False precision

False precision 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.

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 by the precision of those data. For example, if one instrument can read to tenths of a unit of measurement, calculations related to data obtained from that instrument can only be confidently stated to the tenths place, regardless of what the raw calculation returns or even if other data used in the calculation can be obtained more precisely. 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.

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

• “Bobo the Elephant weighs 10 tonnes. I weigh 79 kilograms. Together, Bobo and I weigh 10,079 kg.” A proper way to state this is as follows: “Bobo the elephant and I weigh 10 tonnes.”

• “Twenty seven years ago, Luis Alvarez first proposed that the Cretaceous–Tertiary extinction event was caused by an asteroid that struck the earth 65.5 million years earlier. This means the dinosaurs died out 65,500,027 years ago.”

• “European authorities estimated that the bomb used 220 pounds of explosive.” In this example, European authorities, which express measurements in SI units (the metric system), 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 actual. A proper way to state this is as follows: “European authorities estimated the bomb used 100 kg (220 lbs) of explosives.”

• In the United States, normal human body temperature is commonly quoted with false precision as 98.6 °F (37.0 °C). In Russia, the commonly quoted value is 36.6 °C (97.88 °F). These values appear to be the result of the same classic German study that found the average body temperature of healthy humans is 36.6 °C. Because of the normal variation in human body temperature, this value would properly be rounded to 37 °C (implying a precision on 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 on the order of 0.05 °F, far better than warranted by the data.

See also

• Carl Reinhold August Wunderlich
• Rounding
• Round-off error
• Propagation of uncertainty

External links

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