Usually in sample surveys more than one population characteristics are estimated (multi-item). These characteristics may be of conflicting nature. Optimal allocation using a stratified random sample solves the statistical problem that may be found with proportional allocation, by ensuring that enough respondents are studied in each segment to provide the highest level of accuracy for the overall results. The study compared optimum allocation in stratified and post stratified sampling using multi-items and determined the variations of the components of the multi-items in the proposed model. The idea of optimum allocation based on the multi-items was approached using a linear programming problem that minimizes the covariance of the stratified variable subject to a fixed cost. The covariance matrix was defined based on the four socio-economic characteristics of 400 heads of household in Abeokuta South and Ijebu North Local Government Areas of Ogun State, Nigeria. The characteristics were occupation, income, household size and educational level. The data from the survey was transformed for each of the four characteristics. The estimates used in the computation were calculated using statistical analysis software Splus. From the analysis, it was seen that for both Abeokuta and Ijebu data sets, the variance based on the four characteristics as multivariate is less than that of the variables when considered as a univariate. From the results, it was seen that there was no difference in the percentage of the total variance accounted for by the different components from the merged sample when compared with the individual sample.


Optimum allocation, stratified sampling, post stratified sampling, multi-items, optimization

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