On Precision

Wilcox, Allen J.

doi: 10.1097/01.ede.0000101026.08873.14

    In North Carolina, you don’t have to go far outside town to encounter deer. I occasionally spot them grazing along the 2-lane road that winds between Durham and Chapel Hill. On this road, there is a state highway sign that warns of deer in the next “1.8 miles.”

    “1.8 miles”?

    What is the highway department thinking? Are they advising us to keep an eye on our odometer so we will know when the threat of deer has passed? Are they counting on the deer to know their boundaries?

    We are bombarded with too much data, and much of it is expressed with too much precision. This pseudo-precision is an effortless gift from our computers, used not to inform but to convey authority. Our own scientific discipline is not immune to this temptation.

    This is not merely a matter of style. Pseudo-precision hides more than it reveals. A number with too many digits becomes anonymous, blandly forgettable. A response rate among 67 participants is described as 74.6%, as if there were a denominator of a thousand. How much kinder if the authors had told us the response rate was 75%— a number we might actually be able to recall later.

    There is misinformation that comes with pseudo-precision. Take the matter of body temperature. In the United States (where we still use the archaic Fahrenheit scale), any person can tell you that “normal” body temperature is 98.6°F. Biology is seldom so constant or predictable, so where did we get such a precise number? It comes from the conversion of 37°C. How much more “accurate” it would be (in the sense of truthful) if we would convert the rough number 37°C to the rough number 99°F. Instead, we have inexperienced parents worrying that their restless baby’s temperature of 99° is an impending fever.

    Perhaps the knottiest problem for epidemiologists is in the expression of ratios. Readers of Epidemiology might wonder about the inconsistency of ratios in our pages, shown to 2 decimal places in one paper and to 1 decimal place in another. There is an inherent asymmetry of ratios on the arithmetic scale. A difference of 0.1 makes a big difference to a ratio of 0.4 but matters hardly at all to a ratio of 4. There are no easy rules. A relative risk of 1.006 can become the stuff of national legislation (as with air pollution studies), but more often those decimal places are useless appendages, distracting us from the underlying realities. Even 1 decimal place can be frivolous, as in the upper end of a confidence interval that extends from 2.0 to 47.6.

    Numbers, like words, are tools of communication. However, numbers are uniquely seductive. They have the aura of pure information, as if they stand apart from the usual considerations of clarity. They do not. Numbers must be handled with the same care and restraint as words. Warn us of deer, but do not make us more concerned about our odometer than about the road ahead.

    © 2004 Lippincott Williams & Wilkins, Inc.