View source for Semivariance

:''For the measure of downside risk, see [[Variance]]
In [[Spatial statistics|spatial statistics]], the '''empirical semivariance''' is described by
semivariance,<math>\gamma(h)=\dfrac{1}{2n(h)}\sum_{i=1}^{n(h)}[z(x_i + h) - z(x_i)]^2</math>where z is the attribute value 

where ''z'' is a [[Data|datum]] at a particular location, ''h'' is the distance between ordered data, and ''n''(''h'') is the number of paired data at a distance of ''h''. The semivariance is half the variance of the increments <math>z(x_i+h)-z(x_i)</math>, but the whole variance of z-values at given separation distance ''h'' (Bachmaier and Backes, 2008). 

A plot of semivariances versus distances between ordered data in a graph is known as a semivariogram rather than a [[Variogram|variogram]]. Many authors call <math>2\hat\gamma(h)</math> a variogram, others use the terms variogram and semivariogram synonymously. However,  Bachmaier and Backes (2008), who discussed this confusion, have shown that <math>\hat\gamma(h)</math> should be called a variogram, terms like semivariogram or semivariance should be avoided.

==See also==
* [[Variance]]
* [[Earth:Geostatistics|Geostatistics]]
* [[Kriging]]

==References==
*Bachmaier, M and Backes, M, 2008, "Variogram or semivariogram? Understanding the variances in a variogram". Article {{doi|10.1007/s11119-008-9056-2}}, ''Precision Agriculture'', [[Physics:Springer-Verlag|Springer-Verlag]], Berlin, Heidelberg, New York.
* Clark, I, 1979, ''Practical Geostatistics'', Applied Science Publishers
* David, M, 1978, ''Geostatistical Ore Reserve Estimation'', Elsevier Publishing
* Hald, A, 1952, ''Statistical Theory with Engineering Applications'', John Wiley & Sons, New York
* Journel, A G and Huijbregts, Ch J, 1978 ''Mining Geostatistics'', Academic Press

==External links==
* Shine, J.A., Wakefield, G.I.: A comparison of supervised imagery classification using analyst-chosen and geostatistically-chosen training sets, 1999, https://web.archive.org/web/20020424165227/http://www.geovista.psu.edu/sites/geocomp99/Gc99/044/gc_044.htm



{{statistics|state=collapsed}}
[[Category:Geostatistics]]
[[Category:Statistical deviation and dispersion]]



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