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Random Errors
Observational error (or measurement error) is the difference between a measured value of a quantity and its true value.Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP. In statistics, an error is not necessarily a " mistake". Variability is an inherent part of the results of measurements and of the measurement process. Measurement errors can be divided into two components: ''random'' and ''systematic''. Random errors are errors in measurement that lead to measurable values being inconsistent when repeated measurements of a constant attribute or quantity are taken. Systematic errors are errors that are not determined by chance but are introduced by repeatable processes inherent to the system. Systematic error may also refer to an error with a non-zero mean, the effect of which is not reduced when observations are averaged. Measurement errors can be summarized in terms of accuracy and precision. Measurement error should not be confused with measurement unce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Measurement
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. Measurement is a cornerstone of trade, science, technology and quantitative research in many disciplines. Historically, many measurement systems existed fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Errors And Residuals In Statistics
In statistics and optimization, errors and residuals are two closely related and easily confused measures of the deviation of an observed value of an element of a statistical sample from its "true value" (not necessarily observable). The error of an observation is the deviation of the observed value from the true value of a quantity of interest (for example, a population mean). The residual is the difference between the observed value and the ''estimated'' value of the quantity of interest (for example, a sample mean). The distinction is most important in regression analysis, where the concepts are sometimes called the regression errors and regression residuals and where they lead to the concept of studentized residuals. In econometrics, "errors" are also called disturbances. Introduction Suppose there is a series of observations from a univariate distribution and we want to estimate the mean of that distribution (the so-called location model). In this case, the errors are th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distance
Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two counties over"). Since spatial cognition is a rich source of conceptual metaphors in human thought, the term is also frequently used metaphorically to mean a measurement of the amount of difference between two similar objects (such as statistical distance between probability distributions or edit distance between strings of text) or a degree of separation (as exemplified by distance between people in a social network). Most such notions of distance, both physical and metaphorical, are formalized in mathematics using the notion of a metric space. In the social sciences, distance can refer to a qualitative measurement of separation, such as social distance or psychological distance. Distances in physics and geometry The distance between physical loca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Percentage Error
The approximation error in a data value is the discrepancy between an exact value and some ''approximation'' to it. This error can be expressed as an absolute error (the numerical amount of the discrepancy) or as a relative error (the absolute error divided by the data value). An approximation error can occur because of computing machine precision or measurement error (e.g. the length of a piece of paper is 4.53 cm but the ruler only allows you to estimate it to the nearest 0.1 cm, so you measure it as 4.5 cm). In the mathematical field of numerical analysis, the numerical stability of an algorithm indicates how the error is propagated by the algorithm. Formal definition One commonly distinguishes between the relative error and the absolute error. Given some value ''v'' and its approximation ''v''approx, the absolute error is :\epsilon = , v-v_\text, \ , where the vertical bars denote the absolute value. If v \ne 0, the relative error is : \eta = \frac = \left, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fiducial Marker
A fiducial marker or fiducial is an object placed in the field of view of an imaging system that appears in the image produced, for use as a point of reference or a measure. It may be either something placed into or on the imaging subject, or a mark or set of marks in the reticle of an optical instrument. Applications Microscopy In high-resolution optical microscopy, fiducials can be used to actively stabilize the field of view. Stabilization to better than 0.1 nm is achievable. Physics In physics, 3D computer graphics, and photography, fiducials are reference points: fixed points or lines within a scene to which other objects can be related or against which objects can be measured. Cameras outfitted with Réseau plates produce these reference marks (also called Réseau crosses) and are commonly used by NASA. Such marks are closely related to the timing marks used in optical mark recognition. Geographical survey Airborne geophysical surveys also use the term "fiducial" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biophysical Environment
A biophysical environment is a biotic and abiotic surrounding of an organism or population, and consequently includes the factors that have an influence in their survival, development, and evolution. A biophysical environment can vary in scale from microscopic to global in extent. It can also be subdivided according to its attributes. Examples include the marine environment, the atmospheric environment and the terrestrial environment. The number of biophysical environments is countless, given that each living organism has its own environment. The term ''environment'' can refer to a singular global environment in relation to humanity, or a local biophysical environment, e.g. the UK's Environment Agency. Life-environment interaction All life that has survived must have adapted to the conditions of its environment. Temperature, light, humidity, soil nutrients, etc., all influence the species within an environment. However, life in turn modifies, in various forms, its conditions. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Deviation
