##
Overview
Section* *

In Section 10.1, we introduce double sampling and discuss the application of double sampling for ratio estimation. We then provide the formula for the variance of the ratio estimator while double sampling is used. An example is given to illustrate how to conduct the double sampling and how to compute the ratio estimator as well as the estimated variance of the estimator. The allocation in double sampling is then discussed.

In Section 10.2, double sampling for stratification is discussed. An example is then used to illustrate the use of double sampling for stratification and the computation of the estimate as well as the estimated variance of the estimate.

*Sampling* by Steven Thompson, 3rd edition

## Objective

- Use double sampling to collect information for ratio estimation,
- Compute the optimal allocation in double sampling for ratio estimation,
- Use double sampling to collect information for stratification,
- Compute the estimate when double sampling is used to collect information for stratification, and
- Compute the estimated variance of the estimate when double sampling is used to collect information for stratification