Potential gains from using unit level cost information in a model-assisted framework

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David G. Steel and Robert Graham Clark^Note 1

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Abstract

In developing the sample design for a survey we attempt to produce a good design for the funds available. Information on costs can be used to develop sample designs that minimise the sampling variance of an estimator of total for fixed cost. Improvements in survey management systems mean that it is now sometimes possible to estimate the cost of including each unit in the sample. This paper develops relatively simple approaches to determine whether the potential gains arising from using this unit level cost information are likely to be of practical use. It is shown that the key factor is the coefficient of variation of the costs relative to the coefficient of variation of the relative error on the estimated cost coefficients.

Key Words

Optimal allocation; Optimal design; Sample design; Sampling variance; Survey costs.

Table of content

• 1. Introduction
• 2. Notation and objective criterion
• 3. Optimal design with known cost and variance parameters
• 4. The effect of using estimated cost parameters
• 5. Examples of cost models
• 6. Discussion
• Appendix
• References

Notes