MULTISTAGE CLUSTER SAMPLING
    Multistage Designs and Sampling Error
    Stratification in Multistage Cluster Sampling
    Probability Proportionate to Size (PPS) Sampling
    Disproportionate Sampling and Weighting
    Illustration: Sampling Churchwomen

    Often there is no single list of the population we are interested in studying: all college students in the nation, for example.  In such cases, however, the people we are interested in can be found in identifiable clusters.  College students are at particular colleges, churchmembers belong to churches, voters are registered in states, cities, or precints.

    In such situations, we can select a sample of the relevant clusters (e.g., a sample of colleges), get lists of individuals (e.g., students) from each of the selected clusters, and study those ultimately selected.

    While it is possible to select the clusters with equal probabilities and do the same at the second stage of sampling, probability proportionate to size (PPS) is a superior method.  Since college students at a particular college will be more homogeneous than would be true of college students across the nation, a more accurate representation will be accomplished by picking more colleges and fewer students at each of those selected.  We do this by giving colleges a chance of select proportionate to their size and then picking the same number of students at each of those selected.

    In the chapter, you'll see how PPS results in each student in the nation ultimately having the same chance of selection.  More generally, you'll see how the probabilities of selection may be varied in a number of ways, later balanced out by weighting the results.