##
Overview
Section* *

In Section 9.1, we introduce multi-stage design and give a few practical examples. We then provide the notations for two stage design. The unbiased estimators for two stage design with simple random sampling at each stage is discussed. Then we discuss the ratio estimator for two stage design with simple random sampling at each stage.

In Section 9.2, we discuss the two stage design with primary units selected with probability proportional to size and secondary units selected with simple random sampling. The Hansen-Hurwitz estimator is computed for this situation. We also show how to compute the estimated variance for the H-H estimator.

*Sampling *by Steven Thompson, 3rd edition.

## Objectives

Upon completion of this lesson you should be able to:

- know why and when to use multi-stage sampling,
- compute unbiased estimator and its estimated variance for the two stage design when srs is used at each stage,
- compute ratio estimator and its estimated variance for the two stage design when srs is used at each stage, and
- compute the Hansen-Hurwitz estimator and its estimated variance when primary units are selected with probability proportional to size and secondary units selected with srs.