# Semivariance

For the measure of downside risk, see Variance#Semivariance

{{ safesubst:#invoke:Unsubst||$N=Merge to |date=__DATE__ |$B= Template:MboxTemplate:DMCTemplate:Merge partner }} In spatial statistics, the empirical semivariance is described by

${\displaystyle {\hat {\gamma }}(h)={\frac {1}{2}}\cdot {\frac {1}{n(h)}}\sum _{i=1}^{n(h)}(z(x_{i}+h)-z(x_{i}))^{2}}$

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.