods high in sugar, salt and fat as those who rarely ate healthy foods, found a research team led by Sarah Anderson, associate professor of epidemiology at The Ohio State University.

"We assumed that children who ate a lot of healthy foods would also be children who did not eat a lot of unhealthy foods," Anderson said.

"I just thought that was the way the world was and it turned out not to be the case."

When she and her colleagues looked for connections, studying their data in multiple ways, they found zero link.

It's too soon to call for policy changes based on this work alone, the researchers said. A larger national study is underway.

But if replicated on a larger scale, the surprising discovery could lead to the reframing of conversations about how to improve children's diets and lower rates of childhood obesity, the researchers said.

Instead of assuming a strategically located farmer's market, for instance, will by default mean kids in the neighborhood eat less food high in fat, sugar and salt, policymakers might want to also consider emphasizing the downsides of those choices.

"This suggests that we have to have two conversations," said co-author Phyllis Pirie, professor of health behavior and health promotion at Ohio State.

"There has been a kind of assumption there that if you encourage people to adopt healthy eating that it naturally leads to a decline in unhealthy eating," Pirie said.

Efforts to lower childhood obesity rates often focus on adding "good" foods, rather than on avoiding "bad foods," she said.

Trained interviewers met with parents or guardians of 357 children 2 to 5 years old and asked them to recall how often the children ate certain foods in the past week. About 60 percent of the children were black and almost all were Medicaid recipients. Almost half were not in child care - a higher percentage than in the general U.S. population.

The research team asked them about the children's diets and categorized foods and drinks into healthy and unhealthy categories. Healthy choices included fruits, vegetables and milk. Unhealthy choices included sweetened drinks, fast food, sweets and salty snacks.

Regardless of age, there was no evidence kids who frequently ate fruits and vegetables and drank milk were any less likely to partake in the unhealthy foods. The study appeared in the December 2015 issue of the Maternal and Child Health Journal.

Anderson and her colleagues were surprised to find that this conventional assumption had not been well tested and didn't hold up in this study.

This research doesn't mean parents and policymakers should give up efforts to increase intake of more-nutritious foods, she said. But it does challenge the idea that good automatically replaces bad.

Anderson compared the discovery to previous research showing that a person can at once be both very active and highly sedentary. Just because you run marathons on the weekend doesn't mean that you don't sit in a desk chair most of your waking hours during the work week.

About half the children in the study ate fruit two or more times a day. Some rarely ate vegetables, but more than a third had them multiple times a day. Most of the children drank milk at least once a day. In the week prior to the interview with a parent or guardian, only a third of the children did not drink sugar-sweetened beverages including soda pop and 29 percent had not eaten fast food.

The study was conducted in 2012 and 2013 as part of a larger project supported by the Centers for Disease Control and Prevention.

A larger-scale study looking at how this plays out in a more-diverse group of children throughout the U.S. is underway.