Introduction

The term pseudoreplication was introduced by Hurlbert (1984) to describe analyses in which ‘treatments are not replicated (though samples may be) or replicates are not statistically independent’. In survey sampling terms, the problem arises when a multistage design is employed but the data are treated as a one-stage sample in the analysis. For example suppose m secondary units are selected in each of n primary units. In most cases the nm observations do not provide as much information as nm observations selected by simple random sampling. The correct approach is to base the analysis on the means per primary unit.

The initial point made by Hurlbert and soon thereafter by Machlis et al. (1985) was incontrovertible. When multistage sampling is employed, ignoring the sampling plan and treating the data set as though it is a simple random sample can lead to gross errors during interval estimation and testing. This point is emphasized in survey sampling books, and calling attention to the error, which was quite common at the time, was a service to the discipline. Subsequently, however, cases began to appear in which the proper analytical approach was more difficult to agree on. These cases often did not involve large, clearly described populations, and well-defined sampling plans. Instead, they usually involved some combination of incompletely specified populations, nonrandom sampling, nonindependent selection, and small sample sizes. As noted in Chapter Four these issues are inherently difficult and full agreement on the best analytical approach and most appropriate interpretation cannot always be attained. Nonetheless, we believe that progress may be attainable in some cases by applying the ideas developed in Chapter Four.