The researchers found that kids who ate fruits and vegetables and drank milk every day were as likely to eat foods high in sugar and salt as those who rarely ate healthy foods.
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"There has been a kind of assumption that if you encourage people to adopt healthy eating it naturally leads to a decline in unhealthy eating," said study co-author Phyllis Pirie from the Ohio State University in the US.
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 between the ages of two and five, and asked them to recall how often the children ate certain foods in the past week.
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The research team asked them about the children's diets and categorised foods and drinks into healthy and unhealthy categories.
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.
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 Maternal and Child Health Journal.
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