# 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.

## 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

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