##
Overview
Section* *

In Section 6.1, we discuss when and why to use stratified sampling. The estimate for mean and total are provided when the sampling scheme is stratified sampling. An example of using stratified sampling to compute the estimates as well as the standard deviation of the estimates is provided. Confidence intervals for these estimates are then discussed.

In Section 6.2, the optimal allocation of sample size under different conditions is given. Then we discuss post-stratification. It is important to note that the variance of estimates under post-stratification is different from under stratification. In Section 6.3, we use an example to illustrate that a stratified sample may not be better than a simple random sample if the variable one stratifies on is not related to the response. At the end of section 6.3, we discuss stratified sampling for proportions.

*Sampling *by Steven Thompson, 3rd edition

## Objectives

- Identify the appropriate reasons and situations for using stratified sampling,
- Estimate mean and total when stratified sampling is used,
- Compute confidence interval for the stratified mean and stratified total,
- Determine the optimal allocation of sample sizes,
- Compute estimates when post-stratification is used,
- Compute the variance for the estimates when post-stratification is used, and
- Estimate population proportions when stratified sampling is used.