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