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 0.3 1.2 2.2 1.8 3.8 1.7 1.4 2.8 3.2 0.4 0.6 2.6 2.3 1.2 1.6 2.6 2 3.2 1.6 2.2 0.6 1.2 1.6 1 2.7 1 2.2 0.6 1.4 1.6 3.3 2.7 2.2 2.9 3.7 2.6 0.9 0.7 3.4 3.1 2.6 1.7 0.8 1.8 2 1.4 1.6 4.1 1.7 0.9 3.3 2.3 1.6 1.1 3.5 1.4 3.5 1.9 0.4 4.2 1.5 2.3 2.2 2.9 1.4 2.2 2.7 2.8 2.1 1.9 1.9 3.9 1.5 2.7 0.8 1.5 1 3 2.1 3.7 1.5 0.9 2.4 1.9 2.7 3.2 0.8 2.7 2.2 2.9 1.8 1.2 2.4 1.7 3.2 1.3 2.2 2.4 1.1 1 2.6 2 2.4 3.8 0.9 1.3 1.8 1.9 1.7 1.7 1.2 3.8 1.3 0 3.3 3 1.9 2.5 1.1 1.8 0 3.6 1.8 2.9 2.1 3.2 2.9 2.8 3.2 1.8 0.8 2.3 1 3 4.4 2.2 1.8 0.2 2.3 2.3 1.8 4.1 3.6 2.2 1.5 2 2.2 1.9 3.1 2.6 2.7 2.8 2.1 1.3 1.1 2.5 0.7 1.5 0.8 4 0.7 2.6 2.1 3 1.9 1.3 1.7 3.3 3.2 0.9 1.4 2.4 4 0 4 2.2 1.8 1.6 2.8 3.2 2.8 2 0.6 1.3 1.9 2.4 0.6 2.3 1 2.4 1.8 2.4 3.1 0.9 1.8 3.9 This is the summary table for the ANOVA test: S.S. d.f. M.S. Between 12.783010204082 3 4.2610034013606 Within 168.27714285714 192 0.87644345238095 TOTAL 181.06015306122 195 From this table, you obtain the necessary statistics for the ANOVA: F-ratio: 4.8616980248812 p-value: 0.00278 η2= 0.070600902451238 What is your final conclusion? Use a significance level of α=0.02. These data do not provide evidence of a difference between the treatments There is a significant difference between treatments Explain what this tells us about the equality of means.
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 0.3 1.2 2.2 1.8 3.8 1.7 1.4 2.8 3.2 0.4 0.6 2.6 2.3 1.2 1.6 2.6 2 3.2 1.6 2.2 0.6 1.2 1.6 1 2.7 1 2.2 0.6 1.4 1.6 3.3 2.7 2.2 2.9 3.7 2.6 0.9 0.7 3.4 3.1 2.6 1.7 0.8 1.8 2 1.4 1.6 4.1 1.7 0.9 3.3 2.3 1.6 1.1 3.5 1.4 3.5 1.9 0.4 4.2 1.5 2.3 2.2 2.9 1.4 2.2 2.7 2.8 2.1 1.9 1.9 3.9 1.5 2.7 0.8 1.5 1 3 2.1 3.7 1.5 0.9 2.4 1.9 2.7 3.2 0.8 2.7 2.2 2.9 1.8 1.2 2.4 1.7 3.2 1.3 2.2 2.4 1.1 1 2.6 2 2.4 3.8 0.9 1.3 1.8 1.9 1.7 1.7 1.2 3.8 1.3 0 3.3 3 1.9 2.5 1.1 1.8 0 3.6 1.8 2.9 2.1 3.2 2.9 2.8 3.2 1.8 0.8 2.3 1 3 4.4 2.2 1.8 0.2 2.3 2.3 1.8 4.1 3.6 2.2 1.5 2 2.2 1.9 3.1 2.6 2.7 2.8 2.1 1.3 1.1 2.5 0.7 1.5 0.8 4 0.7 2.6 2.1 3 1.9 1.3 1.7 3.3 3.2 0.9 1.4 2.4 4 0 4 2.2 1.8 1.6 2.8 3.2 2.8 2 0.6 1.3 1.9 2.4 0.6 2.3 1 2.4 1.8 2.4 3.1 0.9 1.8 3.9 This is the summary table for the ANOVA test: S.S. d.f. M.S. Between 12.783010204082 3 4.2610034013606 Within 168.27714285714 192 0.87644345238095 TOTAL 181.06015306122 195 From this table, you obtain the necessary statistics for the ANOVA: F-ratio: 4.8616980248812 p-value: 0.00278 η2= 0.070600902451238 What is your final conclusion? Use a significance level of α=0.02. These data do not provide evidence of a difference between the treatments There is a significant difference between treatments Explain what this tells us about the equality of means.
