Frequently asked questions

0. Please see this paper: Leito, I., Helm, I. Metrology in chemistry: some questions and answers. J.Chem.Metrol. 2020, 14:2, 83-87 for a number of questions and answers relevant to practical chemical analysis situations.

1. How many decimal places should we leave after comma when presenting results?

The number of decimals after the comma depends on the order of magnitude of the result and can be very different. It is more appropriate to ask, how many significant digits should be in the uncertainty estimate. This is explained in the video in section 4.5. The number of decimals according to that video is OK for the results, unless there are specific instructions given how many decimals after the point should be presented. When presenting result together with its uncertainty then the number of decimals in the result and in uncertainty must be the same.

2. If we need to find standard deviation of those wihtin-lab reproducibility measurments, then we need certainly use the pooled one? We can not take the simpliest standard deviation, which is calculated by standard deviation formula?

The within-lab reproducibility standard deviation s_RW characterises how well can the measurement procedure reproduce the same results on different days with the same sample. If the sample is not the same (as in this self-test) then if you just calculate the standard deviation of the results then the obtianed standard deviation includes both the reproducibility of the procedure and also the difference between the samples. The difference between the samples is in the case of this self-test much larger than the within-lab reproducibility. So, if you simply calculate the standard deviation over all the results then you will not obtain within-lab reproducibility but rather the variability of analyte concentrations in samples, whith a (small) within-lab reproducibility component added.

3. In estimation of uncertainty via the modelling approach: When when we can use the Kragten approach and when we just use the combination of uncertainties?

In principle, you can always use the Kragten approach. However, if the relative uncertainties of the input quantities are large, and especially if such a quantity happens to be in the denominator, then the uncertainty found with the Kragten approach can differ from that found using equation 4.11. This is because the Kragten approach is an approximative approach.

4. Exactly what is human factor? I thought that it may be for example person’s psychological conditions and personal experience and so on? This will definitely influence measurement, but is this taken into account then?

The "human factor" is not a strict term. It collectively refers to different sources of uncertainty that are due to the person performing the analysis. These uncertainty sources can either cause random variation of the results or systematic shift (bias). In the table below are some examples, what uncertainty sources can be caused by the "human factor". In correct measurement uncertainty estimation the “human factor” will be automatically taken into account if the respective uncertainty sources are taken into account.

5. Can we report as V = (10.006 ± 0.016) mL at 95 % CL at coverage factor of 2?

We use in this course the conventional rounding rules for uncertainty. Therefore uncertainty ±0.0154 ml is rounded to ±0.015 ml. Sometimes it is recommended to round uncertainties only upwards (leading in this case to ±0.016 ml). However, in the graded test quizes please use the conventional rounding rules.

6. How can I attach my photo into Moolde profile?

This is done from your profile in Moodle. Click on your name on the right on the status bar, then click "Profile", then "Edit profile".

7. In case of a simple titration, if replicate titrations are carried out then in the uncertainty of pipetting the uncertainty contribution of  repeatability is omitted. Why we ignore the repeatability effect in this case when calculating the result of the titration?

In this case we have results of repeated titrations. Their scatter is caused among other effects also by pipetting repeatability. I.e. one of the reasons why different amounts of titrant were consumed in replicate titrations is the fact that the amount of pipetted acidic liquid slightly differed from titration to titration. For this reason, the repeatability of consumed titrant volume automatically takes into account also pipetting repeatability. If we would take it into account in the uncertainty of pipetted volume, we would account for it two times.

8. Can systematic effects really count as uncertainty sources? The GUM says that the recognized systematic effects should be corrected for and the uncertainties of the resulting corrections should be taken into account.

Indeed, systematic effects (sources of bias) can often be reduced significantly by determining corrections and applying them. The corrections are never perfect and have uncertainties themselves. However, the resulting uncertainties from corrections will be mostly caused by different random effects.

However, the fact that systematic effects influence measurement results, automatically means that they cause uncertainty and are thus uncertainty sources. Furthermore, although the GUM (https://www.bipm.org/en/publications/guides/gum.html) says that known systematic effects should preferably be corrected, in many cases – in particular in chemistry and especially at routine lab level – correcting for the systematic effects is either impossible to do reliably or is not practical, as it would make the measurement much more expensive. It also is often unclear whether a systematic effect exists at all – in this course we often speak about possible systematic effects. As a conclusion, it is often more practical to include the possible systematic effects as additional uncertainty components, rather than try to correct for all of them. Probably the best practical guide on this issue is the Eurachem leaflet Treatment of observed bias (https://www.eurachem.org/index.php/publications/leaflets/bias-trt-01).

