August 28, 1972 -2- Dr. Don Hendricks criteria for determining the number of samples to be assigned to a particular such unit. We assume that al] concerned understand that there is no single "best" sample size and that someone has to judce what criteria will serve the objectives of the survey--this process ought not to devolve on us, since we're not sufficiently familiar with the problem and the Atoll. A common tendency is to try to find an acceptable number of samples per unit area (say one per so many thousand square feet). This comes from the usual lay opinion that a big area should have more samples than a small one. Although a smal] adjustment can be made for size of area, it is generally true that the controlling factor is not size, but is variability from spot to spot. Sometimes this is a hard point for field workers to accept, but I think that most of those who have had a look at data on radionuclide concentrations due to fallout will remember that samples taken a few feet apart are often just as different as are those separated by much greater distances (see for example, P. 6 of the study by Held et al. of atoll soils and radionuclides;, VWFL-92, 1965). , A good deal of experience with radionuclides in a variety of substances suggests that the coefficient of variation is relatively constant, if the data are taken from situations having some degree of homogeneity. This observation, plus other information, indicates that the frequency distri- butions of observed data will be "skewed", i.e., if one plots the relative numbers of soil samples having specific concentrations, there will be a sizable number at some point to the right of zero (with the appropriate scale) and a long "tail" off to the right. The commonly used distributions for representing such data are the lognormal and gamma distributions. The existence of such skewed distributions has some important implications when it comes to Clean-up, and we will return to this point later. Criteria for selecting sample sizes If it is assumed that the coefficient of variation is a constant, j.e., that the standard deviation (s) divided by the mean (x) is approximately Se coef. of variation = c = xf [4% constant, then we can compute a standard error of the mean: ~- Standard error = = [rT