Does Qualitative Measurement Uncertainty Exist?

I have heard it said that forensic-science standards for interpreting the results of chemical or other tests need not discuss uncertainty in measurements of qualitative properties. For instance, ASTM International appropriately requires standards for test methods to include a section reporting on precision and bias as manifested in interlaboratory tests. Yet, it applies this requirement exclusively to quantitative measurements. Its 2021 style manual is unequivocal:

When a test method specifies that a test result is a nonnumerical report of success or failure or other categorization or classification based on criteria specified in the procedure, use a statement on precision and bias such as the following: “Precision and Bias—No information is presented about either the precision or bias of Test Method X0000 for measuring (insert here the name of the property) since the test result is nonquantitative" (ASTM 2020, § A21.5.4, pp. A3-A14).

Qualitative measurements are observation-statements such as the ink is blue, the friction ridge skin pattern includes loops, the bloodstain displays a cessation pattern, the blood group is type A, the glass fragments fit together perfectly, or the material contains cocaine. Likewise, the statements could be comparative: the recording of an unknown bell ringing sounds like it has a higher pitch than the ringing of a known bell; the hairs are microscopically indistinguishable; or the striations on the recovered bullet and the test bullet line up when viewed in the comparison microscope.

“Precision” is defined as “the closeness of agreement between test results obtained under prescribed conditions” (ibid. § A21.2.1, at A12). “A statement on precision allows potential users of the test method to assess in general terms its usefulness in proposed applications” and is mandatory (ibid. § A21.2, at A12). So how can it be that statements of precision and bias are not allowed for qualitative as opposed to quantitative findings? In both situations, the system that generates the findings could be noisy or skewed in its outcomes.

The only answer I have heard is that measurements cannot be qualitative because the word "measurement" is reserved for determining the magnitude of quantities such as length or mass. The values of these quantitative variables are basically isomorphic to the nonnegative real numbers. Counts, such as the number of alpha particles emitted in a given interval of time by radium atoms, also qualify as measurements because there is a quantitative, additive structure to them. The values of the variable are basically isomorphic to the natural numbers. Properties that only have names are described by nominal variables. Although numbers can assigned (1 for a match and 0 for a nonmatch, for example) these numbers are no more a measurement than a social security number is. In short, the argument is that because “measurements” do no not include qualitative judgments, classifications, decisions, identifications, or whatever one might call them, no statement of measurement uncertainty or error is possible, let alone required.

This argument is incredibly weak. To begin with, the definition of “measurement” is a highly contested concept. As one guide from NIST explains, a “much wider” conception of measurement than the one “contemplated in the current version of the International vocabulary of metrology (VIM)” has been developed in the metrology literature, and the measurand “may be ... qualitative (for example, the provenance of a glass fragment determined in a forensic investigation" (Possolo 2015). Broader conceptions of measurement have been the subject of many decades of writing in psychology and psychometrics (see, e.g., Humphry 2017; Mitchell 1990). Philosophers have been struggling to describe the scope and meaning of "measurement" at least since Aristotle (see, e.g., Tal 2015).

Second, even if one agrees with the definition in one NIST publication that “[m]easurement is [confined to] an experimental process that produces a value that can reasonably be attributed to a quantitative property of a phenomenon, body, or substance” (NIST 2019), some qualitative observations fit this definition. The color of a strip of litmus paper, for instance, can be understood as a value “that can reasonably be attributed to a quantitative property,” It is simply a crude measurement of pH.

Finally, the argument that there can be no measurement error for qualitative properties because those properties are not really “measured” is a semantic ploy that misses the point. The observations or estimates of nonquantitative properties as well as the individual measurements of quantitative properties are all subject to possible random and systematic error, and statements expressing the range of probable error for all measurements, observations, estimates, and classifications are essential. The need for these statements cannot be avoided for qualitative properties or judgments by the fiat of the VIM or some other dictionary. Even if “measurement” must be read in one particular, narrow, technical sense, “evaluation uncertainty” or “examination uncertainty” still must be reckoned with (Mari et al. 2020).

In sum, there is no excuse for ASTM and other organizations promulgating standards for forensic-science test methods to exempt any reported findings from required statements of uncertainty. Many statistics can be used to indicate how reliable (repeatable and reproducible) and valid (accurate) the test results may be (ibid.; Ellison & Gregory 1998; Pendrill & Petersson 2016). The qualitative-quantitative distinction affects the choice of the statistical method or expression but not the need to have one.

REFERENCES

• ASTM Int’l, Form and Style for ASTM Standards (2020), https://www.astm.org/FormStyle_for_ASTM_STDS.html.
• Stephen L. R. Ellison & Soumi Gregory, Perspective: Quantifying Uncertainty in Qualitative Analysis, Analyst 123, 1155-1161 (1998), https://doi.org/10.1039/A707970B
• Stephen M. Humphry, Psychological Measurement: Theory, Paradoxes, and Prototypes, 27(3) Theory & Psychology 407–418 (2017)
• L. Mari, C. Narduzzi, S. Trapmann, Foundations of Uncertainty in Evaluation of Nominal properties, 152 Measurement 107397 (2020), DOI:10.1016/j.measurement.2019.107397
• Joel Mitchell, An Introduction to the Logic of Psychological Measurement (1990)
• NIST, Statistical Engineering Division, Measurement Uncertainty, updated Nov. 15, 2019, https://www.nist.gov/itl/sed/topic-areas/measurement-uncertainty
• Leslie Pendrill & Niclas Petersson, Metrology of human-based and other qualitative measurements, 27(9) Measurement Sci. Technol. 27 094003 (2016)
• A. Possolo, Simple Guide for Evaluating and Expressing the Uncertainty of NIST
  Measurement Results (NIST Technical Note 1900), 2015, doi: 10.6028/NIST.TN.1900
• Eran Tal, Measurement in Science, in Stanford Encyclopedia of Philosophy (Edward N. Zalta ed. 2015), https://plato.stanford.edu/archives/fall2017/entries/measurement-science/

