Repeated Systematic Sampling; More about Variance Estimation

Repeated Systematic Sampling: As we have seen, the problem with systematic random sampling is that the validity of  SRS formulas for variance estimation depend on the assumption of a random population.  One way to address this problem is to instead use repeated systematic sampling.  Essentially, instead of taking one 1-in-k sample, we take ns samples that are each 1-in-k', where k' = kns . For example, instead of taking one 1-in-5 sample to yield 60 measurements, we can take 10 1-in-50 samples to get the same sample size.  We then use the variation between the repeated samples to obtain a more accurate variance estimate.