The smooth fractionator

A modification of the general fractionator sampling technique called the smooth fractionator is presented. It may be used in almost every situation in which sampling is performed from distinct items that are uniquely defined, often they are physically separated items or clusters like pieces, blocks, slabs, sections, etc. To each item is associated a 'guesstimate' or an associated variable with a more-or-less close--and possibly biased--relationship to the content of the item. The smooth fractionator is systematic sampling among the items arranged according to the guesstimates in a unique, symmetric sequence with one peak and minimal jumps. The smooth fractionator is both very simple to implement and so efficient that it should probably always be used unless the natural sequence of the sampling items is equally smooth. So far, there is no theory for the prediction of the efficiency of smooth fractionator designs in general, and their properties are therefore illustrated with a range of real and simulated examples. At the cost of a slightly more elaborate sampling scheme, it is, however, always possible to obtain an unbiased estimate of the real precision and of some of the variance components. The only real practical problem for always obtaining a high precision with the smooth fractionator is specimen inhomogeneity, but that is detectable at almost no extra cost. With careful designs and for sample sizes of about 10, the sampling variation for the primary, smooth fractionator sampling step may in practice often be small enough to be ignored.