©Fluke Calibration 2011 Basics Of Measurement Uncertainty for DMM Calibration 54
Adjusting k for a smaller set of
measurements or samples
• Adjusting k is done using the:
students’ t distribution table
• A coverage factor adjustment
is needed because our data
set had a fewer number of
values, rather than a larger set
(such as 20, 50, or 100)
• The table lists the proper
coverage factor for populations
with smaller degrees of
freedom
68.27 90 95 95.45 99 99.73
1 1.84 6.31 12.71 13.97 63.66 235.8
2 1.32 2.92 4.3 4.53 9.92 19.21
3 1.2 2.35 3.18 3.31 5.84 9.22
4 1.14 2.13 2.78 2.87 4.6 6.62
5 1.11 2.02 2.57 2.65 4.03 5.51
6 1.09 1.94 2.45 2.52 3.71 4.9
7 1.08 1.89 2.36 2.43 3.5 4.53
8 1.07 1.86 2.31 2.37 3.36 4.28
9 1.06 1.83 2.26 2.32 3.25 4.09
10 1.05 1.81 2.23 2.28 3.17 3.96
20 1.03 1.72 2.09 2.13 2.85 3.42
50 1.01 1.68 2.01 2.05 2.68 3.16
100 1.005 1.66 1.984 2.025 2.626 3.077
1 1.645 1.96 2 2.576 3
For our example with the effective degrees of freedom (V
eff
) of 5.2,
a coverage factor of 2.57 expands u
c
to a value with 95% confidence
(compared to 1.96 for an infinite set of measurements/samples).
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