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Stratified Sampling

Sample selection is said to be stratified if some form of random sampling is separately applied in each of a set of distinct groups formed from all of the entries on the sampling frame from which the sample is to be drawn. By strategically forming these groups, called “strata,” stratification becomes a feature of sample designs that can improve the statistical quality of survey estimates. Procedurally, stratum formation and sample allocation to strata are important preliminary steps to sample selection. After the sample has been selected, data are gathered from its members, and analysis accommodating the use of stratification is conducted.

Stratification and sampling clusters are sometimes confused, as both involve groups of one form or another. These two design features are distinguishable by how sampling is applied to the groups. Whereas sampling is done within each of the groups (strata) in stratified samples, only some of the groups (clusters) are randomly selected in cluster samples.

Stratified sampling is statistically beneficial in two ways. First, it may be used to enable the sample to better represent the measurements that define the mean, total, or other population characteristics to be estimated from the sample. A sample also may be stratified to promote adequate sample sizes for analysis of important subgroups of the populations, such as racial/ethnic minority groups.

Forming Strata

Strata are formed by deciding on one or more stratification variables and then defining the actual strata in terms of those variables. Improving the statistical quality of sample estimates through stratification implies that the stratification variables should (a) be statistically correlated with the measurements that define the main population characteristics to be estimated, (b) effectively isolate members of important analysis subgroups, or both. Indeed, the first goal implies that useful strata will be internally homogeneous with respect to the main study measurements, while the second goal suggests that key subgroups should be identifiable by one or more strata. Although the number of formed strata need not be large, it should be large enough to meet the needs of later analysis.

There are two common misconceptions about stratum formation. One is that subgroup analysis will be valid only if the subgroups are defined by those comprising one or more sampling strata. In fact, valid estimates can be produced for subgroups defined by portions of one or more strata, although their precision will be slightly less than if complete strata define the subgroup. Another myth is that incorrect stratum assignment (e.g. due to measurement error in the values of the stratification variables) will invalidate sample estimates. In reality, bias does not result from stratum assignment errors provided random selection is done in each stratum, although the precision that is gained from strata with assignment errors may be compromised by these errors.

Sample Allocation to Strata

Deciding how a stratified sample will be distributed among all strata is called “stratum allocation.” The most appropriate allocation approach depends on how stratification is being used. If, for example, the main purpose of stratification is to control sample sizes for important population subgroups, stratum sample sizes should be sufficient to meet precision requirements for subgroup analysis. A special case of this occurs when the subgroups of interest are explicitly defined by individual strata (e.g. stratification by geographic region) and an important part of analysis is to produce comparisons among all subgroup strata. In this instance, equal allocation (i.e. equal sample sizes) among subgroups would be appropriate. Meeting sample size needs for subgroups usually makes the allocation disproportionate, wherein sampling rates differ among strata.

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