Abstract:
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The main objective of sampling is to obtain a representative sample for an unbiased and efficient estimate within a budget constraint. The current paper is to develop a new measure of representativeness of a sample for a multipurpose survey. A population characteristics or measures of N population elements could be interpreted as a vector on N-dimensional space. The sample representativeness can be measured as a ratio of the weighted length of a sample vector to the length of the population vector (Shin, 2016). Most of large-scale surveys are multipurpose (Kish, 1988). That is, there are many items of interest (Y's) in a single survey. The best index for a particular item may not be the best for the other items. In this paper, an index of sample representativeness for a multipurpose survey will be explored considering the angles between the variables of interest on the n-dimensional subspace as an extension of the index for a single variable of interest. Simulation results using 2016 National Health Interview Survey public use file will be presented to show the effectiveness of the index.
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