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Statistical Dispersion
In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed. Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range. For instance, when the variance of data in a set is large, the data is widely scattered. On the other hand, when the variance is small, the data in the set is clustered. Dispersion is contrasted with location or central tendency, and together they are the most used properties of distributions. Measures of statistical dispersion A measure of statistical dispersion is a nonnegative real number that is zero if all the data are the same and increases as the data become more diverse. Most measures of dispersion have the same units as the quantity being measured. In other words, if the measurements are in metres or seconds, so is the measure of dispersion. Examples of dispersion measures include: * Standard deviation * Interquartile ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Comparison Standard Deviations
Comparison or comparing is the act of evaluating two or more things by determining the relevant, comparable characteristics of each thing, and then determining which characteristics of each are Similarity (psychology), similar to the other, which are Difference (philosophy), different, and to what degree. Where characteristics are different, the differences may then be evaluated to determine which thing is best suited for a particular purpose. The description of similarities and differences found between the two things is also called a comparison. Comparison can take many distinct forms, varying by field: To compare things, they must have characteristics that are similar enough in relevant ways to merit comparison. If two things are too different to compare in a useful way, an attempt to compare them is colloquially referred to in English as "comparing apples and oranges." Comparison is widely used in society, in science and the arts. General usage Comparison is a natural act ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distance Standard Deviation
In statistics and in probability theory, distance correlation or distance covariance is a measure of dependence between two paired random vector In probability, and statistics, a multivariate random variable or random vector is a list or vector of mathematical variables each of whose value is unknown, either because the value has not yet occurred or because there is imperfect knowledge ...s of arbitrary, not necessarily equal, Euclidean vector, dimension. The population distance correlation coefficient is zero if and only if the random vectors are Independence (probability theory), independent. Thus, distance correlation measures both linear and nonlinear association between two random variables or random vectors. This is in contrast to Pearson's correlation, which can only detect linear association between two random variables. Distance correlation can be used to perform a Statistical hypothesis testing, statistical test of dependence with a permutation test. One first co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gini Coefficient
In economics, the Gini coefficient ( ), also known as the Gini index or Gini ratio, is a measure of statistical dispersion intended to represent the income distribution, income inequality, the wealth distribution, wealth inequality, or the consumption inequality within a nation or a social group. It was developed by Italian statistics, statistician and Sociology, sociologist Corrado Gini. The Gini coefficient measures the economic inequality, inequality among the values of a frequency distribution, such as income levels. A Gini coefficient of 0 reflects perfect equality, where all income or wealth values are the same. In contrast, a Gini coefficient of 1 (or 100%) reflects maximal inequality among values, where a single individual has all the income while all others have none. Corrado Gini proposed the Gini coefficient as a measure of social inequality, inequality of income inequality metrics, income or Wealth concentration, wealth. For Organisation for Economic Co-operatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relative Mean Difference
Relative may refer to: General use *Kinship and family, the principle binding the most basic social units of society. If two people are connected by circumstances of birth, they are said to be ''relatives''. Philosophy *Relativism, the concept that points of view have no absolute truth or validity, having only relative, subjective value according to differences in perception and consideration, or relatively, as in the relative value of an object to a person * Relative value (philosophy) Economics * Relative value (economics) Popular culture Film and television * ''Relatively Speaking'' (1965 play), 1965 British play * ''Relatively Speaking'' (game show), late 1980s television game show * ''Everything's Relative'' (episode)#Yu-Gi-Oh! (Yu-Gi-Oh! Duel Monsters), 2000 Japanese anime ''Yu-Gi-Oh! Duel Monsters'' episode *'' Relative Values'', 2000 film based on the play of the same name. *'' It's All Relative'', 2003-4 comedy television series *''Intelligence is Relative'', tag lin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quartile Coefficient Of Dispersion
In statistics, the quartile coefficient of dispersion () is a descriptive statistic which measures dispersion and is used to make comparisons within and between data sets. Since it is based on quantile information, it is less sensitive to outliers than measures such as the coefficient of variation. As such, it is one of several robust measures of scale. The statistic is easily computed using the first and third quartiles, and , respectively) for each data set. The quartile coefficient of dispersion is the ratio of half of the interquartile range () to the average of the quartiles (the midhinge):\begin \mathrm &= \frac \\ &= . \end Example Consider the following two data sets: : ''A'' = :: ''n'' = 7, range = 12, mean = 8, median = 8, ''Q''1 = 4, ''Q''3 = 12, quartile coefficient of dispersion = 0.5 : ''B'' = :: ''n'' = 7, range = 1.2, mean = 2.4, median = 2.4, ''Q''1 = 2, ''Q''3 = 2.9, quartile coefficient of dispersion = 0.18 The quartile coefficient of dispersion of da ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coefficient Of Variation
