# Semivariance

*For the measure of downside risk, see Variance#Semivariance*

In spatial statistics, the **empirical semivariance** is described by
semivariance,\({\displaystyle \gamma (h)={\dfrac {1}{2n(h)}}\sum _{i=1}^{n(h)}[z(x_{i}+h)-z(x_{i})]^{2}}\)where z is the attribute value

where *z* is a 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 \({\displaystyle z(x_{i}+h)-z(x_{i})}\), 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. Many authors call \({\displaystyle 2{\hat {\gamma }}(h)}\) a variogram, others use the terms variogram and semivariogram synonymously. However, Bachmaier and Backes (2008), who discussed this confusion, have shown that \({\displaystyle {\hat {\gamma }}(h)}\) should be called a variogram, terms like semivariogram or semivariance should be avoided.

## See also

## 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*, 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