Geoscience Reference
In-Depth Information
cells is constant across a variety of treatment effects. This assumption is often
not true; that is, the sampling variance of a binomial distribution is a function
of the binomial probability. Thus, as the probability changes across cells, so does
the variance. Another common violation of this assumption is caused by the
variable of interest being distributed log-normally, so that the coefficient of
variation is constant across cells and the cell variance is a function of the cell
mean. Furthermore, the empirical estimation of the variance from replicate
measurements may not be the most efficient procedure. Therefore, the re-
mainder of this section describes methods that can be viewed as extensions of
the usual variance component analysis based on replicate measurements within
cells. We examine estimators for the situation in which the within-cell variance
is estimated by an estimator other than the moment estimator based on repli-
cate observations.
Assume that we can estimate the sampling variance for each year, given a
value of
ˆ
i
for the year. For example, an estimate of the sampling variation for
a binomial is
S
&
i
(
1
n
S
&
i
)
}
-
vâr (
S
&
i
?
S
i
) =
}
i
where
n
i
is the number of animals monitored to see whether they survived.
Then, can we estimate the variance term due to environmental variation, given
that we have estimates of the sampling variance for each year?
If we assume all the sampling variances are equal, the estimate of the over-
all mean is still just the mean of the 10 estimates:
10
S
S
&
i
-
=
S
&
i
=1
}
10
}
with the theoretical variance being
r(
S
&
?
-
) =
s
2
+ E
[v
S
)]
}
a
var(
S
&
}
1
0
