13. Multistage Designs

  1. Steven K. Thompson

Published Online: 10 FEB 2012

DOI: 10.1002/9781118162934.ch13

Sampling, Third Edition

Sampling, Third Edition

How to Cite

Thompson, S. K. (2012) Multistage Designs, in Sampling, Third Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118162934.ch13

Author Information

  1. Simon Fraser University, Canada

Publication History

  1. Published Online: 10 FEB 2012
  2. Published Print: 23 FEB 2012

Book Series:

  1. Wiley Series in Probability and Statistics

Book Series Editors:

  1. Walter A. Shewhart and
  2. Samuel S. Wilks

ISBN Information

Print ISBN: 9780470402313

Online ISBN: 9781118162934



  • multistage designs;
  • simple random sampling


If, after selecting a sample of primary units, a sample of secondary units is selected from each of the primary units selected, the design is referred to as two-stage sampling. If in turn a sample of tertiary units is selected from each selected secondary unit, the design is three-stage sampling. Higher-order multistage designs are also possible. This chapter considers first a two-stage design with simple random sampling at each stage. Next it considers a two-stage design in which primary units are selected with replacement, with probabilities proportional to size, and a sample of secondary units is selected independently using simple random sampling without replacement each time a primary unit is selected. Finally, the chapter presents derivations for multistage designs.

Controlled Vocabulary Terms

probability; random sampling