—
One way of comparing results for the five aliquot sizes is to consider
the question:
''How many aliquots of size less than 100 g would be _
required to achieve the same precision
(standard error)
in the mean x
for a field sample as was achieved using 100-g aliquots?" The SE for
100-g aliquots was 0.04 nCi/g (Figure 1).
If we solve the equation
SE = s/vn for n we obtain n = (s/SE)?.
By using SE = 0.04 and the estimate
of s obtained for a smaller aliquot size, we may use this equation to
estimate the number of smaller aliquots required to achieve a SE of
0.04.
Results are given in Table 2.
As expected, the smaller size
aliquots require substantially more aliquots than the 100-g size to
achieve the desired SE.
For example, an estimated 31 fifty-g aliquots
and a phenomenal 1,444 one-g aliquots are required to achieve the precision obtained using only 20 aliquots of 100-g size.
This illustrates
the point that stringent requirements on sampling precision require
either a great many small aliquots or relatively large aliquots.
This
same conclusion was reached by Wallace and Romney (1977) based on Pu
particle size distribution arguments.
Table 2.
Number of Aliquots of Size Less Than 100 g Required to
Achieve the Same Precision (SE) in the Estimated Mean
of the Field Sample as Obtained Using 20 Aliquots of
100-g Size
Aliquot Size (g)
Standard Error’
Standard Deviation(s)*
n =
(s/0.04)"
1006
50
0.04
0.05
0.179
20
Ratio of Sample Sizes Or
0.224]
32
1
25
10
1
0.12
0.11
0.34
0.537]
181
1.6
0.492
152
9
7.6
1.52
1,444
72.2
‘units of nCi/g.
VARIABILITY AND THE NUMBER OF ALIQUOTS PER FIELD SAMPLE
We noted above that between-aliquot variability is an important parameter
in designing environmental transuranic studies to meet precision requirements.
For example, one may want to estimate the number of aliquots, n,
per field sample needed to be (1-a)% confident that the estimated mean
concentration x of the individual sample is within, say, d% of the true
mean m of that sample.
An estimate of n can be obtained from the equation
_
n= (2,79 e/d)
2
(1)
(Snedecor and Cochran, 1967, page 516), where Z
:
:
9
:
a
is the standard
:
:
normal deviate corresponding to a% (two-tailed) confidence, c is the
known or estimated coefficient of variation in percent [100(s//x)],
412