A NOTE ON OPTIMUM STRATIFICATION OF POPULATIONS FOR ESTIMATING THE POPULATION MEANS

The note gives the results of a study carried out to find the optimum points of stratification (OPS) for estimating the population means of some standard distributions. The distributions considered here are the normal and the set of chi-square distributions. The OPS for the various gamma distributions can be easily derived from the known OPS of the corresponding chi-square distributions. The OPS depend on the type of allocation envisaged. In this note attention has been confined to the proportional, equal, and optimum allocations.
Tables of OPS are given for the distributions and allocations mentioned above. Some other interesting results follow:
(i) Equalization of stratum totals as suggested by Ransen, Hurwitz and Madow (1953) does not lead to OPS for any of the populations considered.
(ii) Equalization of {f(x)}^½ dx gives an excellent approximabioii to the OPS for both equal and optimum allocations.
(iii) The OPS for equal and optimum allocations almost coincide. To put in other words, if strata are defined by OPS optimum allocation differs only slightly from equal allocation.
New rules are suggested for the family of distributions considered in this paper for all the three types of allocations.