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
3.3	0.7	2	2.8
0	2.7	2.3	3.2
3.2	4	1.1	1.9
2.6	1.4	1	4.2
0.8	2.8	2.7	1.4
2.9	2.5	3.3	1.7
1.1	0	1.8	1.1
2.9	2.6	1.8	3.2
4.5	2	4.7	3.5
1.6	0.3	1.5	1.5
3.3	1.6	0.7	3.4
1	1.5	3	3.2
0.6	2.2	1.8	2.1
2.3	2.6	2.7	1.4
3.7	1.9	1.1	2.1
2.8	4.7	1.9	1.5
1.7	1.2	1.5	2.6
1.6	0.9	0	4.1
1.8	3.4	1.4	3.6
2.1	2	1.4	2.3
2.1	0.2	2.4	0.7
2.4	1.1	2.1	1.9
3.3	3.4	2.2	2.4
0.1	0.3	2.2	2.6
4.5	2.5	1.1	3.5
2.6	1.9	3.7	3.1
2.7	1.3	3.1	2.5
1.9	2.5	1.1	2.6
1.7	2	1.7	3.8
1.3	2.5	2.9	2.5
1.5	1.5	2.2	3.3
2.5	4.2	1.6	3.2
4.2	3.3	2.1	3.4
2.1	1.4	3.3	2.1
1.5	2.7	0.4	1.5
1.2	3	1.4	1.5
1.9	1	1.7	3.8
1.1	1.5	2.8	2.6
3.4	1.5	1.5	1.1
1.2	2.5	1.3	2.5
3.5	1.8	0	1.9
1.1	3.7	0.2	2.5
2.8	1.5	0.9	2.5
1.2	0.7	3.7	0
1.1	1.5	1.3	3.4
3.2	2.5	2.7	1.9
0.3	1.2	1.3	3.1
0.4	1.9	3.8	2.1
1.6	2.8	2.5	4.1
2.2	2.2	2	4.1
3.5	2.6	0.3	2.1
2	3.9	4	3.8
2.4	1.6	2	4.1
0	1.3	1.4	3.6
3.7	2	2.8	2.5
0.8	1.5	2.4	1.5
4.4	0.5	2.2	3.2
2.8	2.1	1.8	1.5
3	3.1	2.4	1.8
1.6	0.7	1	2.6
1.7	1.8	3.7	3.9

This is the summary table for the ANOVA test:

	S.S.	d.f.	M.S.
Between	14.348360655737	3	4.7827868852458
Within	260.6737704918	240	1.0861407103825
TOTAL	275.02213114754	243

From this table, you obtain the necessary statistics for the ANOVA:
F-ratio: 4.4034689424001
p-value: 0.00489
η2=η2= 0.052171658316617

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

Let's look at the boxplot for each treatment:

012345Depression ScoresLow ModerateHigh ModerateModerately SevereSevere

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

Edit

Insert

Formats

Answer 1

1)

final conclusion? Use a significance level of α=0.02

Since p-value = 0.00489 < significance level of α=0.02 so we reject the Null hypothesis and conclude that there is a significant difference between treatments.

2)

about the equality of mean

since our Null hypothesis is that means for treatments are equal and our alternative hypothesis is that means for treatments are not equal.

Since p-value = 0.00489 < significance level of α=0.02 so we reject the Null hypothesis and conclude that means for treatments are not equal.

3)

boxplot for each treatment

since boxplot for each treatment was not given , so i have ploted the boxplots

From above boxplot there is one outlier is present in the high moderate treatment.

Since The boxplots are not overlapped to each other we can conclude that that there is a significant difference between treatments.