Expanded Uncertainty: After getting the combined standard uncertainty, it would be necessary to multiply it by a coverage factor k, to make the uncertainty applicable to a large number values falling within the distribution curve. The value so obtained is “Expanded uncertainty”. A coverage factor of 2 generally gives a value of expanded uncertainty that
- it gives the required level of confidence
- it includes underlying distributions
- it encompasses the number of values used to estimate random effects
However, this coverage factor 2 will apply when the number of degrees of freedom for calculating the uncertainty are more than 6. If the degrees of freedom are less than or equal to 6, values of k given in the following table should be used.
Degrees of
Freedom Value of k
1 12.7
2 4.3
3 3.2
4 2.8
5 2.6
6 2.5
More than 6 2.0
Example:
Let us take the earlier example of flash point of kerosene.
Standard uncertainty due to calibration = 0.061
Standard uncertainty due to reading thermometer scale = 0.2256
Combined standard uncertainty = Positive Square Root of [(0.061^2) + (0.2256^2) = 0.2337
There are 10 observations of flash point viz: 38.0, 38.2. 38.5, 38.1, 37.9, 37.8, 38.0, 38.4, 38.2, 37.8 degrees C
Degrees of Freedom are 10 – 1 = 9
From the table above, value of coverage factor for 9 degrees of freedom is 2.0
So the Expanded Uncertainty for 95 % confidence level = 0.2337 * 2 = 0.4674 or 0.47 deg C in the range of 35 to 40 deg C.