The term is a buzzword, and is frequently misused to mean any form of large-scale data or information processing ( collection, extraction, warehousing, analysis, and statistics ) but is also generalized to any kind of computer decision support system, including artificial intelligence, machine learning, and business intelligence.

B – E statistics was introduced for photons in 1924 by Bose and generalized to atoms by Einstein in 1924-25.

In a well defined sense it generalized the classical notion of minimal sufficient statistics from parametric statistics to arbitrary distributions, not necessarily of exponential form.

In statistics, the generalized linear model ( GLM ) is a flexible generalization of ordinary linear regression that allows for response variables that have other than a normal distribution.

In probability theory and statistics, the generalized inverse Gaussian distribution ( GIG ) is a three-parameter family of continuous probability distributions with probability density function

The Cauchy distribution is often used in statistics as the canonical example of a " pathological " distribution.

A canonical partition function, which has a given number of particles is in fact difficult to write down because of spin statistics.

In statistics, canonical correlation analysis, introduced by Harold Hotelling, is a way of making sense of cross-covariance matrices.

In statistics, canonical analysis ( from Gk. κανων bar, measuring rod, ruler ) belongs to the family of regression methods for data analysis.

In statistics, the autocorrelation of a random process describes the correlation between values of the process at different points in time, as a function of the two times or of the time difference.

covers statistical study, descriptive statistics ( collection, description, analysis, and summary of data ), probability, and the binomial and normal distributions, test of hypotheses and confidence intervals, linear regression, and correlation.

Quantitative methods used in I – O psychology include both descriptive statistics and inferential statistics ( e. g., correlation, multiple regression, and analysis of variance ).

Methods of bivariate statistics, for example simple linear regression and correlation, are NOT special cases of multivariate statistics because only one outcome variable is involved.

" Correlation does not imply causation " is a phrase used in science and statistics to emphasize that a correlation between two variables does not automatically imply that one causes the other.

In probability and statistics, Simpson's paradox ( or the Yule – Simpson effect ) is a paradox in which a correlation present in different groups is reversed when the groups are combined.

This is true of some correlation statistics as well as their population analogues.

Some correlation statistics, such as the rank correlation coefficient, are also invariant to monotone transformations of the marginal distributions of X and / or Y.

* Kendall tau rank correlation coefficient in statistics.

" Citing admissions statistics, the Chief Justice noted the tight correlation between the percentage of applicants and admittees of a given race and argued that the numbers were " far too precise to be dismissed as merely the result of the school paying ' some attention to numbers.

In statistics, the Pearson product-moment correlation coefficient ( sometimes referred to as the PPMCC or PCC, or Pearson's r, and is typically denoted by r ) is a measure of the correlation ( linear dependence ) between two variables X and Y, giving a value between + 1 and − 1 inclusive.

In statistics, Spearman's rank correlation coefficient or Spearman's rho, named after Charles Spearman and often denoted by the Greek letter ( rho ) or as, is a non-parametric measure of statistical dependence between two variables.

* Concordance correlation coefficient, in statistics, a measurement of the agreement between two variables

The use of the adjective empirical, especially in scientific studies using statistics, may also indicate that a particular correlation between two parameters has been found, but that so far, no theory for the mechanism of the connection is known.

* Francis Galton introduces the concept of correlation in statistics.

Item analysis within the classical approach often relies on two statistics: the P-value ( proportion ) and the item-total correlation ( Point-biserial_correlation_coefficient ).

* In statistics to represent Spearman's rank correlation coefficient, commonly known as Spearman's rho

In statistics, a spurious relationship ( or, sometimes, spurious correlation or spurious regression ) is a mathematical relationship in which two events or variables have no direct causal connection, yet it may be wrongly inferred that they do, due to either coincidence or the presence of a certain third, unseen factor ( referred to as a " confounding factor " or " lurking variable ").

Another popular example is a series of Dutch statistics showing a positive correlation between the number of storks nesting in a series of springs and the number of human babies born at that time.

In statistics, the Page test for multiple comparisons between ordered correlated variables is the counterpart of Spearman's rank correlation coefficient which summarizes the association of continuous variables.

However, the statistical offices of both governments were assigned responsibility for the planning and analysis of these statistics.

In statistics, analysis of variance ( ANOVA ) is a collection of statistical models, and their associated procedures, in which the observed variance in a particular variable is partitioned into components attributable to different sources of variation.

In statistics, the term analysis may refer to any method used

* Scale analysis ( statistics ) – methods to analyse survey data by scoring responses on a numeric scale

Business statistics is the science of good decision making in the face of uncertainty and is used in many disciplines such as financial analysis, econometrics, auditing, production and operations including services improvement, and marketing research.

Johann Carl Friedrich Gauss (;, ) ( 30 April 177723 February 1855 ) was a German mathematician and physical scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.

Even when a data analysis draws its main conclusions using inferential statistics, descriptive statistics are generally also presented.

However the general concept of linear filtering is broader, also used in statistics, data analysis, and mechanical engineering among other fields and technologies.

Using techniques from science, engineering and statistics, such as the systematic review of medical literature, meta-analysis, risk-benefit analysis, and randomized controlled trials ( RCTs ), EBM aims for the ideal that healthcare professionals should make " conscientious, explicit, and judicious use of current best evidence " in their everyday practice.

General semantics ' view of " time-binding " and modern theories of scenario analysis and financial risk ( based on statistics ) emphasize a need to keep time frames of measurement and analysis carefully aligned.

Functional programming is also supported in some domain-specific programming languages like R ( statistics ), Mathematica ( symbolic math ), J, K and Q from Kx Systems ( financial analysis ), XQuery / XSLT ( XML ) and Opal.

Fourier analysis has many scientific applications – in physics, partial differential equations, number theory, combinatorics, signal processing, imaging, probability theory, statistics, option pricing, cryptography, numerical analysis, acoustics, oceanography, sonar, optics, diffraction, geometry, protein structure analysis and other areas.

* In statistics, Wilks's lambda is used in multivariate analysis of variance ( MANOVA analysis ) to compare group means on a combination of dependent variables.

Mathematicians do research in fields such as logic, set theory, category theory, abstract algebra, number theory, analysis, geometry, topology, dynamical systems, combinatorics, game theory, information theory, numerical analysis, optimization, computation, probability and statistics.

As well as statistics, means are often used in geometry and analysis ; a wide range of means have been developed for these purposes, which are not much used in statistics.