False precision
Encyclopedia
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 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
.
Accuracy and precision
In the fields of science, engineering, industry and statistics, the accuracy of a measurement system is the degree of closeness of measurements of a quantity to that quantity's actual value. The precision of a measurement system, also called reproducibility or repeatability, is the degree to which...
than is actually the case; since precision is a limit to accuracy, this often leads to overconfidence in the accuracy as well.
In science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...
and engineering
Engineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...
, convention dictates that unless a margin of error is explicitly stated, the number of significant figures
Significant figures
The significant figures of a number are those digits that carry meaning contributing to its precision. This includes all digits except:...
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
Conversion of units
Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.- Process :...
.
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 SIInternational System of UnitsThe International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. The older metric system included several groups of units...
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 temperatureNormal human body temperatureNormal human body temperature, also known as normothermia or euthermia, is a concept that depends upon the place in the body at which the measurement is made, and the time of day and level of activity of the person...
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. Because of the normal variation in human body temperature, 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 uncertaintyPropagation of uncertaintyIn statistics, propagation of error is the effect of variables' uncertainties on the uncertainty of a function based on them...
- RoundingRoundingRounding a numerical value means replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit representation; for example, replacing $23.4476 with $23.45, or the fraction 312/937 with 1/3, or the expression √2 with 1.414.Rounding is often done on purpose to...
- Round-off errorRound-off errorA round-off error, also called rounding error, is the difference between the calculated approximation of a number and its exact mathematical value. Numerical analysis specifically tries to estimate this error when using approximation equations and/or algorithms, especially when using finitely many...
- Precision biasPrecision biasPrecision bias is a form of cognitive bias in which an evaluator of information commits a logical fallacy as the result of confusing accuracy and precision...
- Significant figuresSignificant figuresThe significant figures of a number are those digits that carry meaning contributing to its precision. This includes all digits except:...