Draft version 1.7 beta — Revised November 1, 2026
← Return to the table in Chapter 4 § 5
Data: Insufficient error analysis
A topic page linked from Chapter 4 § 5, Examples of Reported Violations of Enforceable Ethics Codes.
Definition
An error analysis can be considered insufficient for several reasons. The most obvious reason is if an error analysis is missing in a final report or manuscript. Or perhaps the error analysis is incomplete, inconsistent, or uses methods that are not referenced or explained. Or the problem could be that uncertainties in the primary data were not propagated through the various analytical steps to derive a reasonable estimate of the result's uncertainty. The error analysis could also be implausible or apparently incorrect.
Some members of the general public fault scientists for being arrogant in their professed certainty about their results, when in fact the work of a scientist is immersed in uncertainty, which is quantified using generally accepted protocols.1,2 In science, every measurement, every location, and every numerical observation has an uncertainty associated with it. Every calculation that uses scientific data should propagate the data uncertainties in a standard way to properly assess the uncertainty of the result.
Our understanding of the structure of an atom includes a nucleus surrounded by the space in which we would most probably find the associated electron(s). A nucleus by itself does not constitute an atom — both the nucleus and the electron cloud are needed to form an atom. In a broadly similar manner, a numerical datapoint or datum has a value expressed in a standard unit such as a second, meter, kilogram, Kelvin, or degree Celsius,. A scientific datum has that value at the center of an uncertainty interval containing other values that might also represent the "true" (perfectly accurate) value, although with decreasing probabilities away from the central value. We say that we have a 95% confidence that the "true" value is within the uncertainty interval associated with that level of confidence. So, a complete scientific datum has a central value and an uncertainty, together with a statement of the confidence level that uncertainty represents (1σ, 2σ, 3σ…), just as an atom has a nucleus and its electron cloud.
A scientific data or data-reduction process without appropriate and reproducible error analyses is not reliable. That critical deficiency should be caught by the investigator first, or later by competent reviewers. In a court case, inability to explain and defend the uncertainty in the data and the propagation of those uncertainties through the analytical process can make it difficult to prevail in a legally contested matter involving your work. (Opposing litigators always try to turn any statement of uncertainty into a tacit admission that "you don't really know the answer." If they can establish that there is uncertainty in the way the uncertainty in your report was determined, they are very likely to be positively gleeful at your expense.)
There is likely an established "best practice" within the geoscience community for assigning or computing the measurement uncertainty for a given type of investigation, and for uncertainty propagation through the related analysis. Seek information about that "best practice" — how to do it correctly and how to cite or reference the process. More generally, time and effort spent improving your knowledge and skills related to error analysis, from measurement through analysis and conclusions, for all of your routine tasks as a geoscientist is time well spent. If there is nobody in your immediate work environment who can teach or mentor you about practical geostatistics, and no relevant courses available at a community college or university accessible to you, here are some suggestions.
- Take advantage of geostatistical expertise within the geoscience societies you are a member of.
- Look for recorded short courses or webinars, such as the GOLI online courses through AIPG (aipg.org/general/custom.asp?page=OnlineCourses).
- Become familiar with publications and periodicals from organizations that focus on mathematical or computational geoscience, like the International Association for Mathematical Geosciences, whose headquarters is in Houston (iamg.org). They might have publications or other resources that specifically address the use cases that you are interested in.
- Take advantage of some of the universe of online courses offered by many universities and private companies, covering a range of topics in math, statistics, and probability. These include courses from Stanford, MIT, PennState, and many others. A private source for online learning about statistics is Statology (www.statology.org/). Another private source is Udemy, which offers courses in QGIS and spatial analysis using QGIS at a modest cost (www.udemy.com/course/practical-qgis-for-spatial-data-analysis-beginner-to-expert/). Please Note — These references are intended as general illustrations of some educational paths forward that are available to you, and are not intended as specific recommendations. Caveat emptor!
- Pick-up and work through some "statistics for geoscientists" or "statistics for physical scientists and engineers" books to build your background the old-fashioned way. I usually economize by starting my search in a public or university library, in the Internet Archive (archive.org), or by ordering used books in "very good," "fine," or "like new" condition.
A brief list of several statistics books that I have found useful is in the references below.2-8
Relevant provisions in geoethics codes
AGU – § IIIB3; GSA – § 3.1b.
Code Abbreviations
- AGU — American Geophysical Union, AGU Scientific Integrity and Professional Ethics (2023), Link to current document
- GSA — Geological Society of America, GSA Code of Ethics & Professional Conduct (2023), Link to current document
Notes and References
1 Bureau International des Poids et Mesures (BIPM), 2026, Guide to the expression of uncertainty in measurement (GUM): JCGM GUMsuite:2026 accessed November 1, 2026, via Link to this document, as listed in the BIPM metrology portal
2 Kirkup, L, and Frenkel, B., 2006, An Introduction to Uncertainty in Measurement [an explanation of GUM]/b>: Cambridge, UK, Cambridge University Press, 233 p., ISBN 978 0 521 60579 3.
3 Till, R., 1974, Statistical Methods for the Earth Scientist, An Introduction: New York, John Wiley & Sons, 154 p., ISBN 0 470-26340-7.
4 McKillup, S., and Dyar, M.D., 2010, Geostatistics Explained, An Introductory Guide for Earth Scientists: Cambridge, Cambridge University Press, 396 p., ISBN 978-0-521-74656-4.
5 Willink, R., 2013, Measurement Uncertainty and Probability: Cambridge, Cambridge University Press, 276 p., ISBN 978-1-107-02193-8.
6 Taylor, J.R., 2022, An Introduction to Error Analysis, The Study of Uncertainties in Physical Measurements [3rd Edition]: New York, University Science Books, 371 p., ISBN 978-1-940380-08-7.
7 Bevington, P., and Robinson, D.K., 2002, Data Reduction and Error Analysis for the Physical Sciences [3rd Edition]: McGraw-Hill Education, 336 p., ISBN 9780072472271.
8 Box, G.E.P., Hunter, J.S., and Hunter, W.G., 2005, Statistics for Experimenters, Design, Innovation, and Discovery [2nd Edition]: Hoboken, NJ, John Wiley & Sons, 639 p., paperback ISBN 0-471-71813-0.
9 Menke, W., 2024, Geophysical Data Analysis and Inverse Theory with MATLAB and Python: Academic Press, 342 p., ISBN 9780443137945, eBook ISBN 9780443137952.