In probability theory and statistics, the coefficient of variation (CV), also known as normalized root-mean-square deviation (NRMSD), percent RMS, and relative standard deviation (RSD), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is defined as the ratio of the standard deviation \sigma to the mean \mu (or its absolute value, , and often expressed as a percentage ("%RSD"). The CV or RSD is widely used in analytical chemistry to express the precision and repeatability of an assay. It is also commonly used in fields such as engineering or physics when doing quality assurance studies and ANOVA gauge R&R, by economists and investors in economic models, in epidemiology, and in psychology/neuroscience. Definition The coefficient of variation (CV) is defined as the ratio of the standard deviation \sigma to the mean \mu, CV = \frac. It shows the extent of variability in relation to the mean of the population. The coefficien ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dimensionless
Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that align with another system, these quantities do not necessitate explicitly defined units. For instance, alcohol by volume (ABV) represents a volumetric ratio; its value remains independent of the specific units of volume used, such as in milliliters per milliliter (mL/mL). The number one is recognized as a dimensionless base quantity. Radians serve as dimensionless units for angular measurements, derived from the universal ratio of 2π times the radius of a circle being equal to its circumference. Dimensionless quantities play a crucial role serving as parameters in differential equations in various technical disciplines. In calculus, concepts like the unitless ratios in limits or derivatives often involve dimensionless quantities. In differential geom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Absolute Value
In mathematics, the absolute value or modulus of a real number x, is the non-negative value without regard to its sign. Namely, , x, =x if x is a positive number, and , x, =-x if x is negative (in which case negating x makes -x positive), and For example, the absolute value of 3 and the absolute value of −3 is The absolute value of a number may be thought of as its distance from zero. Generalisations of the absolute value for real numbers occur in a wide variety of mathematical settings. For example, an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces. The absolute value is closely related to the notions of magnitude, distance, and norm in various mathematical and physical contexts. Terminology and notation In 1806, Jean-Robert Argand introduced the term ''module'', meaning ''unit of measure'' in French, specifically for the ''complex'' absolute value,Oxford English Dictionary, Draft Revision, Ju ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Transformation
In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping V \to W between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism. If a linear map is a bijection then it is called a . In the case where V = W, a linear map is called a linear endomorphism. Sometimes the term refers to this case, but the term "linear operator" can have different meanings for different conventions: for example, it can be used to emphasize that V and W are real vector spaces (not necessarily with V = W), or it can be used to emphasize that V is a function space, which is a common convention in functional analysis. Sometimes the term ''linear function'' has the same meaning as ''linear map' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Variable
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a Mathematics, mathematical formalization of a quantity or object which depends on randomness, random events. The term 'random variable' in its mathematical definition refers to neither randomness nor variability but instead is a mathematical function (mathematics), function in which * the Domain of a function, domain is the set of possible Outcome (probability), outcomes in a sample space (e.g. the set \ which are the possible upper sides of a flipped coin heads H or tails T as the result from tossing a coin); and * the Range of a function, range is a measurable space (e.g. corresponding to the domain above, the range might be the set \ if say heads H mapped to -1 and T mapped to 1). Typically, the range of a random variable is a subset of the Real number, real numbers. Informally, randomness typically represents some fundamental element of chance, such as in the roll of a dice, d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Outliers
In statistics, an outlier is a data point that differs significantly from other observations. An outlier may be due to a variability in the measurement, an indication of novel data, or it may be the result of experimental error; the latter are sometimes excluded from the data set. An outlier can be an indication of exciting possibility, but can also cause serious problems in statistical analyses. Outliers can occur by chance in any distribution, but they can indicate novel behaviour or structures in the data-set, measurement error, or that the population has a heavy-tailed distribution. In the case of measurement error, one wishes to discard them or use statistics that are robust to outliers, while in the case of heavy-tailed distributions, they indicate that the distribution has high skewness and that one should be very cautious in using tools or intuitions that assume a normal distribution. A frequent cause of outliers is a mixture of two distributions, which may be two d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robust Measures Of Scale
In statistics, robust measures of scale are methods which quantify the statistical dispersion in a sample of numerical data while resisting outliers. These are contrasted with conventional or non-robust measures of scale, such as sample standard deviation, which are greatly influenced by outliers. The most common such robust statistics are the ''interquartile range'' (IQR) and the '' median absolute deviation'' (MAD). Alternatives robust estimators have also been developed, such as those based on pairwise differences and biweight midvariance. These robust statistics are particularly used as estimators of a scale parameter, and have the advantages of both robustness and superior efficiency on contaminated data, at the cost of inferior efficiency on clean data from distributions such as the normal distribution. To illustrate robustness, the standard deviation can be made arbitrarily large by increasing exactly one observation (it has a breakdown point of 0, as it can be contaminat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
