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Precision And Accuracy
Precision is a description of random errors, a measure of statistical variability. Accuracy has two definitions:More commonly, it is a description of systematic errors, a measure of statistical bias; as these cause a difference between a result and a "true" value, ISO calls this trueness. Alternatively, ISO defines accuracy as describing a combination of both types of observational error above (random and systematic), so high accuracy requires both high precision and high trueness.In simplest terms, given a set of data points from repeated measurements of the same quantity, the set can be said to be precise if the values are close to each other, while the set can be said to be accurate if their average is close to the true value of the quantity being measured
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Random Errors
Observational error
Observational error
(or measurement error) is the difference between a measured value of a quantity and its true value.[1] In statistics, an error is not a "mistake." Variability is an inherent part of the results of measurements and of the measurement process. Measurement
Measurement
errors can be divided into two components: random error and systematic error.[2] Random errors are errors in measurement that lead to measurable values being inconsistent when repeated measurements of a constant attribute or quantity are taken
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Grouping (firearms)
In shooting sports, a shot grouping, or simply grouping, is the pattern of projectile impacts on a target from multiple shots taken in one shooting session. The tightness of the grouping (the proximity of all the shots to each other) is a measure of the precision of a weapon, and a measure of the shooter's consistency and skill.[1][2] On the other hand, the grouping displacement (the distance between the calculated group center and the intended point of aim) is a measure of accuracy. Tightness of shot groupings are calculated by measuring the distance between bullet holes on the target (center-to-center) in length measurements such as millimeters or inches. Often that measurement is converted into angular measurements, such as milliradians (mils) or minutes of angle (MOAs), which expresses the size of shot spreads regardless of the target distance
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SI
The International System of Units
International System of Units
(SI, abbreviated from the French Système international (d'unités)) is the modern form of the metric system, and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units (ampere, kelvin, second, metre, kilogram, candela, mole) and a set of twenty decimal prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system also specifies names for 22 derived units for other common physical quantities like lumen, watt, etc. The base units, except for one, are derived from invariant constants of nature, such as the speed of light and the triple point of water, which can be observed and measured with great accuracy
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Standards Organization
A standards organization, standards body, standards developing organization (SDO), or standards setting organization (SSO) is an organization whose primary activities are developing, coordinating, promulgating, revising, amending, reissuing, interpreting, or otherwise producing technical standards[1] that are intended to address the needs of a group of affected adopters. Most standards are voluntary in the sense that they are offered for adoption by people or industry without being mandated in law. Some standards become mandatory when they are adopted by regulators as legal requirements in particular domains. The term formal standard refers specifically to a specification that has been approved by a standards setting organization. The term de jure standard refers to a standard mandated by legal requirements or refers generally to any formal standard
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National Institute Of Standards And Technology
The National Institute of Standards and Technology
Technology
(NIST) is a measurement standards laboratory, and a non-regulatory agency of the United States Department of Commerce
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Standard Error (statistics)
The standard error (SE) of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution[1] or an estimate of the standard deviation[2]. If the parameter or the statistic is the mean, it is called the standard error of the mean (SEM). The sampling distribution of a population mean is generated by repeated sampling and recording of the means obtained. This forms a distribution of different means, and this distribution has its own mean and variance. Mathematically, the variance of the sampling distribution obtained is equal to the variance of the population divided by the sample size. This is because as the sample size increases, sample means cluster more closely around the population mean. Therefore, the relationship between the standard error and the standard deviation is such that, for a given sample size, the standard error equals the standard deviation divided by the square root of the sample size
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Central Limit Theorem
In probability theory, the central limit theorem (CLT) establishes that, in most situations, when independent random variables are added, their properly normalized sum tends toward a normal distribution (informally a "bell curve") even if the original variables themselves are not normally distributed. The theorem is a key concept in probability theory because it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions. For example, suppose that a sample is obtained containing a large number of observations, each observation being randomly generated in a way that does not depend on the values of the other observations, and that the arithmetic average of the observed values is computed. If this procedure is performed many times, the central limit theorem says that the computed values of the average will be distributed according to a normal distribution
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Probability Distribution
In probability theory and statistics, a probability distribution is a mathematical function that, stated in simple terms, can be thought of as providing the probabilities of occurrence of different possible outcomes in an experiment. For instance, if the random variable X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 for X = heads, and 0.5 for X = tails (assuming the coin is fair). In more technical terms, the probability distribution is a description of a random phenomenon in terms of the probabilities of events. Examples of random phenomena can include the results of an experiment or survey. A probability distribution is defined in terms of an underlying sample space, which is the set of all possible outcomes of the random phenomenon being observed
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Mean
In mathematics, mean has several different definitions depending on the context. In probability and statistics, population mean and expected value are used synonymously to refer to one measure of the central tendency either of a probability distribution or of the random variable characterized by that distribution.[1] In the case of a discrete probability distribution of a random variable X, the mean is equal to the sum over every possible value weighted by the probability of that value; that is, it is computed by taking the product of each possible value x of X and its probability P(x), and then adding all these products together, giving μ = ∑ x P ( x ) displaystyle mu =sum xP(x) .[2] An analogous formula applies to the case of a continuous probability distribution
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Bias Of An Estimator
In statistics, the bias (or bias function) of an estimator is the difference between this estimator's expected value and the true value of the parameter being estimated. An estimator or decision rule with zero bias is called unbiased. Otherwise the estimator is said to be biased. In statistics, "bias" is an objective property of an estimator, and while not a desired property, it is not pejorative, unlike the ordinary English use of the term "bias". Bias
Bias
can also be measured with respect to the median, rather than the mean (expected value), in which case one distinguishes median-unbiased from the usual mean-unbiasedness property
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Calibration
Calibration
Calibration
in measurement technology and metrology is the comparison of measurement values delivered by a device under test with those of a calibration standard of known accuracy. Such a standard could be another measurement device of known accuracy, a device generating the quantity to be measured such as a voltage, or a physical artefact, such as a metre ruler. The outcome of the comparison can result in no significant error being noted on the device under test, a significant error being noted but no adjustment made, or an adjustment made to correct the error to an acceptable level
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Significant Figures
The significant figures of a number are digits that carry meaning contributing to its measurement resolution. This includes all digits except:[1]All leading zeros; Trailing zeros when they are merely placeholders to indicate the scale of the number (exact rules are explained at identifying significant figures); and Spurious digits introduced, for example, by calculations carried out to greater precision than that of the original data, or measurements reported to a greater precision than the equipment supports. Significance arithmetic are approximate rules for roughly maintaining significance throughout a computation
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Evaluation Of Binary Classifiers
Sources: Fawcett (2006) and Powers (2011).[1][2]From the confusion matrix you can derive four basic measuresThe evaluation of binary classifiers compares two methods of assigning a binary attribute, one of which is usually a standard method and the other is being investigated. There are many metrics that can be used to measure the performance of a classifier or predictor; different fields have different preferences for specific metrics due to different goals. For example, in medicine sensitivity and specificity are often used, while in computer science precision and recall are preferred
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Traceability
Traceability
Traceability
is the capability to trace something.[1] In some cases, it is interpreted as the ability to verify the history, location, or application of an item by means of documented recorded identification.[2] Other common definitions include the capability (and implementation) of keeping track of a given set or type of information to a given degree, or the ability to chronologically interrelate uniquely identifiable entities in a way that is verifiable.
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Binary Classification
Binary or binomial classification is the task of classifying the elements of a given set into two groups (predicting which group each one belongs to) on the basis of a classification rule
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