— 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