5.4. Treatment of random and systematic effects

Brief summary: Although within a measurement series random and systematic effects influence measurement results differently, they are mathematically taken into account the same way – as uncertainty components presented as standard uncertainties.

Treatment of random and systematic effects
http://www.uttv.ee/naita?id=17712

https://www.youtube.com/watch?v=hdh5xVVZTbg

In the case of pipetting (demonstrated and explained in sections 2 and 4.1) there are three main sources of uncertainty: repeatability, calibration uncertainty of the pipette and the temperature effect. These effects influence pipetting in different ways.

1. Repeatability is a typical random effect. Every pipetting operation is influenced by random effects that altogether cause the differences between the volumes that are pipetted under identical conditions;
2. The uncertainty due to calibration of the pipette is a typical systematic effect: If instead of 10.00 ml the mark on the pipette is, say, at 10.01 ml then the pipetted volume will be systematically too high. This means that although individual pipetting results can be lower than 10.01 ml (and in fact even below 10.00 ml), the average volume will be higher than 10.00 ml: approximately 10.01 ml.
3. The temperature effect can be, depending on the situation, either systematic or random effect or (very commonly) mixture of the two. Which way it is depends on the stability of the temperature during repetitions (which is influenced by the overall duration of the experiment).

Although the three uncertainty sources influence pipetting results in different ways they are all taken into account the same way – via uncertainty contributions expressed as standard uncertainties.

In principle, it is possible to investigate the systematic effects, determine their magnitudes and take them into account by correcting the result. When this is practical, this should be done. If this is not done then the result will possibly [1] be biased, i.e. it may be systematically shifted from the true value. And obviously, this possible systematic effect has to be covered by the uncertainty of the result.

An example where systematic effect can be determined and correction introduced with reasonable effort is calibration of pipette, explained in the example in section 4. Two cases were examined: without correcting and with correcting:

1. In subsection 4.1 the calibration uncertainty of ± 0.03 ml as specified by the producer is used. This corresponds to the situation that there is possibly a systematic effect – the possible [2] difference of the true pipette volume from its nominal volume, but it is not closely investigated or corrected and the uncertainty ± 0.03 ml is assigned to it, which with very high probability covers this effect. As a result the standard uncertainty of calibration was u (V, CAL) = 0.017 ml (rectangular distribution is assumed).
2. In subsection 4.6 it was explained how to determine the actual volume of pipette by calibration. It was found that the pipette volume was 10.006 ml. The calibration that was carried out in the laboratory still has uncertainty, but this uncertainty now is due to the repeatability during calibration (i.e. random effects) and is by almost 10 times smaller: u (V, CAL) = 0.0018 ml.

Thus, when correcting for systematic effects can be done with reasonable effort then it can lead to significant decrease of measurement uncertainty. However, in many cases accurate determination of a systematic effect (accurate determination of bias) can involve a very large effort and because of this can be impractical. It can also happen that the uncertainty of correction is not much smaller than the uncertainty due to possible bias. In fact, with reasonable (i.e. not very large) effort the outcome of bias determination often is that there may be a systematic effect and may not be. In such cases correction cannot be done and the uncertainty due to the effect has to cover the possible systematic effect (possible bias).

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[1] The word possibly here means that if we did not investigate systematic effect it is also possible that there is actually no systematic effect, i.e. the bias is zero. We simply do not know.

[2] The word possible means here that in fact there may be no systematic effect – the actual pipette volume can be 10.00 ml. We simply do not know.