Similar to strata, population units may instead be grouped into clusters. Usually, units within clusters are geographically or genetically close to one another—all households on a city block, individuals within a single family. In (single-stage) equal size cluster sampling, the total population consists of N clusters, with equal numbers of population units within each cluster. A sample of n clusters is selected by SRS, y values of all population units within clusters are measured, and an unbiased estimator of the population mean is the simple average of cluster means in the sample. An ANOVA sum of squares partition can be used to show that this strategy will outperform SRS with mean-per-unit estimation whenever the mean square between clusters is less than the finite population variance. This means that it is desirable for clusters to have similar means but a great deal of variability within clusters, a contrast with the desirable characteristics of strata (little variability within strata, substantial difference between stratum means). Many methods of collection of samples in fisheries (seines, nets) and wildlife (mist nets, live traps) involve collection of individuals as clusters. Unfortunately, clusters (e.g., human families) often consist of closely related or similar individuals. Because within cluster variation is often relatively low, it is often advantageous and cost-effective to instead adopt two-stage cluster sampling (considered in Chapter 9) for which only a sample of units within each selected cluster are examined, thereby allowing more clusters to be examined for the same total survey cost.
Analysis of Medium Scale Solar PV System Performance on Grid tied single-stage Conversion System