A research study was conducted to examine the clinical effic

A research study was conducted to examine the clinical efficiency 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 Back Depression Inventory. The higher the score, the more depressed the patient. The data is presented below. Compute the appropriate test.

Placebo

Low Dose

Moderate Dose

38

22

14

47

19

26

39

8

11

25

23

18

42

31

5

What would be the null & alternate hypothesis?

What probability level did you choose and why?

What is your F critical?

Is there a significant difference between the groups?

If there is a significant difference, where specifically are the differences?

Solution

Sol)

1) Null hypothesis: There is no difference between means of all the groups

Alternative hypothesis: There is a difference between means of all the groups

2) Level of signifiacnce: 5% level

3) Test Statistics:

We use F statistic

From Excel

Conclusion: F cal=11.267 and f crtical value at 5% level =3.885

4) F cal > F critical value at 5% level of significance. We reject the null hypothesis.

Hence There is a significant difference between the groups