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.

Low Moderate	High Moderate	Moderately Severe	Severe
2.6	2.7	2.6	2.2
2.5	1.6	3.3	3.6
2.7	3.7	2.1	1.1
1.8	2.7	2.7	3.9
1	1.3	0.6	5.5
1.6	2.7	2.6	0.4
1.1	3.4	1.1	1.9
2.4	2.2	3.2	2.9
0.6	1.9	1.2	1.6
3.7	2.7	2.5	1.7
3.4	2	2.2	2.8
2	3	1.2	3.5
1.9	0.4	3.2	1.7
1.3	0	1.8	4.3
1.8	4.7	2.3	3.2
0	1.8	3.5	1.4
2	2.8	2.5	1.4
1.5	1.3	2.3	3.4
2.4	0.8	2.1	3.1
3.1	3.1	2.9	3.8
1.3	1.5	2.1	1.7
2.3	0.8	0.5	2.8
1.5	2.1	1.9	3.7
4	0.9	1.7	2.7
2	0.4	2.8	2.1
0.5	2.7	2.6	1.7
1.8	1.6	2	1.7
1	3.6	1	1.5
1.4	2.3	2.2	1.9
2.7	1	1.2	1.3
2.6	2.7	1.8	2.6
0.9	1.3	0.8	2.4
1.2	2.9	0.9	1.6
2.4	2.1	2.8	5.4
3	1.1	2.3	4.1
3.1	1.4	1.6	4.6
1.1	3.1	1.8	0.6
3.3	2.7	1.8	1.3
2.1	1.4	4.5	2.3
0.8	0.8	0.8	4.5
0.5	2.5	1.9	3
1.5	1.9	3	1.2
3.7	0.5	2.4	2.6
1.4	1.3	1.2	2.7
0	0.9	2.5	0.5
1.2	2	2.7	0.9
3.3	0.5	2	1.4
2.6	1.3	3	1.8
2.9	1.8	1	1.9
1.4	1.2	2.1	2.1
2.2	2	2.8	1.6
1.1	1	2.3	3.4
1.8	0.4	2	3
3.1	0.6	1.6	3.5
2.3	1.6	3.3	0.6
1.8	3.1	1.7	3.1
0.1	1.5	2.8	4.5
2.5	2.8	1.8	3.2
1.3	3.9	3	2.9

This is the summary table for the ANOVA test:

	S.S.	d.f.	M.S.
Between	14.091694915254	3	4.6972316384181
Within	237.5593220339	232	1.0239625949737
TOTAL	251.65101694915	235

From this table, you obtain the necessary statistics for the ANOVA:
F-ratio: 4.5873078386605
p-value: 0.00385
η2= 0.055996971862432

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

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

*Explain what this tells us about the equality of means.

*How could boxplots refine our conclusion in an ANOVA test? Your answer should address this specific problem.

Answer 1

p-value: 0.00385 < 0.02 hence we reject null hypothesis

• There is a significant difference between treatments

• then the data provide some evidence of difference between the treatments and therefore, it is concluded that there is a significant difference between the treatments. Hence, the mean depression scores of four groups of patients are not equal

*Explain what this tells us about the equality of means.

It tells some of the mean are different

*How could boxplots refine our conclusion in an ANOVA test? Your answer should address this specific problem.

• Also, the Box plots between the four treatments are not overlapping with their notches, then the median scores between the four treatments are not equal and are significantly different. Therefore, it supports the conclusion obtained in ANOVA F test, that there is a significant difference between the treatments and hence, the mean depression scores of four groups of patients ie, low moderate, high moderate, moderately severe and severe are not equal.