Die beste Schichtung einer Gesamtheit bei optimaler Aufteilung der Probe

Summary

In a previous note the author proposed a graphic procedure permitting the optimal stratification of a given population when a proportional allocation of the sample units is desired. The present paper deals with the same type of problem in the case of optimal allocation again using as a starting point the analytical solution found by Dalenius. The cumulative distribution function, the curve of concentration, and the “second order moment curve” are assumed to be known. With this information at hand a procedure, partly graphic and partly computational, yielding the boundaries of the strata can be given. The solution is unique provided the density in any one of the strata can at least roughly be approximated by a trapezoidal density, a condition generally fulfilled. An example taken from the field of farm statistics serves as an illustration.