Suppose the following table summarizes the differences observed between 4 treatm
ID: 3319647 • Letter: S
Question
Suppose the following table summarizes the differences observed between 4 treatment groups and a control using the least squares difference test for difference in means. Assume that the treatment groups represent three dosages of a new drug (Dose I 10 mg, Dose II 12 mg, Dose III 15 mg) and the treatment group represents a placebo. The outcome of interest is increase in CD4 cell count for immunosuppressed patients with HIV or related illnesses.Assume the above table is an output from the Bonferroni correction as a post-hoc comparison after an ANOVA procedure. Are there any relationships that are significant with the correction?
Group___? v Group__?
Group____? v Group___?
Group____? v Group____?
Group
I
Group
J
Mean Difference
(I-J)
Significance
Lower Bound of
95% CI
Upper Bound of
95% CI
1
2
3
4
6.57
3.54
17.38
0.12
0.23
0.00032
-0.978
-1.42
11.432
9.76
8.46
23.41
2
1
3
4
-6.57
4.51
14.20
0.12
0.19
0.0042
-9.76
-3.41
8.65
0.978
9.78
21.05
3
1
2
4
-3.54
-4.51
11.02
0.23
0.19
0.0234
-8.46
-9.78
6.21
1.42
3.41
18.63
4
1
2
3
-17.38
-14.20
-11.02
0.00032
0.0042
0.0234
-23.41
-21.05
-18.63
-11.432
-8.65
-6.21
Group
I
Group
J
Mean Difference
(I-J)
Significance
Lower Bound of
95% CI
Upper Bound of
95% CI
1
2
3
4
6.57
3.54
17.38
0.12
0.23
0.00032
-0.978
-1.42
11.432
9.76
8.46
23.41
2
1
3
4
-6.57
4.51
14.20
0.12
0.19
0.0042
-9.76
-3.41
8.65
0.978
9.78
21.05
3
1
2
4
-3.54
-4.51
11.02
0.23
0.19
0.0234
-8.46
-9.78
6.21
1.42
3.41
18.63
4
1
2
3
-17.38
-14.20
-11.02
0.00032
0.0042
0.0234
-23.41
-21.05
-18.63
-11.432
-8.65
-6.21
Explanation / Answer
In the majority of analyses, an alpha of 0.05 is used as the cutoff for significance. If the p-value is less than 0.05, we reject the null hypothesis that there's no difference between the means and conclude that a significant difference does exist.
So, if p value < alpha (0.05 here) the relationship would be significant:
We can see from above table the relationships that are significant are:
Group 1 and Group 4 (p value = 0.00032 < 0.05)
Group 2 and Group 4 (p value = 0.0042 < 0.05)
Group 3 and Group 4 (p value = 0.0234 < 0.05)
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