# Semivariance

(Redirected from Semi-variance)
For the measure of downside risk, see Variance#Semivariance

In spatial statistics, the empirical semivariance is described by

$\hat\gamma(h)=\frac{1}{2}\cdot\frac{1}{n(h)}\sum_{i=1}^{n(h)}(z(x_i+h)-z(x_i))^2$

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 $z(x_i+h)-z(x_i)$, 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 $2\hat\gamma(h)$ a variogram, others use the terms variogram and semivariogram synonymously. However, Bachmaier and Backes (2008), who discussed this confusion, have shown that $\hat\gamma(h)$ should be called a variogram, terms like semivariogram or semivariance should be avoided.