Animal-assisted therapy for heart patients. Refer to the American Heart Association Conference (Nov. 2005) study to gauge whether animal-assisted therapy can improve the physiological responses of heart failure patients, presented in Exercise 2.112 (p. 106). Recall that 76 heart patients were randomly assigned to one of 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 LO4 for patients in the three groups. The mean drops in anxiety levels of the three groups of patients were compared with the use of an analysis of variance. Although the ANOVA table was not provided in the article, sufficient information is given to reconstruct it.

Sample Size Mean Drop Std.

Dev.

Group T: Volunteer + Trained Dog 26 10.5 7.6 Group V: Volunteer only 25 3.9 7.5 Group C: Control group (no visit) 25 1.4 7.5 Based on Cole, K., et al. “Animal assisted therapy decreases hemodynamics, plasma epinephrine and state anxiety in hospitalized heart failure patients.”

American Journal of Critical Care, 2007, 16: 575–585.

a. Compute SST for the ANOVA, using the formula

(on p. 541)

SST = a3 i = 1 ni1xi - x22 where x is the overall mean drop in anxiety level of all 76 subjects. [Hint: x = 1Σ3i

= 1 ni 1xi2 >76.]

b. Recall that SSE for the ANOVA can be written as SSE = 1n1 - 12s1 2 + 1n2 - 12s2 2 + 1n3 - 12s3 2 where s1 2 , s2 2 , and s3 2 are the sample variances associated with the three treatments. Compute SSE for the ANOVA.

c. Use the results from parts a and b to construct the ANOVA table.

d. Is there sufficient evidence (at a = .01) of differences among the mean drops in anxiety levels by the patients in the three groups?

e. Comment on the validity of the ANOVA assumptions.

How might this affect the results of the study?