Practice Problems: ANOVA

A research study was conducted to examine the clinical efficacy of a new antidepressant. Depressed patients were randomly assigned to one of three groups: a placebo group, a group that received a low dose of the drug, and a group that received a moderate dose of the drug. After four weeks of treatment, the patients completed the Beck Depression Inventory. The higher the score, the more depressed the patient. The data are presented below. Compute the appropriate test.

1. What is your computed answer? F = 11.26 (2,12) p < .01

2. What would be the null hypothesis in this study? There will be no difference in depression levels between the three groups. The groups taking the drug will not be different than the groups taking the placebo.

3. What would be the alternate hypothesis? There will be a difference somewhere in depression levels between the three levels of drug groups.

4. What probability level did you choose and why? p = .01. There is a risk involved with a Type I error. I do not want to erroneously say the drug works and then later find out that it doesn't.

5. What is your F_crit? F_crit = 6.93

6. Is there a significant difference between the groups? Yes - a significant difference exists somewhere between the three groups.

7. If there is a significant difference, where specifically are the differences? There is a significant difference between the placebo group and the low dose group (F_comp = 11.75 and q_obs= 4.84, p < .05). There is a significant difference between the placebo group and the moderate dose group (F_comp = 20.77 and q_obs= 6.44, p < .01). There is no significant difference between the low dose and the moderate dose groups (F_comp = 1.27 and q_obs= 1.59, n.s.).

8. Interpret your answer. The drug appears to help alleviate depression. However, as there is no significant difference between taking a low or moderate dose, a low dose would be recommended.