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False precision (also called overprecision, fake precision, misplaced precision and spurious precision) occurs when numerical data are presented in a manner that implies better precision than is justified; since precision is a limit to accuracy (in the ISO definition of accuracy), this often leads to overconfidence in the accuracy, named precision bias. [1]
Madsen Pirie defines the term "false precision" in a more general way: when exact numbers are used for notions that cannot be expressed in exact terms. For example, "We know that 90% of the difficulty in writing is getting started." Often false precision is abused to produce an unwarranted confidence in the claim: "our mouthwash is twice as good as our competitor's". [2]
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 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 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, when using an electronic calculator, and in conversion of units.
False precision is the gist of numerous variations of a joke which can be summarized as follows: A tour guide at a museum says a dinosaur skeleton is 100,000,005 years old, because an expert told him that it was 100 million years old when he started working there 5 years ago.
If a car's speedometer indicates a speed of 60 mph, converting it to 96.5606 km/h makes it seem like the measurement was very precise, when in fact it was not. Assuming the speedometer is accurate to 1 mph, a more appropriate conversion is 97 km/h.
Measures that rely on statistical sampling, such as IQ tests, are often reported with false precision. [3]
In computing, floating-point arithmetic (FP) is arithmetic that represents subsets of real numbers using an integer with a fixed precision, called the significand, scaled by an integer exponent of a fixed base. Numbers of this form are called floating-point numbers. For example, 12.345 is a floating-point number in base ten with five digits of precision:
Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events. In other words, measurement is a process of determining how large or small a physical quantity is as compared to a basic reference quantity of the same kind. The scope and application of measurement are dependent on the context and discipline. In natural sciences and engineering, measurements do not apply to nominal properties of objects or events, which is consistent with the guidelines of the International vocabulary of metrology published by the International Bureau of Weights and Measures. However, in other fields such as statistics as well as the social and behavioural sciences, measurements can have multiple levels, which would include nominal, ordinal, interval and ratio scales.
Observational error is the difference between a measured value of a quantity and its unknown true value. Such errors are inherent in the measurement process; for example lengths measured with a ruler calibrated in whole centimeters will have a measurement error of several millimeters. The error or uncertainty of a measurement can be estimated, and is specified with the measurement as, for example, 32.3 ± 0.5 cm.
Accuracy and precision are two measures of observational error. Accuracy is how close a given set of measurements are to their true value. Precision is how close the measurements are to each other.
A micrometer, sometimes known as a micrometer screw gauge, is a device incorporating a calibrated screw widely used for accurate measurement of components in mechanical engineering and machining as well as most mechanical trades, along with other metrological instruments such as dial, vernier, and digital calipers. Micrometers are usually, but not always, in the form of calipers. The spindle is a very accurately machined screw and the object to be measured is placed between the spindle and the anvil. The spindle is moved by turning the ratchet knob or thimble until the object to be measured is lightly touched by both the spindle and the anvil.
Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial two-dimensional or three-dimensional positions of points and the distances and angles between them. These points are usually on the surface of the Earth, and they are often used to establish maps and boundaries for ownership, locations, such as the designated positions of structural components for construction or the surface location of subsurface features, or other purposes required by government or civil law, such as property sales.
Uncertainty or incertitude refers to epistemic situations involving imperfect or unknown information. It applies to predictions of future events, to physical measurements that are already made, or to the unknown. Uncertainty arises in partially observable or stochastic environments, as well as due to ignorance, indolence, or both. It arises in any number of fields, including insurance, philosophy, physics, statistics, economics, finance, medicine, psychology, sociology, engineering, metrology, meteorology, ecology and information science.
Rounding or rounding off means replacing a number with an approximate value that has a shorter, simpler, or more explicit representation. For example, replacing $23.4476 with $23.45, the fraction 312/937 with 1/3, or the expression √2 with 1.414.
Statistical bias, in the mathematical field of statistics, is a systematic tendency in which the methods used to gather data and generate statistics present an inaccurate, skewed or biased depiction of reality. Statistical bias exists in numerous stages of the data collection and analysis process, including: the source of the data, the methods used to collect the data, the estimator chosen, and the methods used to analyze the data. Data analysts can take various measures at each stage of the process to reduce the impact of statistical bias in their work. Understanding the source of statistical bias can help to assess whether the observed results are close to actuality. Issues of statistical bias has been argued to be closely linked to issues of statistical validity.
