In Section 8.1, we introduce systematic sampling and state why it may be a challenge to estimate the variance when only one primary unit is taken. Then repeated systematic sampling is introduced so that the variance can be estimated. We then provide an example of repeated systematic sampling.

In Section 8.2, variance for cluster and systematic sampling is decomposed in terms of between-cluster and within-cluster variances. We then provide an estimate for the relative efficiency of simple random sampling versus simple random cluster sampling. An example is provided to compare the variances for these two sampling methods. One should note that it is not uncommon to see examples that cluster sampling is much less efficient than simple random sampling, as illustrated in this example.

 Lesson 8:  Ch. 12.4-12.5 of Sampling by Steven Thompson, 3rd edition