9. What is the difference between confidence interval and measurement uncertainty?

Measurement uncertainty defines a range (also called interval), around the measured value where the true value of the measurand lies in with some predefined probability. This interval is called coverage interval and measurement uncertainty is (usually) its half-width. Coverage interval has to take into account all possible effects that cause uncertainty, i.e. both to random and systematic effects.

Confidence interval is somewhat similar to coverage interval. It typically refers to some statistical interval estimate. It expresses the level of confidence that the true value of a certain statistical parameter resides within the interval. A typical example is the confidence interval of a mean value found from a limited number of replicates, which is calculated from the standard deviation of the mean and the respective Student coefficient. The main difference is that we speak only of the mean value, not the true value, and only random effects are accounted for – i.e. all replicate measurements can be biased but the confidence interval does not account for that in any way.

10. What is the basis for the rule (explained in Section 4.5) that when the first significant digit of uncertainty is 1 .. 4 then it is presented with 2 significant digits and when it is 5 .. 9 then it is presented with one significant digit?

The rationale behind this rule is that the uncertainty should change by less than 10%, relative, when rounding it. If uncertainty would be e.g. 0.15 g then rounding it to 0.2 would change it by 33%. At the same time if it is e.g. 0.55 g then by rounding it to 0.6 g would change it by 9% relative.

11. The true value lies within the uncertainty range with some probability. Therefore, is it OK if it is sometimes outside that range?

The situation that the true value is outside the uncertainty range is not impossible, but its probability is low. If it is strongly outside (i.e. far from the uncertainty range) or if it is outside for several measurement results obtained with the same method during a short period then the most probable reason is underestimated uncertainty.

Of course, we (almost) never know the true value, so instead of true values we usually operate with their highly reliable estimates, such as e.g. certified values of certified reference materials.

12. Why do we used two-tailed t values in calculating expanded uncertainty, not one-tailed values?

One-tailed t values would be justified if we would know for sure that the true value is smaller or larger than our measured value. This is usually not the case and thus it is not justified to use one-tailed values. One-tailed values are also smaller than two-tailed values (for example: ca 1.7 vs ca 2.0, in the case of large number of degrees of freedom and 95% coverage probability), so that the use of one-tailed t values would artificially decrease the uncertainty estimate, possibly leading to underestimated uncertainty.

13. When converting from rectangular or triangular distribution to the Normal distribution, where do the rules of dividing by SQRT(3) and SQRT(6) come from?

This is clearly beyond the scope of our course. This derivation can be found in specialised books, e.g.: Rein Laaneots, olev Mathiesen An Introduction to Metrology Tallinn University of Technology press, Tallinn, 2006.

Unfortunately I do not have a freely available source in English. There is one in Estonian: http://tera.chem.ut.ee/~ivo/metro/Room/II_vihik.pdf The derivation is on pages 12-13. You will probably understand the mathematical equations and you can try to translate the text with Google translator.

14. Please explain regarding triangular and rectangular distribution function with some real laboratory examples. What is the concept that this is triangular and this is rectangular distribution?

There are in broad terms two types of situation where rectangular or triangular distribution are used:

--1-- When the quantity under question is indeed distributed according to these distributions. In chemistry this occurs first of all in the case of rounding of a digital reading. Example: if a thermometer shows 22 °C then, because of rounding, the value could be anywhere between 21.5 and 22.5 °C. Thus, rounding uncertainty in this case is ±0.5 °C. If rounding uncertainty is the dominant uncertainty component, then we could say that this temperature is distributed according to rectangular distribution. 0.5 °C is half of the last digit of the digital reading. And this is a general rule: rounding uncertainty of a digital reading is "± half of the last digit". In order to convert this uncertainty estimate to standard uncertainty it has to be divided by square root of 3.
It can be shown that if two rectangularly distributed quantities (with equal uncertainty) are added or subtracted then the resulting quantity is distributed according to triangular distribution.
These were examples of situations when these distribution functions are “real”.

