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Optimum Allocation in Stratified Random Sampling with Ratio Estimation as Applied to the Northern Ireland December Agricultural Sample

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  • T. McCALLION

Abstract

The optimum allocation of sample sizes in the Northern Ireland December agricultural sample is considered for three strata based on gross margins where seven variables are to be estimated using the separate ratio method. Nine farm types are then introduced making a total of 27 strata and optimum allocation is also considered for this situation using combined ratio estimates within each gross margin size group. The optimum allocations for acceptable levels of precision of the seven variables, allowing for non‐response in the December sample postal questionnaire, are formulated as mathematical programming problems which are then transformed to make the constraints linear and the objective functions non‐linear. Solutions are found using a routine from the Numerical Algorithms Group library which uses sequential quadratic programming. Substantial reductions in sample sizes required to satisfy precision constraints are obtained by the introduction of the additional stratification variable farm type.

Suggested Citation

  • T. McCALLION, 1992. "Optimum Allocation in Stratified Random Sampling with Ratio Estimation as Applied to the Northern Ireland December Agricultural Sample," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(1), pages 39-45, March.
    • Handle: RePEc:bla:jorssc:v:41:y:1992:i:1:p:39-45
    DOI: 10.2307/2347615
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