APPENDIX: ADDITIONAL PUBLICATIONS ON "QUALITATIVE MEASUREMENT"

1. Mary J. Allen & Wendy M. Yen, Introduction to Measurement Theory 2 (1979) ("In measurement, numbers are assigned systematically and can be of various forms. For example, labeling people with red hair "1" and people with brown hair "2" is a measurement. Since numbers are assigned to individuals in a systematic way and differences between scores represent differences in the property being measured (hair color).")
2. Peter-Th. Wilrich, The determination of precision of qualitative measurement methods by interlaboratory experiments, Accreditation and quality assurance, 15: 439-444 (2010)
3. Boris L. Milman, Identification of chemical compounds, Trends in Analytical Chemistry, 24:6, 2005 ("identification itself is considered as measurement on a qualitative scale")
4. NIST Expert Working Group on Human Factors in Latent Print Analysis, Latent Print Examination and Human Factors: Improving the Practice Through a Systems Approach, Gaithersburg: National Institute of Standards and Technology, David H. Kaye ed., 2012 (defining "measurement" broadly, to encompass categorical variables, including the examiner's judgment about the source of a print).
5. Lim, Yong Kwan, Kweon, Oh Joo, Lee, Mi-Kyung and Kim, Hye Ryoun. Assessing the measurement uncertainty of qualitative analysis in the clinical laboratory. Journal of Laboratory Medicine, vol. 44, no. 1, 2020, pp. 3-10. https://doi.org/10.1515/labmed-2019-0155 ("Measurement uncertainty is a parameter that is associated with the dispersion of measurements. Assessment of the measurement uncertainty is recommended in qualitative analyses in clinical laboratories; however, the measurement uncertainty of qualitative tests has been neglected despite the introduction of many adequate methods.")
6. Donald Richards, Simultaneous Quantitative and Qualitative Measurements in Drug-Metabolism Investigations, Pharmaceutical Technology 2013
7. Kadri Orro, Olga Smirnova, Jelena Arshavskaja, Kristiina Salk, Anne Meikas, Susan Pihelgas, Reet Rumvolt, Külli Kingo, Aram Kazarjan, Toomas Neuman & Pieter Spee, Development of TAP, a non-invasive test for -qualitative and quantitative measurements of biomarkers from the skin surface, Biomarker Research 2: 20 (2014)
8. J M Conly & K Stein, Quantitative and qualitative measurements of K vitamins in human intestinal contents, Am J Gastroenterol. 1992 Mar;87(3):311-316
9. Wenjia Meng, Qian Zheng, Gang Pan, Qualitative Measurements of Policy Discrepancy for Return-Based Deep Q-Network, IEEE Transactions on Neural Networks and Learning Systems 2020
10. Rudolf M. Verdaasdonk, Jovanie Razafindrakoto, Philip Green, Real time large scale air flow imaging for qualitative measurements in view of infection control in the OR (Conference Presentation) Proceedings Volume 10870, Design and Quality for Biomedical Technologies XII; 1087002 (2019) https://doi.org/10.1117/12.2511185
11. Rashis, Bernard, Witte, William G. & Hopko, Russell N., Qualitative Measurements of the Effective Heats of Ablation of Several Materials in Supersonic Air Jets at Stagnation Temperatures Up to 11,000 Degrees F, National Advisory Committee for Aeronautics, July 7, 1958
12. Lawrence F Cunningham and Clifford E Young, Quantitative and Qualitative Approaches, Journal of Public Transportation 1(4) (1997) ("The study also contrasts the results of quantitative and qualitative measurements and methodologies for assessing transportation service quality")
13. JM Conly, K Stein, Quantitative and qualitative measurements of K vitamins in human intestinal contents, American Journal of Gastroenterology, 1992
14. P Sinha, Workshop on Biologically Motivated Computer Vision, 2002 - Springer ("Our emphasis on the use of qualitative measurements renders the representations stable in the presence of sensor noise and significant changes in object appearance. We develop our ideas in the context of the task of face-detection under varying illumination")
15. D Michalski, S Liebig, E Thomae & A Hinz, Pain in Patients with Multiple Sclerosis: a Complex Assessment Including Quantitative and Qualitative Measurements, 40 J. Pain 219–225 (2011), https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3160835/
16. Cécilia Merlen, Marie Verriele, Sabine Crunaire,Vincent Ricard, Pascal Kaluzny, Nadine Locoge, Quantitative or Only Qualitative Measurements of Sulfur Compounds in Ambient Air at Ppb Level? Uncertainties Assessment for Active Sampling with Tenax TA®, 132 Microchemical J. 143-153 (2017)
17. Tomomichi Suzuki, Jun Ichi Takeshita, Mayu Ogawa, Xiao-Nan Lu, Yoshikazu Ojima, Analysis of Measurement Precision Experiment with Categorical Variables, 13th International Workshop on Intelligent Statistical Quality Control 2019, Hong Kong ("Evaluating performance of a measurement method is essential in metrology. Concepts of repeatability and reproducibility are introduced in ISO5725-1 (1994) including how to run and analyse experiments (usually collaborative studies) to obtain these precision measures. ISO5725-2 (1994) describe precision evaluation in quantitative measurements but not in qualitative measurements. Some methods have been proposed for qualitative measurements cases such as Wilrich (2010), de Mast & van Wieringen (2010), Bashkansky, Gadrich & Kuselman (2012). Item response theory (Muraki, 1992) is another methodology that can be used to analyse qualitative data.").