# 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.