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Understanding Measurement Uncertainty and Test Results Over 100%

The goal of this article is to provide context around measurement uncertainty and understanding analytical test results over 100%. The concept of measurement uncertainty is introduced and discussed in terms of high purity samples. Sources of measurement uncertainty are considered, and the process of estimating measurement uncertainty in the cannabis potency laboratory is briefly explained.


Question: “How can my CBD Isolate test result be greater than 100%, and is this normal?”

Answer: “Analytical testing provides a best estimate of the analytical composition of a sample; it is not an exact determination. So yes, it is completely normal (statistically) to see potency results over 100% in high-purity samples. This is because an analytical result is an estimate of the potency and there’s a range of uncertainty around that estimate that could also equally represent the composition of that sample.”

Let us discuss!

In order to understand test results over 100%, we need to understand the laboratory process of generating a potency test result and the uncertainty or error associated with each step in the potency testing process as well as how those errors combine together to affect the final analytical result that gets reported. Measurement uncertainty is a parameter characterizing the dispersion of the quantity values being attributed to a measurand (the thing you are trying to measure), based on the information or tools used [1]. In terms of a potency result, it is the range of values that accurately describes the actual concentration of an analyte given some level of statistical certainty. Stated another way, the potency result reported plus or minus the measurement uncertainty, accurately represents the actual potency of the sample, 95% of the time.

While the definition of measurement uncertainty may do little to clarify the meaning of the term, surely an example will help provide lucidity? Every analytical potency test starts with an analytical sample weight. Modern analytical balances are almost exclusively digital with a particular resolution on the display; a common resolution may be 0.01mg, or 1/100th of a milligram. So right off the bat we know we cannot with any degree of certainty determine the difference between a sample that is 60.016 mg and 60.019 mg. Both masses would look identical to us, 60.02 mg, even though they are different and neither is “actually” 60.02 mg. This creates a level of uncertainty in our final potency result that we have no way to resolve given the hardware and methodology we are employing. This resolution limit alone creates an uncertainty in our mass measurement of about 0.02%!

We can understand readily how balance resolution and digital rounding adds some uncertainty to the final potency result, but there is more to it than that. You can take the same object with an unchanging mass and weigh it 10 times and you can generate 10 different weights. There is a repeatability uncertainty in the mass determination as well, and it is never less than the resolution of the balance. To add insult to injury each analytical sample weight determination actually requires 2 balance readings, a tare weight and a net weight; so, go ahead and essentially double that repeatability uncertainty!

To minimize the effect the mass determination step has on the uncertainty of the final analytical result, the analytical lab can model the uncertainty due to the mass determination and set a lower limit for allowed sample weights in their protocols. This ensures the uncertainty due to the mass determination never exceeds an accepted criterion, 0.1% for example. This is shown graphically in Figure 1. For this particular balance, all sample weights above 60 mg will result in mass uncertainties less than 0.1%. In other words, if the minimum sample weight is set in the testing protocol at 60 mg, the uncertainty due to the mass determination will be less than 0.1%. Each balance performs a little bit differently depending on the operator and environment it is placed in, so this should be evaluated on a regular basis.

Figure 1. Mass by difference uncertainty as a function of the sample mass. As the sample mass increases the error in the mass by difference determination decreases. An accepted level of error equal to 0.1% is shown by the solid black line. For this specific balance, this corresponds to a sample mass ≥ 60 mg.

We have discussed the uncertainty arising from the mass determination and considered strategies for minimizing its effect on the final potency result, but every step in the sample preparation procedure has some level of uncertainty associated with it. For example, there’s an initial extraction/dilution used to retrieve the analytes from the matrix, a series of serial dilutions may be required to get the various analytes in a good analytical working range, there is uncertainty in the preparation of calibration standards, and uncertainty in the best fit regression line from the calibration, the instrument has its own variability leading to an uncertainty in the raw data signal it produces, and the processing software introduces uncertainty when it detects and integrates analyte peaks. At the end of the sample preparation and analysis procedure, all these opportunities for uncertainty combine to produce the “measurement” or “method uncertainty.” Hemp potency testing laboratories for THC compliance are required by the USDA to go through each step of their sample preparation and analysis methods and determine the measurement uncertainty in their testing protocol [2]. Once the lab understands this, they should not deviate from those protocols without understanding how it will affect the uncertainty in the final potency result.

Any one of these uncertainties can manifest in a positive or negative deviation between the reported analyte concentration and the actual analyte concentration. If by chance the net uncertainty contributions result in a positive deviation in the analytical result, the reported analyte concentration will be greater than the actual analyte concentration. This concept is easy to reconcile for physical measurements, like the balance example above, and it is relatively straightforward for chemical measurements with intermediate analyte concentrations. For example, a flower result of 12.3% CBD ± 0.6% makes sense, and a distillate result of 78.3% CBD ± 3.1% conceptually makes sense. Still, many people struggle at first to conceptualize a test result of 101.3% CBD ± 1.9%. All this means is that the assay had a net positive impact from the various sources of uncertainty on the reported analytical concentration. What about results that fall outside of the range of what would be considered “possible”, for example a test result for isolate that is 102.1% ± 1.9%? 100% purity is not within the uncertainty range in this case. Different labs may choose to handle these cases differently, but these results are still valid potency results. Statistically, the uncertainty range is stated based on a given confidence interval, 95% is common (Yes, there is uncertainty in the confidence of the uncertainty claim!). This means that given all of the preparations and analyses a laboratory does, 95% of the actual analyte concentrations will fall within the reported concentration plus or minus the uncertainty range; 5% will fall outside of this range due to the perfect combination of analytical errors. However, it should be comforting that if the same sample were tested twice there would be a 0.25%, or 25 in 10,000, chance that both of the analyses test outside of the uncertainty range, barring any systematic laboratory errors.

At the end of the day, it is essential to understand that yes, even analytical chemistry is an inexact science filled with uncertainty. We do our best to understand and characterize and avoid measurement errors, but there is still uncertainty in every analytical result, whether your analytical lab likes to admit it or not.


[1] NIST Measurement Uncertainty, Antonio Possolo, National Institute of Standards and Technology, Updated November 15, 2019, Accessed online September 10, 2020

[2] USDA-AMS Guidelines for Hemp Testing, Accessed online September 10, 2020


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