In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the values are spread out over a wider range. Standard deviation may be abbreviated SD, and is most commonly represented in mathematical texts and equations by the lower case Greek letter σ (sigma), for the population standard deviation, or the Latin letter '' s'', for the sample standard deviation. The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance. It is algebraically simpler, though in practice less robust, than the average absolute deviation. A useful property of the standard deviation is that, unlike the variance, it is expressed in the same unit as the data. The standard deviation of a popu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Society Of Mechanical Engineers
The American Society of Mechanical Engineers (ASME) is an American professional association that, in its own words, "promotes the art, science, and practice of multidisciplinary engineering and allied sciences around the globe" via "continuing education, training and professional development, codes and standards, research, conferences and publications, government relations, and other forms of outreach." ASME is thus an engineering society, a standards organization, a research and development organization, an advocacy organization, a provider of training and education, and a nonprofit organization. Founded as an engineering society focused on mechanical engineering in North America, ASME is today multidisciplinary and global. ASME has over 85,000 members in more than 135 countries worldwide. ASME was founded in 1880 by Alexander Lyman Holley, Henry Rossiter Worthington, John Edison Sweet and Matthias N. Forney in response to numerous steam boiler pressure vessel failures. Kno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Experiment
An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into Causality, cause-and-effect by demonstrating what outcome occurs when a particular factor is manipulated. Experiments vary greatly in goal and scale but always rely on repeatable procedure and logical analysis of the results. There also exist natural experiment, natural experimental studies. A child may carry out basic experiments to understand how things fall to the ground, while teams of scientists may take years of systematic investigation to advance their understanding of a phenomenon. Experiments and other types of hands-on activities are very important to student learning in the science classroom. Experiments can raise test scores and help a student become more engaged and interested in the material they are learning, especially when used over time. Experiments can vary from personal and in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surroundings
Surroundings are the area around a given physical or geographical point or place. The exact definition depends on the field. Surroundings can also be used in geography (when it is more precisely known as vicinity, or vicinage) and mathematics, as well as philosophy, with the literal or metaphorically extended definition. In thermodynamics, the term (and its synonym, environment) is used in a more restricted sense, meaning everything outside the thermodynamic system. Often, the simplifying assumptions are that energy and matter may move freely within the surroundings, and that the surroundings have a uniform composition. See also {{wiktionary-inline, surroundings, ambiance *Distance *Environment (biophysical) *Environment (systems) *Neighbourhood (mathematics) *Social environment *Proxemics Proxemics is the study of human use of space and the effects that population density has on behaviour, communication, and social interaction. Proxemics is one among several subcategories ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Observation
Observation is the active acquisition of information from a primary source. In living beings, observation employs the senses. In science, observation can also involve the perception and recording of data via the use of scientific instruments. The term may also refer to any data collected during the scientific activity. Observations can be qualitative, that is, only the absence or presence of a property is noted, or quantitative if a numerical value is attached to the observed phenomenon by counting or measuring. Science The scientific method requires observations of natural phenomena to formulate and test hypotheses. It consists of the following steps: # Ask a question about a natural phenomenon # Make observations of the phenomenon # Formulate a hypothesis that tentatively answers the question # Predict logical, observable consequences of the hypothesis that have not yet been investigated # Test the hypothesis' predictions by an experiment, observational study, field study, or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Measurement In Quantum Mechanics
In quantum physics, a measurement is the testing or manipulation of a physical system to yield a numerical result. The predictions that quantum physics makes are in general probabilistic. The mathematical tools for making predictions about what measurement outcomes may occur were developed during the 20th century and make use of linear algebra and functional analysis. Quantum physics has proven to be an empirical success and to have wide-ranging applicability. However, on a more philosophical level, debates continue about the meaning of the measurement concept. Mathematical formalism "Observables" as self-adjoint operators In quantum mechanics, each physical system is associated with a Hilbert space, each element of which represents a possible state of the physical system. The approach codified by John von Neumann represents a measurement upon a physical system by a self-adjoint operator on that Hilbert space termed an "observable". These observables play the role of measurable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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