Question

Recent research indicates that the effectiveness of antidepressant medication is directly related to the severity of...

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.

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

Homework Answers

Answer #1

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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