2
95% confidence interval for Sigma, given normal distribution
Degrees of
LCL
UCL Multiplier
Freedom Multiplier Multiplier
Ratio
1 0.446 31.910 71.52
2 0.521 6.285 12.07
3 0.566 3.729
6.58
4 0.599 2.874
4.80
5 0.624 2.453
3.93
<-- Long considered the minimum d.f. needed to estimate Sigma
6 0.644 2.202
3.42
7 0.661 2.035
3.08
<-- Rough 'knee' of the multiplier ratio curve
8 0.675 1.916
2.84
9 0.688 1.826
2.65
10 0.699 1.755
2.51
12 0.717 1.651
2.30
15 0.739 1.548
2.10
18 0.756 1.479
1.96
20 0.765 1.444
1.89
25 0.784 1.380
1.76
30 0.799 1.337
1.67
35 0.811 1.304
1.61
0
1
10
100
0
5
10
15
20
25
30
35
Degrees of Freedom
LCL Multiplier
UCL Multiplier
Multiplier Ratio
Recommended to OMB by Committee on Statistics: 07-17-2013
Reviewed and approved by OMB: 07-18-2013
19
by Committee on S atistics: 07-17-2 13
50
