**Sankhya: The Indian Journal of Statistics**

1995, Volume 57, Series B, Pt. 3, pp. 391--404

**APPROXIMATELY OPTIMUM STRATIFIED DESIGN FOR A FINITE POPULATION-II**

By

HARI R. SHILEDAR BAXI, *Schenectady*

SUMMARY. This paper is a sequel to an earlier paper by the author (1982) in which the modified Kossack and Shiledar Baxi procedure was given to obtain an improved "unit-stratified" design. A further refinement has been suggested to the modified procedure so as to obtain an allocation more closer to the true optimum allocation than that obtainable through the modified procedure.

Starting with an initial approximately optimal design obtained by using Dalenius and Hodges (1959) Cum $\sqrt {f}$ rule, the present procedure reduces intra-stratum variances of all strata that are candidates for reducing their variances in each subsequent cycle. For this purpose, the present procedure involves all strata of the design , rather than a few strata as suggested in the modified procedure, even if the number of strata is large.

A small population (N = 44) is used to demonstrate the gains in efficiency of the present procedure, relative to the cum $\sqrt {f}$ rule. Although this efficiency does not increase as the number of strata increases, the gain in efficiency is generally large enough to strongly recommend the use of the present procedure.

*AMS (1990) subject classification.* 62D05.

*Key words and phrases*. Stratified sampling, sampling finite populations, optimum stratified design, sampling discrete populations.