# Measurement Uncertainty

Every measurement made by human beings has an inherent uncertainty associated with it. This is natural, expected, and not in the least bit undesirable. One of the intrinsic difficulties with the concept of uncertainty, particularly in the world of forensic science, is how the term *uncertainty* is used in daily conversation. Uncertainty in everyday language implies error, mistakes, even distrust. The term *error* is a weighty and scary word, but in this context, uncertainty is *not* synonymous with error or with doubt. Rather, uncertainty is simply a range that represents the expected variation or dispersion of a measurement. In the forensic context, measurement assurance is a range of number, not a descriptor or an evaluation. It is the “±” range

^{1} The sections Uncertainty, Measurement Uncertainty, and Goodness of Measurements are contributed by Suzanne Bell.

that accompanies a quantitative measurement, and that range can be critical. Although different forensic disciplines may have slightly different wording in place, all are predicated on the definition put forth in 2008 in the *Guide to the Uncertainty of Measurement* (GUM):

non-negative parameter characterizing the dispersion of the quantity values being attributed to a measurand, based on the information used. [JCGM 200:2008 (VIM) 2.26]

The GUM is “Evaluation of measurement data—Guide to the expression of uncertainty in measurement,” JCGM 100:2008: GUM 1995 with minor corrections, published in 2008 by the International Joint Commission for Guides in Metrology. It is commonly and informally referred to as *the GUM. *The document and several supplements are available online at the website for the International Bureau of Weights and Measures (Bureau International des Poids et Measures, www.bipm.org). This is an international organization that coordinates weights, measurements, and metrological conventions. The VIM noted in the definition is the *International Vocabulary of Measurement* (also available at the BIPM site) that sets forth the internationally accepted terms related to measurements.

To further deconstruct the definition, uncertainty is the dispersion of values associated with the measurement of interest. The dispersion or range cannot be negative. For example, if a weight of 50.0 ± 1.0 g is obtained, the range or dispersion is 2.0 g; the range covering the lowest value of the measurand to the highest is 2.0 g. An example of how this definition is presented in a forensic context comes from the Scientific Working Group for Seized Drug Analysis (SWGDRUG):

parameter, associated with the measurement result, or test result, that characterizes the dispersion of the values that could reasonably be attributed to the particular quantity subject to the measurement or characteristic subject to test. [Recommendations (www.swgdrug.org) June 2016 Annex A Glossary, A.2.54]

In simple terms then, the measurement uncertainty represents the range/ spread/desperation of the measured value that would be expected to occur if the measurement was conducted under the same conditions. Measurement uncertainty is a range.

Consider a simple forensic example. A seized drug analyst receives a single plastic bag containing a white powder. The analyst is tasked with determining if the powder contains a controlled substance, and if so, the weight of the powder. The weight is the measurand and weighing powders is a straightforward process. Suppose that the analyst follows standard lab procedure, works with care and good technique, and determines that the powder is methamphetamine that is >99% pure. The analyst also obtains a weight of 50.004 g for the powder using a reliable and properly functioning balance.

The jurisdiction in which this hypothetical laboratory operates follows a Drug Enforcement Administration (DEA)/Federal Trafficking Penalty guidelines. Currently, the sentencing guidelines for metham- phetamine are categorized by severity based on the weight (pure or mixtures). *Pure* here denotes the weight of the controlled substance alone; mixtures refer to the combined weight of the controlled substance and all the other components of the sample. In this case, methamphet- amine weighing *5-49 grams pure or 50-499 grams mixture* is associated with the lesser penalties and *50 grams of more pure or 500 grams or more mixture* (www.dea.gov/druginfor/) for the more severe penalties including the possibility of a life sentence.

The importance of the uncertainty of the measurement should be clear. The measured value of 50.004 g cannot be properly interpreted or applied without an associated ± range. That is what measurement uncertainty is—a range around a measured value. If the uncertainty is estimated to be ±0.010 g, then the range is 49.994-50.014 g which means there is chance that the weight is less than 50 g, the critical or threshold weight in this example. On the other hand, suppose the range is ±0.001 g and the range is 50.003-50.005 g. The weight is above 50 g and now the guidelines change. This is not just paperwork or rounding. This changes a jail sentence which impacts many lives no matter how the case is decided.

This example illustrates why measurement uncertainty matters and why it is part of forensic professional ethics. *Forensic data has consequence*— consequences to individuals and consequences to society. Critical and momentous decisions are based on such data and as such, these measurements must be comprehensive and complete. Whenever a quantitative measurement such as a weight is made as in this example, the goal is to determine, as best is possible, the true weight of the methamphetamine. However, any measurement, no matter how good, thorough, or complete generates an *estimate* of the true weight. The true value of anything measured can never be known, but using standard and validated methods and procedures, reasonable and defensible estimates of that weight are achievable. In the same way, a measurement uncertainty is always an estimate, but one that can be reasonable, defensibly, and fit-for-purpose. Having a range associated with a measured value is essential, and not just for cases such as this example where the weight fell at a threshold value. Uncertainty estimates should be systematic, reasonable, defensible, and fit-for-purpose and applied to all cases the same way according to laboratory policy and procedures.