##
Overview
Section* *

In Section 7.1, we introduce cluster and systematic sampling and show their similar structure. Graphical representations of primary units and secondary units are given. Notations are introduced.

In Section 7.2, when primary units are selected by srs, unbiased estimators and ratio estimators for cluster sampling are provided. Basic principles to obtain estimators of low variances are discussed. Then we discuss why and when will we use cluster sampling. That is followed by an example showing how to compute the ratio estimator and the unbiased estimator when the cluster sampling with primary units selected by srs is used.

In Section 7.3, cluster sampling with primary units selected by probabilities proportional to size is discussed. Then an example is given.

Lesson 7: Ch. 12.1-12.3 of Sampling by Steven Thompson, 3rd edition

## Objectives

- know why and when to use cluster sampling,
- know the notation for cluster and systematic sampling,
- know what are primary units and what are secondary units,
- compute the unbiased estimator for cluster samples when primary units are selected by srs,
- compute the ratio estimator for cluster samples when primary units are selected by srs, and
- compute the Hansen-Hurwitz estimator for cluster samples when primary units are selected by pps.