Question

Recent research indicates that the effectiveness of antidepressant medication is directly related to the severity of the depression (Khan, Brodhead, Kolts & Brown, 2005). Based on pretreatment depression scores, patients were divided into four groups based on their level of depression. After receiving the antidepressant medication, depression scores were measured again and the amount of improvement was recorded for each patient. The following data are similar to the results of the study.

Run the single-factor ANOVA for this data:

Low Moderate	High Moderate	Moderately Severe	Severe
1.4	2.6	4.1	2.6
1.4	2.3	1.6	2.7
2.8	3.1	3.5	2.1
2.5	3.5	3.6	2.7
1.8	0.3	2.7	3.5
0.6	1.9	3.4	5.3

Fill in the summary table for the ANOVA test:

	S.S.	d.f.	M.S.
Between
Within
TOTAL

From this table, obtain the necessary statistics for the ANOVA:
F-ratio:   
p-value:   
η2=η2=  

What is your final conclusion? Use a significance level of α=0.02α=0.02.

• These data do not provide evidence of a difference between the treatments
• There is a significant difference between treatments

Answer 1

Using excel tool for one way annova for the given sample we get

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Column 1	6	10.5	1.75	0.647
Column 2	6	13.7	2.283333	1.265667
Column 3	6	18.9	3.15	0.779
Column 4	6	18.9	3.15	1.311
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	8.56	3	2.853333	2.851432	0.063189	4.113404
Within Groups	20.01333	20	1.000667
Total	28.57333	23

The f ratio=2.8533 and P-value=0.0632

Hence Conclusion:

Since at 0.02 level of significance the p-value=0.0632>0.02 hence we fail to reject the null hypothesis and we conclude that there is not enough evidence to support that there is a significant differencesbetween treatments.