Gravimetric Uncertainty
Every measurement has uncertainty. When the laboratory provides a mass of dust, that’s not the actual mass of dust. If they report 0.413 milligrams, it’s never actually 0.413 mg. It’s, say, 0.413256…mg and the balance rounds to the nearest 0.01mg. But it’s not just the precision of the balance. There are lots of random (and non-random) factors that mean the real value is higher or lower than what you recorded. This uncertainty in measurement affects how confident we are in individual results, and by extension limits of quantification (LOQ).
Some of the sources of gravimetric measurement uncertainty include:
Balance precision
Static charge on filter
Weigh room temperature, pressure, and humidity
Uptake and loss of water in filter
Sample contamination
Wall deposits not measured
Transport loss
Sample head size selectively and reliability
Timing and flow rate check accuracy
Workplace (sampled area/task) variability
Pump flow rate stability
Weighing technique
Equilibration times
…
How much each of these examples contribute to uncertainty can vary massively from negligible to significant. I think what matters is not how much certainty our measurements have, but how well we understand them.
Australian Standard 2985 (respirable dust measurement) says that if uncertainty information is not available, use 0.01mg/m³ as limit of quantification. Hopefully, it’s self evident that picking an arbitrary limit of reporting is dumb; Particularly as a concentration when they don’t know how much air you have sampled.
Thankfully there is a standard for quantifying your gravimetric analytic uncertainty (field measurement is a whole other kettle of fish!)
Calculating LOD, LOQ and Weighing Uncertainty
ISO 15767 outlines a procedure to estimate the weighing uncertainty (and therefore LOD / LOQ).
The standard breaks it down into uncorrectable and correctable uncertainty.
Uncorrectable uncertainty is the within-lab error. If you gave the same lab the same samples 100x you’ll get slightly different results in each analysis. Improvements to lab procedures or environment control (e.g. humidity) can reduce this error but it cannot be corrected for any given analysis. It’s inherent to that lab and needs to be calculated specifically for each lab.
Correctable uncertainty is the ‘within-project’ error. Every site visit brings different environmental conditions which affect the filters slightly differently. Perhaps the project had mild sample contamination, or something else that affected the filters. Who knows! BUT if you have filters that experience all the same conditions (without being sampled on) you can account for this uncertainty. Field blanks can be used to (partially) correct for correctable uncertainty. Field blank correction is the easy part. Just add the average difference in weight of the field blanks to the sample weights.
ISO 15767 outlines a procedure to estimate the uncorrectable uncertainty for a lab:
Pre-weight 5 batches of 10 filters.
Assemble the filters in cassettes and sample heads as if they were to be used.
Place a batch outside the balance room - ideally in environments mirroring the sample area (without the dust).
Equilibrate and post-weigh the filters like normal.
Repeat for the other batches throughout the year to account for season differences
You would expect all these filter to have a weight change of 0 as they don’t have any dust on them… but that’s not the case. Each batch will have some variance as shown in the table below. If you average the batches’ variance, and square root that number, you get the standard deviation of the uncorrectable weights. This is how much you’d expect a perfectly clean filter to change each time it’s weighed.
Average variance of batches (Uncorrectable variance) = 58.8 μg
Uncorrectable standard deviation of gravimetric analysis = 7.7 μg
Calculating LOD, LOQ
We can use the uncorrectable uncertainty above to calculate our total analytical uncertainty and limit of quantification (LOQ). We first have to also decide how many field blanks we will use. The more field blanks we have, the more reliable our correction factor is for removing that correctable uncertainty. The equation we use is:
To understand what’s happening, let’s imagine the extremes.
With zero blanks, we haven’t corrected for the correctable variance at all. This equation doesn’t work.
With one blank, our total gravimetric variance is about 1.4 times the uncorrectable variance.
With infinite blanks, our total gravimetric variance = uncorrectable variance as we have perfected corrected for the correctable variance.
There are diminishing returns for each additional field blank. In my opinion the sweet spot is about 3 or 4 blanks. This exceeds the AS2985 requirement. For our example here I will use 3 field blanks.
So our estimated total variance and standard deviation (square root of variance) in our gravimetric analysis is 67.9 μg and 8.2μg.
The limit of detection is 3x standard deviation total variance, and the limit of quantification is 10x total standard deviation of the gravimetric analysis.
LOD = 25 μg or 0.025 mg
LOQ = 82 μg or 0.082 mg
When converted to a concentration, our LOQs range from:
0.64 mg/m³ - 2.2 L/min for 1 hours (Task—based) - 2 blanks
0.08 mg/m³ - 2.2 L/min for 8 hours (TWA) - 2 blanks
0.06 mg/m³ - 3 L/min for 8 hours (TWA) - 3 blanks
0.03 mg/m³ - 3 L/min for 12 hours (TWA) - 3 blanks
Impact
The example above gives a few impacts:
The limits of quantification are several times higher than the arbitrary default given in Australian Standard 2985 (0.01 mg/m³)
We have a sense of the uncertainty of our mass (note we haven’t accounted for sampling uncertainty!)
This should give us pause when reviewing and communicating specific results. Direct comparisons between results and OELVs (or action limits) becomes more questionable as our uncertainty increases. In this particular case, the uncertainty doesn’t seem to have a significant impact on the results, reporting and likely decisions. But we at least we can now say that with confidence rather than just making stuff up! Also other laboratory technique uncertainties might not be so small and could have a real impact on how we look at our results.
I’m lead to believe the influence of analysis and sampling uncertainty reduces as more samples are collected and perform statistical analysis. This is because the workplace variability (between tasks, people, days etc) are so much greater.
What should you do?
Read your standards: the lab work is often outside of your control. But understanding what they do can help contextualise your results. There may be other things you can do to minimise uncertainty.
Read similar standards: As we have seen in AS2985, just because it’s in a standard doesn’t mean it’s correct. Comparing your method/standard can help you critically evaluate it.
Talk to your lab: they probably know more than you. Ask questions like: what is the calculated uncertainty? Do they report that with the results? How many blanks are needed? What substrates are they accredited to analysis and how do they compare?