In spatial statistics, the empirical semivariance is described by
γ
^
(
h
)
=
1
2
⋅
1
n
(
h
)
∑
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
γ
^
(
h
)
a variogram, others use the terms variogram and semivariogram synonymously. However, Bachmaier and Backes (2008), who discussed this confusion, have shown that
γ
^
(
h
)
should be called a variogram, terms like semivariogram or semivariance should be avoided.
