Group 1 2 3
Means 10 19 28
Standard Deviations 24 24 24
n 64 64 64
Individual Conficence Intervals Individual Alpha = 0.05 Upper Lower Mean 15.87989 4.120108 24.87989 13.12011 33.87989 22.12011 10 19 28
Groups 1 vs 2 2 vs 3 1 vs 3
Mean Diff 9 9 18
Standard Error of Difference 4.242641 4.242641 4.242641
Difference Confidence Intervals Paired Alpha = 0.05 Mean Upper Lower Difference 17.31542 0.684577 17.31542 0.684577 26.31542 9.684577 9 9 18
Individual Confidence Intervals
30
Confidence Intervals
40 35
30
25 Difference Range 20
15
Mean Range
25 20
Assume that the mean of the second group is higher than the mean of the first group. Then the individual confidence intervals will overlap whenever: 10 15 x 2 z 1 2 x1 z 1 1 n2 n1 10
5 While the confidence interval on the difference will indicate a significant difference when: 0
0 ( x 2 x 1 ) z 2
2 1
n1
2 2
5 0
n2
1 This means that overlapping will give the wrong conclusion whenever:2 Group
Since
z 2
2 1
n1
2 2
n2
3 x 2 x1 z 1 (
1
n1
2
n2
)
1 vs 2
2 1
n1
2 2
n2
(
1
n1
2
n2
)2
2 1 2 n1 n2
and
z 2 z 1
the above interval will always exist.
In contrast, if the individual confidence intervals do not overlap then the two means will be significantly different.
,