A Procedure for Selecting Representative Subsamples of a Population from a Simple Random Sample

This paper proposes a procedure for selecting large subsamples drawn from a large simple random sample that are more representative of the population under study. By means of the so-called constant of proportionality, the procedure seeks to maximize the size of the subsample taken from a stratified random sample with proportional allocation, restricting it to a p-value high enough to achieve a good fit using Pearson's chi-square goodness of fit test. The user has the freedom to choose between a larger subsample with poorer adjustment or a smaller subsample with a better fit. We use the Continuous Sample of Working Lives (CSWL), a set of micro data taken from Spanish Social Security records, to illustrate the procedure, finding large subsamples with better representativeness than the original. The advantages of using this sample selection design procedure can be seen by comparing the estimate of total pension expenditure provided by the CSWL and that provided by the subsamples obtained. Having large subsamples that are more representative leads to better quality in any subsequent analysis of the sustainability of public pension systems