Question

10.58 (20 pts) Refer to the American Heart Association Conference (November 2005) study to gauge whether animal-assisted therapy can improve the physio- logical responses of heart failure patients, presented in Exercise 10.38 (above). You found evidence of a difference among the treatment means for the three treatments: Group T (volunteer plus trained dogs), Group Y (volunteer only), and Group C (control). Conduct a Bonferroni analysis to rank the three treat- ment means. Use an experiment-wise error rate of a = 0.03. Interpret the results for the researchers. Hint: You may use the fact that the Bonferroni formula for a confidence interval for the difference Hi - W; is Ti – ī; £ta-/2(s)1/n; +1/nj, where a* = 2a/{k(k – 1)} is the experiment-wise error rate, and k is the total number of treatment means compared. 10.38 [20 pts) In a study to gauge whether animal-assisted therapy can improve the physiological response of heart failure patients (American Heart Association Conference, November 2005), a team of nurses from the UCLA Medical Center randomly divided 76 heart patients into three groups. Each patient in Group T was visited by a human volunteer accompanied by a trained dog, each patient in group V was visited by a volunteer only, and the patients in Group C were not visited at all. The anxiety level of each patient was measured (in points) both before and after the visits. The accompanying table gives summary statistics for the drop in anxiety level for patients in the three groups. Sample Mean Standard Size Drop Deviation Group T: Volunteer + Trained Dog 10.5 7.6 Group V: Volunteer only 25 3.9 7.5 Group C: Control group (no visit) 25 1.4 26 7.5 The mean drops in anxiety levels of the three groups of patients were com- pared with the use of the analysis of variance. Although the ANOVA table was not provided in the article, sufficient information is given to reconstruct it. (a) [3 pts) Compute SST for the ANOVA, using the formula SST = {:(*– )”, where ī is the overall mean drop in anxiety level of all 76 subjects. (b) [3 pts) Recall that SEE for the ANOVA can be written as SSE = (n1 – 1)sî + (n2 – 1)sź +(n3 – 1) sĩ, where s , s, and s are the sample variances associated with the three treatments. Compute SSE for the ANOVA. (c) [7 pts. Use the results from parts (a) and (b) to construct the ANOVA table. (d) (4 pts) Is there sufficient evidence (at level a = 0.01) of differences among the mean drops in anxiety levels by the patients in the three groups? (e) [3 pts Comment on the validity of the ANOVA assumptions. How might this affect the results of the study?