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'''Multivariate statistics''' is a subdivision of [[statistics]] encompassing the simultaneous observation and analysis of more than one outcome variable. The application of multivariate statistics is multivariate analysis.

Multivariate statistics concerns understanding the different aims and background of each of the different forms of multivariate analysis, and how they relate to each other. The practical application of multivariate statistics to a particular problem may involve several types of univariate and multivariate analyses in order to understand the relationships between variables and their relevance to the problem being studied.

In addition, all of the above are considered "observable analysis" because the analyses are all of observable variables. There is also a corresponding range of techniques that deal with "latent variables" which are not directly observed but are rather inferred from the observed variables.

== History ==

Multivariate statistics have been used for more than a century. The term "multivariate statistics" came into use in the later part of the 20th century. The first forms of multivariate analysis were [[principal component analysis]], which was invented in 1901 by [[Karl Pearson]], and [[canonical correlation analysis]], which was introduced by [[Harold Hotelling]] in the 1930s.

== Techniques ==

There are many different models, techniques and procedures in use which are all under the broad heading of Multivariate Statistics. They are all used to analyze data sets with more than one variable and allow for a more detailed and complex analysis than univariate statistics.

Some of the techniques used in multivariate statistics include:

* [[Cluster analysis]]
* [[Principal component analysis]]
* [[Factor analysis]]
* [[Canonical correlation analysis]]
* [[Discriminant analysis]]
* [[Multivariate analysis of variance]]
* [[Multivariate regression]]
* [[Correspondence analysis]]
* [[Multidimensional scaling]]

== Applications ==

Multivariate statistics can be used in the social sciences, in marketing, in health care, in business, in the field of education, in geology, in the field of manufacturing, in genomics, in image processing, and in many other fields.

== See also ==

* [[Univariate statistics]]
* [[Bivariate analysis]]
* [[Multivariate analysis]]
* [[Multivariate normal distribution]]
* [[Multivariate random variable]]
* [[Multivariate analysis of variance]]
* [[Multivariate regression]]
* [[Multivariate time series]]

== References ==

<references />

== External links ==

* [http://www.statsoft.com/Textbook/Multivariate-Statistics Multivariate Statistics: Concepts, Models, and Applications]
* [http://www.itl.nist.gov/div898/handbook/pmc/section4/pmc4.htm NIST/SEMATECH e-Handbook of Statistical Methods]

[[Category:Multivariate statistics]]
[[Category:Statistical data types]]
[[Category:Statistical analysis]]
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