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
1.5	0.4	2.1	3.6
0.3	1.9	3.4	4.7
2.7	3.3	1.8	4.6
1.9	1.5	3.3	5.4
0.7	3.1	1.8	3.6
2.2	3.4	3.4	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

The statistical software output for this problem is:

From the above output:

ANOVA summary table is:

Source	SS	DF	MS
Columns	21.643	3	7.214
Error	18.697	20	0.935
Total	40.34	23

F = 7.717

P - value = 0.0013

= 21.643/40.34 = 0.537

Final conclusion: There is a significant difference between treatments