Brief summary: The pipetting result – the value and expanded uncertainty – is presented. It is stressed that it is important to clearly say, what was measured. The correct presentation of measurement result includes value, uncertainty and information about the probability of the uncertainty. It is explained that in simplified terms we can assume that k = 2 corresponds to roughly 95% of coverage probability. It is explained how to decide how many decimals to give when presenting a measurement result and the uncertainty.
The correct presentation of the measurement result in this case would look as follows:
| The volume of the pipetted liquid is | V = (10.000 ± 0.038) ml, k = 2, norm. | (4.14) |
The parentheses (brackets) mean that the unit “ml” is valid both for the value and the uncertainty. “norm.” means that the output quantity is expected to be approximately normally distributed. This, together with coverage factor value 2, means that the presented uncertainty is expected to corresponds to approximately 95% coverage probability (see section 3.1 for details).
When can we assume that the output quantity is normally distributed? That is, when can we write “norm.” besides the coverage factor? Rigorous answer to this question is not straightforward, but a simple rule of thumb is that when there are at least three main uncertainty sources of comparable influence (i.e. the smallest and largest of the uncertainty components differ by ca 3 times or less) then we can assume that the distribution function of the output is sufficiently similar to the normal distribution. [1]In this particular case there is a dominating quantity with assumedly rectangular distribution, which leads to a distribution function with very „weak tails“ (meaning: this in fact not exactly a normal distribution). So, 95% coverage probability is achieved already by expanded uncertainty of 0.0034 ml (as evidenced by Monte Carlo simulations). Thus, the presented uncertainty of 0.0038 ml is a conservative estimate (which is not bad as explained in section 3.5).
Section 9.8 presents a more sophisticated approach of calculating expanded uncertainty that corresponds to a concrete coverage probability.
Presenting of measurement result
http://www.uttv.ee/naita?id=17576
https://www.youtube.com/watch?v=x9l1jIVqT7k
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[1] In this particular case there is a dominating quantity with assumedly rectangular distribution, which leads to a distribution function with very „weak tails“ (meaning: this in fact not exactly a normal distribution). So, 95% coverage probability is achieved already by expanded uncertainty of 0.0034 ml (as evidenced by Monte Carlo simulations). Thus, the presented uncertainty of 0.0038 ml is a conservative estimate (which is not bad as explained in section 3.5).
