2.1 What is uncertainty of measurement?
The uncertainty of a measurement tells us something about its quality.
Uncertainty of measurement is the doubt which exists about the result of any measurement. You might think that well-made rulers, clocks and thermometers should be trustworthy, and give the right answers. But for every measurement - even the most careful - there is always a margin of doubt. In everyday speech, this might be expressed as ‘give or take’ ... i.e., a stick might be two meters long ‘give or take a centimeter’.
2.2 Expressing uncertainty of measurement
Since there is always a margin of doubt about any measurement, we need to ask ‘How big is the margin?’ and ‘How bad is the doubt?’ Thus, two numbers are really needed in order to quantify an uncertainty. One is the width of the margin, or interval. The other is a confidence level, and states how sure we are that the ‘true value’ is within that margin.
For example:
We might say that the length of a certain stick measures 20 centimeters plus or minus 1 centimeter, at the 95 percent confidence level. This result could be written:
20 cm ±1 cm, at a level of confidence of 95%.
The statement says that we are 95 percent sure that the stick is between 19 centimeters and 21 centimeters long. There are other ways to state confidence levels. More will be said about this later on, in Section 7.
2.3 Error versus uncertainty
It is important not to confuse the terms ‘error’ and ‘uncertainty’.
Error is the difference between the measured value and the ‘true value’ of the thing being measured.
Uncertainty is a quantification of the doubt about the measurement result.
Whenever possible we try to correct for any known errors; for example, by applying corrections from calibration certificates. But any error whose value we do not know is a source of uncertainty.
2.4 Why is uncertainty of measurement important?
You may be interested in uncertainty of measurement simply because you wish to make good quality measurements and to understand the results. However, there are other more particular reasons for thinking about measurement uncertainty.
You may be making the measurements as part of a:
- calibration - where the uncertainty of measurement must be reported on the certificate
- test - where the uncertainty of measurement is needed to determine a pass or fail
or to meet a
- Tolerance - where you need to know the uncertainty before you can decide whether the tolerance is met.
... Or you may need to read and understand a calibration certificate or a written specification for a test or measurement.
National Physical Laboratory, Teddington, Middlesex, UK, TW11 0LW
2007-07-22, 05:14 PM
What is uncertainty of measurement?
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