Mixed allocation in stratified sampling
by
M. J. Ahsan
Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh-202002 (U. P.)
Coauthors: N. Sehar (Department of Statistics and O. R., Aligarh Muslim University, Aligarh-202002 U. P.), M. G. M. Khan (Department of Mathematics and Computing Science,The South Pacific University , SUVA, FIJI)

In stratified sampling the sampler has to decide about the sample sizes from various strata before drawing a sample. In sampling literature this problem is known as the “Allocation Problem”. Equal, Proportional and Optimum allocations are well known in sampling literature. In practice any one type of allocation is selected according to the prevailing circumstances in the population and is applied to all the strata of the population. However, there are practical situations in which the prevailing circumstances markedly differ from one group of strata to other. In the present paper we propose to divide the group of strata into non-overlapping and exhaustive subgroups according to some common and useful characteristic. The use of a particular allocation is then advised in any particular subgroup depending upon the characteristic property of the subgroup. Since different allocations are to be used in different subgroups we named our proposed allocation as the “Mixed Allocation”. The variance of the estimator based on a stratified sample under mixed allocation is worked out and compared with the variances under the over all proportional and optimum allocations. The relative increase in the variance due the use of mixed allocation is studied to decide whether a mixed allocation is advisable or not in any particular situation. A numerical example is also worked out to illustrate the computational details.

Date received: October 11, 2002