False precision

False precision (also called overprecision, fake precision, misplaced precision and spurious accuracy) occurs when numerical data are presented in a manner that implies better precision than is actually the case; since precision is a limit to accuracy, this often leads to overconfidence in the accuracy as well.^[1]

In science and engineering, convention dictates that unless a margin of error is explicitly stated, the number of significant figures used in the presentation of data should be limited to what is warranted by the precision of those data. For example, if an instrument can be read to an accuracy of tenths of a unit of measurement, results of calculations using data obtained from that instrument can only be confidently stated to the tenths place, regardless of what the raw calculation returns or whether other data used in the calculation are more accurate. Even outside these disciplines, there is a tendency to assume that all the non-zero digits of a number are meaningful; thus, providing excessive figures may lead the viewer to expect better precision than actually exists.

However, in contrast, it is good practice to retain more significant figures than this in the intermediate stages of a calculation, in order to avoid accumulated rounding errors.

False precision commonly arises when high-precision and low-precision data are combined, and in conversion of units.

Examples

• There are numerous variations of a joke which can be summarized as follows: A guard at a museum says a dinosaur skeleton is 70,000,006 years old, because an expert told him that it was 70 million years old when he started working there six years ago.

• "European authorities estimated that the bomb used 220 pounds of explosive." In this example, European authorities, who express measurements in SI units (the metric system), probably estimated that the bomb used 100 kg of explosives. Such estimates are necessarily subject to great uncertainty. When converted by the American media to pounds, the added precision suggests greater accuracy in the estimation of the bomb's size than warranted. A better way to state this is as follows: "European authorities estimated that the bomb used 100 kg (about 220 lbs) of explosives."

• In the United States, normal human body temperature is often quoted as 98.6 °F (37.0 °C). In Russia, the commonly quoted value is 36.6 °C (97.9 °F). These values appear to be the result of the same classic German study that found that the average body temperature of healthy humans is 36.6 °C.^[2] Because of the normal variation in human body temperature,^[3] this value, if quoted in degrees Celsius and one was not concerned about losing some information, would probably be rounded to 37 °C (implying a precision of the order of 0.5 °C). Converting this rounded value to Fahrenheit gives a value of 98.6 °F; however, quoting the '.6' implies a precision of the order of 0.1 °F, better than warranted by the data.

See also

• Propagation of uncertainty
• Rounding
• Round-off error
• Precision bias
• Significant figures

References

1. ^ "Overprecision". Fallacy files. http://www.fallacyfiles.org/fakeprec.html. 
2. ^ Mackowiak, Philip A.; Wasserman, Steven S.; Levine, Myron M. (1992), "A critical appraisal of 98.6 degrees F, the upper limit of the normal body temperature, and other legacies of Carl Reinhold August Wunderlich", Journal of the American Medical Association 268 (12): 1578–1580, doi:10.1001/jama.1992.03490120092034 .
3. ^ One commonly cited normal range for human body temperature is 36.4 – 37.1 °C (97.5 – 98.8 °F).

External links

• Wong, Lena (1997). "Temperature of a Healthy Human (Body Temperature)". The Physics Factbook. http://hypertextbook.com/facts/LenaWong.shtml. 
• Precisely False vs. Approximately Right: A Reader's Guide To Polls