A Practical Balancing for a Random Sample from a Finite Population by Systematic Selection

Hee-Choon Shin, Jibum Kim

Abstract


The main objective of sampling is to obtain a representative sample for an unbiased and efficient estimate within a budget constraint. In a balanced sample, according to Yates’ definition (Yates, 1971), the mean value of the balanced factor in the sample is equal to the mean of the factor in the population. In this study, a balanced sample is not a purposively selected sample but a randomly selected one. Another important reason for a balanced sample is to protect the inference against a model misspecification (Royall & Herson, 1973a; Royall & Herson, 1973b). In this work, we propose and demonstrate a practical balancing method which would be a small modification to currently practiced design-based sampling procedures for small and large-scale surveys. We demonstrate practicality of our approach with a simulation of sample selection from 3,143 U.S. Counties for estimates of the total and mean population sizes in 2010 with Census 2000 count and State indicator as auxiliary variables. Our simulation study indicated that a balanced sample was good for reducing bias regardless of the particular sorting method. Rather than selecting a random sample from an ordered frame, we should try to find a balanced sample for an unbiased estimate.


Keywords


Balanced Sample; Bias; Variance; Mean Squared Error

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