Question

How do you estimate the uncertainty?

Answer 1

Answer :

Uncertainty of measurement is the doubt that 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’ ... e.g. a stick might be two metres long ‘give or take a centimetre’.

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 centimetres plus or minus 1 centimetre, 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 centimetres and 21 centimetres long.

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The main steps to evaluating the overall uncertainty of a measurement are as follows :

1. Decide what you need to find out from your measurements. Decide what actual measurements and calculations are needed to produce the final result.

2. Carry out the measurements needed.

3. Estimate the uncertainty of each input quantity that feeds into the final result. Express all uncertainties in similar terms.

4. Decide whether the errors of the input quantities are independent of each other. If you think not, then some extra calculations or information are needed.

5. Calculate the result of your measurement (including any known corrections for things such as calibration).

6. Find the combined standard uncertainty from all the individual aspects.

7. Express the uncertainty in terms of a coverage factor, together with a size of the uncertainty interval, and state a level of confidence.

8. Write down the measurement result and the uncertainty, and state how you got both of these.