“Sweets May Not Be Culprit in Hyper Kids”—This is a USA Today headliner reporting results of a study that appeared in the New England Journal of Medicine. In this study, the subjects were 25 normal preschoolers, aged 3 to 5, and 23 kids, aged 6 to 10, who had been described as “sensitive to sugar.” The kids and their families were put on three different diets for 3 weeks each. One diet was high in sugar, one was low in sugar and contained aspartame, and one was low in sugar and contained saccharin. The diets were all free of additives, artificial food coloring, preservatives, and chocolate. All food in the household was removed, and the meals were delivered to the families. Researchers gathered information about the kids’ behavior from parents, babysitters, and teachers. In addition, researchers tested the kids for memory, concentration, reading, and math skills. The result: “We couldn’t find any difference in terms of their behavior or their learning on any of the three diets,” says Mark Wolraich, professor of pediatrics at Vanderbilt University Medical Center, who oversaw the project. In another interview, Dr. Wolraich is quoted as saying, “Our study would say there is no evidence sugar has an adverse effect on children’s behavior.”
(a) This research involved comparing several means, not just two. (An introduction to such methods, called analysis of variance, is found in Chapter 11.) However, let us take a simplified view of the problem and consider the difference of behavior when children consumed the diet with sugar compared with their behavior when they consumed the diet with aspartame and low sugar. List some variables that might be measured to reflect the behavior of the children.
(b) Let’s assume that the general null hypothesis was that there is no difference in children’s behavior when they have a diet high in sugar. Was the evidence sufficient to allow the researchers to reject the null hypothesis and conclude that there are differences in children’s behavior when they have a diet high in sugar? When we cannot reject H₀, have we proved that H₀ is true? In your own words, paraphrase the comments made by Dr. Wolraich.