A researcher is studying treatments for back pain. 120 patients were randomly di
ID: 3226693 • Letter: A
Question
A researcher is studying treatments for back pain. 120 patients were randomly divided into four groups of 30 each. One group was assigned to placebo and the other three groups were assigned to one of the other treatments. After 5 weeks on treatment a measure of pain was evaluated (high score indicating a higher level of pain). Assume the data from the four groups are independent and the responses are approximately normal. The researchers did an ANOVA test of the data and obtained the following results.
Source
DF
SS
MS
F
P-value
Groups
3727.8
0.0094
Error
310.87
Total
Fill in the missing pieces of the ANOVA table.
1. Assume the data from the four groups are independent and the responses are approximately normal. What is one additional assumption that we make for the ANOVA procedure to be valid?
2. What is the value of the estimate for the pooled variance within each group?
3. Write the null and alternative hypothesis that we are testing with the ANOVA procedure.
Source
DF
SS
MS
F
P-value
Groups
3727.8
0.0094
Error
310.87
Total
Explanation / Answer
Source
DF
SS
MS
F
P-value
Groups
3
3727.8
1242.6
3.9972
0.0094
Error
116
36060.92
310.87
Total
119
39788.72
All populations have a common variance
Q2. 310.87
Q3. H0: Mu1= Mu2=Mu3 =Mu4
H1: Atleast two means are not equal.
Source
DF
SS
MS
F
P-value
Groups
3
3727.8
1242.6
3.9972
0.0094
Error
116
36060.92
310.87
Total
119
39788.72
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