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
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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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. (see image #1)
This is the summary table for the ANOVA test:
| S.S. | d.f. | M.S. | |
| Between | 22.612239583333 | 3 | 7.5374131944444 |
|---|---|---|---|
| Within | 198.05895833333 | 188 | 1.0535050975177 |
| TOTAL | 220.67119791667 | 191 |
From this table, you obtain the necessary statistics for the ANOVA:
F-ratio: 7.154605338127
p-value: 0.00014
η2=η2= 0.10247028065653
What is your final conclusion? Use a significance level of α=0.01α=0.01.
- 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.
Let's look at the boxplot for each treatment:
Image #2
How could boxplots refine our conclusion in an ANOVA test? Your answer should address this specific problem.
Transcribed Image Text: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.
Moderately
High
Moderate
Low
Moderate
Severe
Severe
0.8
2.2
2
1.9
3.4
3.4
2.8
3
2.5
1.3
1.5
2.2
2.9
3.4
3.1
1.9
2.7
2.5
3
2.3
2.2
1.8
2.5
3.5
2.1
2.1
1.4
1
1.5
3.2
1.5
1.2
1.8
1.6
2.8
1.5
0.3
0.5
1.2
0.4
3.4
1
2
1.3
1.6
3.1
2.1
2.8
3
1.9
4.1
3
0.9
2.6
1.8
2.5
2.3
1.6
3.7
2.6
1.1
2.3
1.6
1.2
0.9
3.4
3.3
1.6
1.8
0.6
1.7
4.1
1.5
0.6
1.1
0.9
2.9
4
1.1
0.7
1.8
5.2
3.4
1.3
4.4
2.3
1.7
0.3
1
2.9
2.4
1.4
2.4
0.8
1.7
1.3
0.5
4.6
2.3
0.8
2.1
2.8
1.2
1.9
3.4
3.1
2.2
2.6
1.8
2.9
2.7
2.9
1.2
1.9
2.3
0.5
1.9
2.1
0.2
2
2.6
2.8
2.2
1.1
2.1
0.8
2.8
2.3
2.2
0.9
2.8
4.4
1
2.4
3.2
2.1
1.9
2.9
2.6
0.8
0.5
0.9
3.2
4.1
1.4
2.4
3
2.9
1.1
2
2.1
4.1
3.4
1.1
2.9
1
2.1
3.8
4.5
1.6
3.6
3.6
1.4
1
2.3
1.1
1.1
2.5
3.1
Transcribed Image Text:Moderately
High
Moderate
Low
Moderate
Severe
Severe
1.1
0.1
2.8
2.8
3
1.6
2.2
3.1
0.1
2.6
3.3
1.7
This is the summary table for the ANOVA test:
S.S.
d.f. || M.S.
Between 22.612239583333
3
7.5374131944444
Within
198.05895833333
188
1.0535050975177
TOTAL
220.67119791667 191
From this table, you obtain the necessary statistics for the ANOVA:
F-ratio: 7.154605338127
p-value: 0.00014
n? = 0.10247028065653
What is your final conclusion? Use a significance level of a = 0.01.
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.
Let's look at the boxplot for each treatment:
Severe
Moderately Severe
High Moderate
Low Moderate
2
3
6
Depression Scores
How could boxplots refine our conclusion in an ANOVA test? Your answer should address this specific
problem.
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