August 28, 1972 -5- Dr. Don Hendricks limits are statements that can be made in advance of sampling or about many future repetitions of the same survey. The actual concentration of plutonium present is some particular value and is not likely to be changed by our confidence limits! It is important to note that these calculations say nothing about area or number of islands involved. As noted above, it is the vari- ability, not the area, that determines sample size. Hence the size of Sample needed goes up or down depending on how islands are grouped or subdivided and on what choices are made as to precision of results needed for a particular sampling unit. A different criterion is available if one chooses to consider the size of sample required to determine whether concentrations differ from place to place. Presumably this sort of judgement may be involved in deciding or confirming whether the seaward and lagoon sides of various islands have different concentrations of plutonium, or whether the several sets of “fallout” contaminated islands have different concentrations. The kind of statements that can be made for given samples sizes notJ/become somewhat more complicated, and there are other features having to do with number of places being compared and differences in sample size. For simplicity we present a comparison of just two areas (or islands or two groups of islands) and assume that each has been sampled with exactly the same number of plots. Then the comparison may be a "t-test" and we are interested in what the statistician calls the "power" of the test--i.e., what is the probability that we will actually detect a difference of a specified magnitude.? The results can be phrased in state- ments like "the probability is .90 that we will be able to detect a difference of 40% in plutonium concentration between seaward and lagoon sides of an island if we take n samples on each side of the island" (for purists, we note that one also needs to set the probability of Type I error, i.e., the chance that we claim a difference when none exists; we have here used the .05 level as is usual). Since the distributions are skewed we have assumed a logarithmic transformation and express the comparisons as a ratio (R), that is, we suppose the "high" area is R times the "low" area. A quick look at the table attached willshow that samples of even 50 won't distinguish (pafels } anything but large differences, whereas with samples of size 30 (in each location) about 70% of the time one would expect to distinguish a difference as large as 50% (R=1.5). Larger differences will of course be picked up with