different between covariance vs correclation

English

Etymology

co- +? variance

Noun

covariance (plural covariances)

1. (statistics) A statistical measure defined as ${\displaystyle \scriptstyle \operatorname {Cov} (X,Y)=\operatorname {E} ((X-\mu )(Y-\nu ))}$ given two real-valued random variables X and Y, with expected values ${\displaystyle \scriptstyle E(X)\,=\,\mu }$ and ${\displaystyle \scriptstyle E(Y)\,=\,\nu }$.
   • 2002, Karl G. Jöreskog, Dag Sörbom, PRELIS 2 User's Reference Guide, Scientific Software International, page 28,

     The elements of such a correlation matrix do not have asymptotic variances and covariances of the form (1.2), even if S has a Wishart distribution.

   • 1997, Michael Patrick Allen, Understanding Regression Analysis, Plenum Press, page 31,

     Consequently, it can be shown that a covariance of two binary variables measures the extent to which the observed joint distribution of these variables differs from their expected joint distribution under the assumption that they are statistically independent.

   • 2005, Steven J. Janke, Frederick Tinsley, Introduction to Linear Models and Statistical Inference, Wiley, page 133,

     The covariance of X and Y is the expected value of the product of two random variables, X ? E(X) and Y ? E(Y). […] If two random variables tend to act like opposites, one is high when the other is low and vice versa, then the covariance will be negative. If two random variables tend to be high and low at the same time, then the covariance will be positive. In fact, the covariance measures the extent of a linear relationship between the two random variables.

2. (object-oriented programming) The conversion of data types from wider to narrower in certain situations.

   Coordinate term: contravariance

   • 2014, Benjamin J Evans, David Flanagan, Java in a Nutshell, "O'Reilly Media, Inc." (?ISBN), page 149:

     As we will see in Chapter 8, we see both covariance and contravariance throughout the Java Collections. They largely exist to ensure that the generics just “do the right thing” and behave in a manner that should not surprise the developer.

Derived terms

Related terms

• covariant

Translations

Further reading

• covariance on Wikipedia.Wikipedia
• covariance and contravariance (computer science) on Wikipedia.Wikipedia
• Covariance on Wolfram MathWorld

French

Pronunciation

• IPA^(key): /k?.va.?j??s/

Noun

covariance f (plural covariances)

1. (statistics) covariance
2. (object-oriented programming) covariance

Further reading

• “covariance” in Trésor de la langue française informatisé (The Digitized Treasury of the French Language).