Parents use many tactics to coerce their children into eating fruits and vegetables. They disguise the foods or promise a dessert after they eat their veggies. But a new study has found that children who frequently eat healthy foods are just as likely to eat junk food as the kids who skip their broccoli.

The findings contradict a conventional assumption that kids who are encouraged to eat healthy are more likely to avoid foods such as candy and French fries. Until now, the focus has been on demonstrating which foods they should eat — not which foods they should avoid.

During the study, Ohio State University researchers analyzed data from low-income neighborhoods in Columbus, Ohio. They interviewed parents or guardians of 357 children between 2 and 5 years old about their children’s diets. They specifically looked at preschoolers who ate multiple servings of fruits and vegetables each day. Those children were just as likely to eat foods with high amounts of salt, sugar and fat as the children who didn’t eat their share of nutritious food.

The researchers noted the study was done on a small scale. But if the results are replicated on a larger scale in the future, parents may have to change the conversations they have with their children to emphasize the consequences of eating junk food. The findings appear in the Maternal and Child Health journal.

A larger-scale study is currently underway with support from the Centers for Disease Control and Prevention. The study’s author said her findings don’t mean parents and policymakers should give up on efforts to get their children to eat healthy foods. Instead, it challenges the notion that the healthy foods will automatically replace junk foods.