median also apply to the geometric mean since for the lognormal distribu-

tion the estimated geometric mean is identical to the estimated median,
i.e., exp(fi).

CONCLUSIONS FOR ALIQUOT SIZE STUDY

The variability with aliquot size study illustrates a number of features
that should be considered at the design stages of an environmental
study.
The choice of aliquot size has been shown in this study to
influence aliquot to aliquot variability as well as the expected value
of the median and geometric mean.
Between-aliquot variability was quite
drastically reduced by using 100-g rather than l-or 10-g aliquots.
This
implies a larger number of l-g aliquots are required to estimate the
true concentration of each field sample with specified accuracy and
precision than would be the case if 25, 50; or 100-g aliquots were used.
The shape of the distribution of aliquot concentrations, as determined
by u and o, was observed to depend on aliquot size.
This change in u
and o is responsible for changes in the median and geometric mean with
aliquot size.
Aliquot size did not, however, have a systematic effect
on the arithmetic mean.
The rationale for these conclusions are illustrated for the lognormal distribution.

The relative stability exp(u + 0*/2) suggests the arithmetic mean is

preferred over the geometric mean and median for comparing studies that
have used different aliquot sizes or other sampling techniques that tend
to change the underlying skewed distribution shape of the data.
A linear regression between the logarithms of aliquot standard deviation
and aliquot size was found to fit the data.
This was combined with cost
functions to obtain an expression for the variance of the mean concentration as a function of analysis cost (or equivalently, the number of
aliquots) and aliquot size.
This variance expression decreases rapidly
as aliquot size increases from 1 to 10 g.
The rate of decline is much

slower for aliquot sizes greater than 10 g.

The question of determining the optimum number of field samples and
number of aliquots per field sample is also discussed.
A method by
Cochran (1977) was cited that takes into account costs of collecting
samples and analyzing aliquots.

VARIABILITY WITH DISTANCE STUDY

MOTIVATION AND BASIC CONCEPTS
The purpose of this study was to obtain data that would be useful in
determining the variogram (correlation structure)

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for Am concentrations

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