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 |
---|---|---|---|
1.4 | 2.6 | 4.1 | 2.6 |
1.4 | 2.3 | 1.6 | 2.7 |
2.8 | 3.1 | 3.5 | 2.1 |
2.5 | 3.5 | 3.6 | 2.7 |
1.8 | 0.3 | 2.7 | 3.5 |
0.6 | 1.9 | 3.4 | 5.3 |
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.
Using excel tool for one way annova for the given sample we get
Anova: Single Factor | ||||||
SUMMARY | ||||||
Groups | Count | Sum | Average | Variance | ||
Column 1 | 6 | 10.5 | 1.75 | 0.647 | ||
Column 2 | 6 | 13.7 | 2.283333 | 1.265667 | ||
Column 3 | 6 | 18.9 | 3.15 | 0.779 | ||
Column 4 | 6 | 18.9 | 3.15 | 1.311 | ||
ANOVA | ||||||
Source of Variation | SS | df | MS | F | P-value | F crit |
Between Groups | 8.56 | 3 | 2.853333 | 2.851432 | 0.063189 | 4.113404 |
Within Groups | 20.01333 | 20 | 1.000667 | |||
Total | 28.57333 | 23 |
The f ratio=2.8533 and P-value=0.0632
Hence Conclusion:
Since at 0.02 level of significance the p-value=0.0632>0.02 hence we fail to reject the null hypothesis and we conclude that there is not enough evidence to support that there is a significant differencesbetween treatments.
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