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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 a series of measurements, the set can be said to be precise if the values are close to the average value of the quantity being measured, while the set can be said to be accurate if the values are close to the true value of the quantity being measured. The two concepts are independent of each other, so a particular set of data can be said to be either accurate, or precise, or both, or neither
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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. 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 = x P ( x ) {displaystyle mu =sum xP(x)} . An analogous formula applies to the case of a continuous probability distribution . Not every probability distribution has a defined mean; see the Cauchy distribution
Cauchy distribution
for an example
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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 {displaystyle X={text{heads}}} , and 0.5 for X = tails {displaystyle X={text{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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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 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 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. Strictly speaking, the term calibration means just the act of comparison, and does not include any subsequent adjustment. The calibration standard is normally traceable to a national standard held by a National Metrological Institute
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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: * 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. The more sophisticated scientific rules are known as propagation of uncertainty
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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 (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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Standard Error (statistics)
The STANDARD ERROR (SE) of a statistic (most commonly the mean ) is the standard deviation of its sampling distribution , or sometimes an estimate of that standard deviation. The equation for the STANDARD ERROR OF THE MEAN (SEM) depicts the relationship between the dispersion of individual observations around the population mean (the standard deviation), and the dispersion of sample means around the population mean (the standard error). Different samples drawn from that same population would in general have different values of the sample mean, so there is a distribution of sampled means (with its own mean and variance). The relationship with 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. As the sample size increases, the sample means cluster more closely around the population mean and the standard error decreases
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Technical Standard
A TECHNICAL STANDARD is an established norm or requirement in regard to technical systems . It is usually a formal document that establishes uniform engineering or technical criteria, methods, processes and practices. In contrast, a custom, convention , company product, corporate standard, and so forth that becomes generally accepted and dominant is often called a de facto standard . A technical standard may be developed privately or unilaterally, for example by a corporation, regulatory body, military, etc. Standards can also be developed by groups such as trade unions, and trade associations. Standards organizations often have more diverse input and usually develop voluntary standards: these might become mandatory if adopted by a government (i.e. through legislation ), business contract, etc. The standardization process may be by edict or may involve the formal consensus of technical experts
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SI
The INTERNATIONAL SYSTEM OF UNITS (abbreviated as SI, from the French Système internationale (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 . The system also establishes a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system was published in 1960 as a result of an initiative that began in 1948. It is based on the metre-kilogram-second system of units (MKS) rather than any variant of the centimetre–gram–second system (CGS). SI is intended to be an evolving system, so prefixes and units are created and unit definitions are modified through international agreement as the technology of measurement progresses and the precision of measurements improves
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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 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 (NIST) is a measurement standards laboratory, and a non-regulatory agency of the United States Department of Commerce
United States Department of Commerce
. Its mission is to promote innovation and industrial competitiveness. NIST's activities are organized into laboratory programs that include Nanoscale Science and Technology, Engineering, Information Technology , Neutron Research, Material Measurement, and Physical Measurement
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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. 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. Thus, by using angular measurements, one can reliably compare the relative tightness of shot groupings fired at different distances
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Evaluation Of Binary Classifiers
Sources: Fawcett (2006) and Powers (2011). From the confusion matrix you can derive four basic measures The 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. An important distinction is between metrics that are independent on the prevalence (how often each category occurs in the population), and metrics that depend on the prevalence – both types are useful, but they have very different properties
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Reliability (statistics)
RELIABILITY in statistics and psychometrics is the overall consistency of a measure. A measure is said to have a high reliability if it produces similar results under consistent conditions. "It is the characteristic of a set of test scores that relates to the amount of random error from the measurement process that might be embedded in the scores. Scores that are highly reliable are accurate, reproducible, and consistent from one testing occasion to another. That is, if the testing process were repeated with a group of test takers, essentially the same results would be obtained. Various kinds of reliability coefficients, with values ranging between 0.00 (much error) and 1.00 (no error), are usually used to indicate the amount of error in the scores." For example, measurements of people's height and weight are often extremely reliable
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Validity (statistics)
VALIDITY is the extent to which a concept , conclusion or measurement is well-founded and corresponds accurately to the real world. The word "valid" is derived from the Latin validus, meaning strong. The validity of a measurement tool (for example, a test in education) is considered to be the degree to which the tool measures what it claims to measure; in this case, the validity is an equivalent to accuracy. In psychometrics , validity has a particular application known as test validity : "the degree to which evidence and theory support the interpretations of test scores" ("as entailed by proposed uses of tests"). It is generally accepted that the concept of scientific validity addresses the nature of reality and as such is an epistemological and philosophical issue as well as a question of measurement . The use of the term in logic is narrower, relating to the truth of inferences made from premises
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