Expressing uncertainty
Since there is always a margin of doubt about any measurement, we need to ask the following questions in order to express uncertainty:
- How big is the margin?
This information partly comes from the standard deviation of repeated measurements and is the ± value when expressing uncertainty - How bad is the doubt?
This relates to the confidence level. The person who is doing the uncertainty calculation will decide which is the appropriate confidence level. The most commonly used is 95%. Confidence level, states how sure we are that the ‘true value’ is within that margin - What is the best estimate of the true value?
This information partly comes from calculating the average (mean) reading.
By quantifying the possible spread of measurements you can then express uncertainty in the mean of the readings and say how confident you are about the mean value. The more measurements that are taken the more confident you can be. Quantify the spread of data (random errors) by using basic statistical calculations.
Suppose we have made some more detailed measurements of Jeff. We might say that the estimated height for Jeff is 152 centimetres plus or minus 1 centimetre at the 95% confidence level. This result could be written:
152 cm +1 cm, at a level of confidence of 95%
The statement says that we are 95% sure (confidence level) that the height of Jeff is between 151 centimetres and 153 centimetres (interval).
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