Ratio of Vector Lengths as an Indicator of Sample Representativeness

• Activity Number: 364
• Type: Contributed
• Date/Time: Tuesday, August 2, 2016 : 10:30 AM to 12:20 PM
• Sponsor: Survey Research Methods Section
• Author(s): Hee-Choon Shin*
• Companies: CDC/NCHS
• Keywords: Sampling ; Bias ; Efficiency ; Representativeness

Abstract

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. A population characteristics or measures of N population elements could be interpreted as a vector on N-dimensional space. Similarly, a sample characteristics or measures of n sample elements could be interpreted as a vector on n-dimensional subspace, imbedded in N-dimensional space. The length of a population vector is defined as the square root of the sum of squares of N components. The length of a sample vector is the square root of the sum of squares of n components. A weighted length of a sample vector could be obtained by weighting the sum of squares of n components with sampling weights. We can measure the sample representativeness by comparing the weighted length of a sample vector with the length of the population vector. Simulation study will be conducted to demonstrate the effectiveness of the measure for sample representativeness.