Meaningless Precision.

Abstract

Over the past 25 years in academia, in peer review of consulting projects, and as an Executive Editor for Groundwater, I have often found that people just do not consider the number of significant figures … significant. The message on significant figures is often hard to get across. Many immediately think of the textbook rules they learned, and forgot, so long ago. Rather than rules on precision and significant figures, we often better relate to the accuracy of equipment we use, such as a pressure transducer accurate to ±0.05 m. However, we recognize that this field equipment accuracy does not directly translate into the degree of precision with which we should represent our mathematical modeling results. Yet, the number of manuscripts and consulting reports that present results to that, and even greater precision, is truly astounding. Why is this so important? It all comes down to public perception and properly conveying just how much potential error or uncertainty there is in our analyses and predictions. “The problem with trying to quantify exactly how certain events will affect investment boils down to this: by putting a number on it (‘If 2008 happens all over again you would expect to lose 16.85 per cent’) gives the analysis far more credence than it deserves. All stress testing, irrespective of (or possibly in direct relation to) its level of sophistication and detail, requires the adoption of a multitude of assumptions that have a lot more to do with the ‘answer’ than does the math itself.” “Thus, to plug numbers into a supercomputer and declare how a particular investment (or portfolio) would fare under something as broad as a future ‘2008 crisis’ – and to two decimal places – lacks any probative value and is nothing but an exercise in meaningless mathematics.” Kaufman goes on to state that he prefers to deal with stress-testing analysis, which is probably more useful, albeit less precise. And of course, that is how we deal with our model predictions as well. The problem, however, is that we often still give our answers to at least two decimal places! So how do we decide on how precise to present our hydrogeological assessments? Quite a few reports have a section on “Uncertainty Assessment,” or “Groundwater Model Limitations.” Here we may find a discussion on the uncertainty around the hydrological parameters that went into the model assessment, various data gaps, and how all this affects model projections. While good in itself, rarely is it reflected in the data presentation or results in the same report. As we are already providing the uncertainty assessments in our methods and modeling, then all that needs to be done is to make a professional judgement on how to present the data and simulations in line with that. An alternative approach is to use multiple standard methods to assess a parameter, and then show the variation in the result. The clearest approach, finally, would be to explicitly represent the precision as x ± δx where x represents our value and δx is the error or uncertainty. But at the very least we can make sure that the number of significant figures in our best estimate is consistent with the uncertainty in the analyses.