Geoscience Reference
In-Depth Information
i.e., the total variance is the sum of the environmental variance plus the
expected sampling variance. This total variance can be estimated as
-
10
i
=1
1
2
2
S
S
&
i
-
S
&
-
) =
r(
S
&
va
&
10(10 - 1
}
We can estimate the expected sampling variance as the mean of the sam-
pling variances
10
S
S
&
i
?
1
2
va
&
r
S
i
&
[var(
S
&
?
i
=1
S
)] =
}
10
}
so that the estimate of the environmental variance is obtained by solving for
s
2
-
10
i
=1
1
10
2
2
S
S
S
&
i
?
S
&
i
-
S
&
1
2
va
&
r
S
i
i
=1
&
2
=
}
(10-1
}
-
}
10
}
However, sampling variances are usually not all equal, so we have to weight
them to obtain an unbiased estimate of
s
2
. The general theory says to use a
weight,
w
i
,
1
s
}
w
i
=
1
S
&
i
?
S
i
2
2
+var
so that by replacing var(
ˆ
i
?
S
i
) with its estimator vâr(
ˆ
i
?
S
i
), the estimator of the
weighted mean is