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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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 |
|---|---|---|---|
| 0.3 | 1.2 | 2.2 | 1.8 |
| 3.8 | 1.7 | 1.4 | 2.8 |
| 3.2 | 0.4 | 0.6 | 2.6 |
| 2.3 | 1.2 | 1.6 | 2.6 |
| 2 | 3.2 | 1.6 | 2.2 |
| 0.6 | 1.2 | 1.6 | 1 |
| 2.7 | 1 | 2.2 | 0.6 |
| 1.4 | 1.6 | 3.3 | 2.7 |
| 2.2 | 2.9 | 3.7 | 2.6 |
| 0.9 | 0.7 | 3.4 | 3.1 |
| 2.6 | 1.7 | 0.8 | 1.8 |
| 2 | 1.4 | 1.6 | 4.1 |
| 1.7 | 0.9 | 3.3 | 2.3 |
| 1.6 | 1.1 | 3.5 | 1.4 |
| 3.5 | 1.9 | 0.4 | 4.2 |
| 1.5 | 2.3 | 2.2 | 2.9 |
| 1.4 | 2.2 | 2.7 | 2.8 |
| 2.1 | 1.9 | 1.9 | 3.9 |
| 1.5 | 2.7 | 0.8 | 1.5 |
| 1 | 3 | 2.1 | 3.7 |
| 1.5 | 0.9 | 2.4 | 1.9 |
| 2.7 | 3.2 | 0.8 | 2.7 |
| 2.2 | 2.9 | 1.8 | 1.2 |
| 2.4 | 1.7 | 3.2 | 1.3 |
| 2.2 | 2.4 | 1.1 | 1 |
| 2.6 | 2 | 2.4 | 3.8 |
| 0.9 | 1.3 | 1.8 | 1.9 |
| 1.7 | 1.7 | 1.2 | 3.8 |
| 1.3 | 0 | 3.3 | 3 |
| 1.9 | 2.5 | 1.1 | 1.8 |
| 0 | 3.6 | 1.8 | 2.9 |
| 2.1 | 3.2 | 2.9 | 2.8 |
| 3.2 | 1.8 | 0.8 | 2.3 |
| 1 | 3 | 4.4 | 2.2 |
| 1.8 | 0.2 | 2.3 | 2.3 |
| 1.8 | 4.1 | 3.6 | 2.2 |
| 1.5 | 2 | 2.2 | 1.9 |
| 3.1 | 2.6 | 2.7 | 2.8 |
| 2.1 | 1.3 | 1.1 | 2.5 |
| 0.7 | 1.5 | 0.8 | 4 |
| 0.7 | 2.6 | 2.1 | 3 |
| 1.9 | 1.3 | 1.7 | 3.3 |
| 3.2 | 0.9 | 1.4 | 2.4 |
| 4 | 0 | 4 | 2.2 |
| 1.8 | 1.6 | 2.8 | 3.2 |
| 2.8 | 2 | 0.6 | 1.3 |
| 1.9 | 2.4 | 0.6 | 2.3 |
| 1 | 2.4 | 1.8 | 2.4 |
| 3.1 | 0.9 | 1.8 | 3.9 |
This is the summary table for the ANOVA test:
| S.S. | d.f. | M.S. | |
| Between | 12.783010204082 | 3 | 4.2610034013606 |
|---|---|---|---|
| Within | 168.27714285714 | 192 | 0.87644345238095 |
| TOTAL | 181.06015306122 | 195 |
From this table, you obtain the necessary statistics for the ANOVA:
F-ratio: 4.8616980248812
p-value: 0.00278
η2= 0.070600902451238
What is your final conclusion? Use a significance level of α=0.02.
- These data do not provide evidence of a difference between the treatments
- There is a significant difference between treatments
Explain what this tells us about the equality of means.
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