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On the allocation of sample size in stratified sampling

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Summary

The problem of optimum allocation of sample size to strata is examined in the light ofa priori distributions. In this context, we discuss with illustrations the justification for the assumption that the unknown proportionate values of σ 2 i ’s can be replaced by the proportionate values of the known σ 2 i ’s, which are estimates of σ 2 i ’s. The sample size is allocated so as to minimize the expected variance of the strategy consisting of πPS sampling scheme and the Horvitz-Thompson estimator under a general super-population model. It is further shown that, in the sense of expected variance, πPS sampling for unstratified sampling is inferior to πPS stratified sampling with this type of allocation, unless the superpopulation parameterg attains the value 2, in which case both schemes are equivalent.

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Authors and Affiliations

  1. Indian Statistical Institute, Calcutta

    T. J. Rao

Authors
  1. T. J. Rao
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Rao, T.J. On the allocation of sample size in stratified sampling. Ann Inst Stat Math 20, 159–166 (1968). https://doi.org/10.1007/BF02911631

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  • DOI: https://doi.org/10.1007/BF02911631

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