--2-- It is, however, much more common that these distribution functions are “assumed” or “postulated” (see Section 3.5). This need comes whenever you need to use some uncertainty estimate that is presented in the form “± X” and we have no knowledge of the underlying distribution of that quantity. In such a case we usually recommend to assume rectangular distribution, as it is safer (lower probability of underestimating uncertainty) than assuming triangular distribution. Examples can be: calibration uncertainties of volumetric ware, uncertainties of purchased standard solution concentrations, uncertainty due to possible interferents (see Section 9.5), uncertainties of educated guesses/expert opinions, uncertainties of various systematic effects of measurement instruments, etc. The course materials contain quite some examples on the use of these distributions, as well as self-tests. Please see sections 3.5, 4.1, 9.5 and self-tests 3.5, 9 A, 9 B.

15. Does failing at even one graded test quiz means total failure (eventhough the rest of the quizzes are successful) and the participant do not receive the digital certificate of completion?

Exactly, failing one graded test means failing the whole course and not getting the certificate of completion for this edition of the course. But of course, you are welcome to attend again next year.

Failing one test means, that you have not acquired the whole knowledge that you should have acquired form this course and the learning outcomes are not fulfilled. For an analogous example, should you get the driver license, when you know really well how to change the gear, but steering the wheel would be an obstacle for you? Probably not – for successful driving you need to be able to handle all aspects of controlling the car. It is the same with uncertainty.

Therefore, we strongly suggest not to waste attempts. For this, before starting a new attempt, please try with the last dataset to obtain the answer provided by the system and find your mistake.

16. Is it always preferable to use your own calibration data of volumetric instruments?

This depends on how high accuracy of volumetric measurement you need.

If high accuracy of volumetric measurements is needed, then it is more correct to calibrate it by herself/himself. Why? Because the uncertainty of the calibration consists to a large extent of the so-called “human factor”. So calibration and working manners should be the same. If more people use the same glassware, then everyone should calibrate it for herself/himself, e.g. person X should not use the pipette with the calibration data, obtained by person Y.

If high accuracy of volumetric measurement is not needed (i.e. if in the used method much more uncertainty comes from other sources than volumetric measurement) then usually the uncertainties assigned to glassware by manufacturers are sufficiently low.

“Incomplete sample matrix decomposition during digestion” causes a systematic effect. Your result will always be somewhat lower than it should be, because you effectively lose some analyte.

But it is important to add, that the “extent of incompleteness” will almost certainly vary from sample to sample. So, you always get a lower result (and there is a systematic effect), but sometimes it is “more lower” sometimes “less lower”. This means that there is additionally a random effect “sitting on top” of the systematic effect. This is actually quite common that with analyte losses by decomposition or incomplete extraction, etc or analyte addition by contamination and other similar systematic effects there are accompanying (and often quite large) random effects.

The best check for the validity of your uncertainty estimate is to compare with an independent result obtained for the same sample. Very common is, e.g. analyzing a CRM and then comparing your result with the reference value of the CRM, e.g. using the zeta score as described in Section 12. Also, if you participate in a PT then comparing your result with the PT consensus value is useful. In the case of a PT the consensus values usually do not have uncertainty estimates. Then a simple, although not 100% rigorous, approach is to see, whether the consensus value is within the k = 2 uncertainty range of your result.

Concerning the two ways proposed by you: Just the fact that s_RW < u_c does not say that u_c has been correctly estimated. It can still be underestimated (or overestimated). And z-scores of PTs do not say anything about the validity of your uncertainty estimate. But of course z-scores are still useful for getting an idea, how similar your measurement result is compared to other laboratories.

Repeatability indeed influences pipetting two times: once when the pipette is calibrated and the second time when actual pipetting is done. So, indeed, it has to be accounted for in both cases. 

However, as you could see, repeatability is taken into account differently. In the case of the actual pipetting you take it into account as the standard deviation of an individual measurement. In the case of calibration – as standard deviation of the mean. The more individual measurements have been done for a pipette calibration, the more reliable is the correction value. Therefore, also the uncertainty of calibration is smaller: we use the standard deviation of the mean for calibration uncertainty and standard deviation of the mean is dependent on the number of individual measurements. Moreover, calibration uncertainty given by the manufacturer is usually much higher: in our example in Section 4.6 it is approximately 10 times higher than the one we have obtained.