Significant figures, also referred to as significant digits or sig figs, are specific digits within a number written in positional notation that carry both reliability and necessity in conveying a particular quantity. When presenting the outcome of a measurement, if the number of digits exceeds what the measurement instrument can resolve, only the number of digits within the resolution's capability are dependable and therefore considered significant.
An approximation is anything that is intentionally similar but not exactly equal to something else.
In science, engineering, and other quantitative disciplines, order of approximation refers to formal or informal expressions for how accurate an approximation is.
A speedometer or speed meter is a gauge that measures and displays the instantaneous speed of a vehicle. Now universally fitted to motor vehicles, they started to be available as options in the early 20th century, and as standard equipment from about 1910 onwards. Other vehicles may use devices analogous to the speedometer with different means of sensing speed, eg. boats use a pit log, while aircraft use an airspeed indicator.
Approximation error refers to the difference between an exact value and its approximation. This discrepancy can be quantified in two ways: as absolute error, which measures the numerical difference, and as relative error, which expresses the absolute error in relation to the true value. By understanding both types of errors, we can better assess the accuracy of our estimates and measurements.
A spectroradiometer is a light measurement tool that is able to measure both the wavelength and amplitude of the light emitted from a light source. Spectrometers discriminate the wavelength based on the position the light hits at the detector array allowing the full spectrum to be obtained with a single acquisition. Most spectrometers have a base measurement of counts which is the un-calibrated reading and is thus impacted by the sensitivity of the detector to each wavelength. By applying a calibration, the spectrometer is then able to provide measurements of spectral irradiance, spectral radiance and/or spectral flux. This data is also then used with built in or PC software and numerous algorithms to provide readings or Irradiance (W/cm2), Illuminance, Radiance (W/sr), Luminance (cd), Flux, Chromaticity, Color Temperature, Peak and Dominant Wavelength. Some more complex spectrometer software packages also allow calculation of PAR μmol/m2/s, Metamerism, and candela calculations based on distance and include features like 2- and 20-degree observer, baseline overlay comparisons, transmission and reflectance.
A cave survey is a map of all or part of a cave system, which may be produced to meet differing standards of accuracy depending on the cave conditions and equipment available underground. Cave surveying and cartography, i.e. the creation of an accurate, detailed map, is one of the most common technical activities undertaken within a cave and is a fundamental part of speleology. Surveys can be used to compare caves to each other by length, depth and volume, may reveal clues on speleogenesis, provide a spatial reference for other areas of scientific study and assist visitors with route-finding.
Extended precision refers to floating-point number formats that provide greater precision than the basic floating-point formats. Extended precision formats support a basic format by minimizing roundoff and overflow errors in intermediate values of expressions on the base format. In contrast to extended precision, arbitrary-precision arithmetic refers to implementations of much larger numeric types using special software.
A test method is a method for a test in science or engineering, such as a physical test, chemical test, or statistical test. It is a definitive procedure that produces a test result. In order to ensure accurate and relevant test results, a test method should be "explicit, unambiguous, and experimentally feasible.", as well as effective and reproducible.
Precision bias also known as numeracy 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. More particularly, in assessing the merits of an argument, a measurement, or a report, an observer or assessor falls prey to precision bias when they believe that greater precision implies greater accuracy ; the observer or assessor are said to provide false precision.
As with other spreadsheets, Microsoft Excel works only to limited accuracy because it retains only a certain number of figures to describe numbers. With some exceptions regarding erroneous values, infinities, and denormalized numbers, Excel calculates in double-precision floating-point format from the IEEE 754 specification. Although Excel allows display of up to 30 decimal places, its precision for any specific number is no more than 15 significant figures, and calculations may have an accuracy that is even less due to five issues: round off, truncation, and binary storage, accumulation of the deviations of the operands in calculations, and worst: cancellation at subtractions resp. 'Catastrophic cancellation' at subtraction of values with similar magnitude.
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