Researchers studied the effect that varying levels of Ritalin and Adderall had on a child's ability to follow rules when the child is diagnosed with attention deficit hyperactivity disorder (ADHD). They randomly assigned children to one of five treatment groups: placebo, 10 mg of Ritalin, 17.5 mg of Ritalin, 7.5 mg of Adderall, or 12.5 mg of Adderall twice a day. They recorded a score that indicated the child's ability to follow rules, with a higher score indicating a higher ability to follow rules. The following data are based on their study, "A Comparison of Ritalin and Adderall: Efficacy and Time-Course in Children with Attention Deficit/ Hyperactivity Disorder," Pediatrics, Vol. 103, No. 4.

(a) The data was collected using a completely randomized design. Explain what this means.
(b) What is the response variable in this study? What explanatory variable was controlled and fixed at five levels?
(c) The children were randomly assigned to one of five treatment groups. What role does randomization play in this study?
(d) What are the null and alternative hypotheses in this study?
(e) Test the null hypothesis that the mean score for each treatment is the same at the a = 0.05 level of significance.
Note: The requirements for a one-way ANOVA are satisfied.
(f) If the null hypothesis is rejected in part (e), use Tukey's test to determine which pairwise means differ using a familywise error rate of a = 0.05.
(g) Draw boxplots of the five treatment levels to support the analytic results obtained in parts (e) and (f).

Transcribed Image Text:

Placebo Ritalin Ritalin Adderall Adderall 7.5 mg 17.5 mg 10 mg 12.5 mg 47 96 37 57 84 20 75 83 71 105 57 34 76 85 83 43 60 44 92 92 28 83 87 75 74 62 72 69 55 92 25 57 99 73 64