4.3. Looking at the obtained uncertainty

Brief summary: The uncertainty components of the previous lecture are compared. The property of squared summing – suppressing the less influential uncertainty components – is explained. The meaning of the obtained combined standard uncertainty estimate is explained in terms of probability (the probability of the true value of pipetted volume being within the calculated uncertainty range).

Comparing the uncertainty components
http://www.uttv.ee/naita?id=17578

https://www.youtube.com/watch?v=Xnq2-7nq_bg

We can see the uncertainty component with the largest magnitude is the calibration uncertainty u(V, CAL) = 0.017 ml. The combined standard uncertainty is in fact quite similar to it: uc(V) = 0.019 ml. If the summing were made not by the squaring and square root approach but by simple arithmetic sum then the value would be 0.028. This is a good illustration of the property of the squared summing: the smaller uncertainty components are suppressed by larger uncertainty components.

The idea of the squared summing of the components is that the different effects causing uncertainty influence the result in different directions (thus partially canceling) and their magnitudes are not necessarily equal to the values of the uncertainty estimates but can also be smaller (see section 1).

Looking at the uncertainty contributions is very useful if one wants to reduce the uncertainty. In order to reduce the uncertainty of a particular measurement it is always necessary to focus on decreasing the uncertainties caused by the largest components. So, in this case it is not very useful to buy a more expensive air conditioner for the room because the resulting uncertainty improvement will be small. It will also not be possible to improve the uncertainty markedly by reducing the repeatability component. Clearly, whatever is done with these two components the combined standard uncertainty u_c(V) (eq 4.4) cannot decrease from 0.019 ml to lower than 0.017 ml, which is not a significant decrease. Thus, if more accurate pipetting is needed, then the way to go is to calibrate the pipette in the laboratory. This way it is realistic to achieve threefold lower calibration uncertainty, which leads to two times lower combined uncertainty of the pipetted volume. See section 4.6 for an example.