Sample Stratification: Key Benefits and Challenges to Stratifying Your Sample

One of the most important tools in survey sampling is stratification, whereby the sample selection process takes place separately within different subgroups (strata). In practice, surveys rarely adopt simple random sampling and instead often rely on some form of stratification for sample selection. Just like any other tool, however, stratification must be employed for the right reasons and implemented properly for its dividends to be realized. Briefly, there are three instances when a stratified sampling design would be preferred over simpler options:

When simple random sampling may fail to provide adequate representation and diversity.
When for analytical reasons, certain small subgroups need to have boosted representations.
When for cost optimizations, units that are “cheaper-to-survey” need to be oversampled.

For any of the above three reasons, instead of selecting a random sample across the entire sampling frame, stratification enables researchers to manage the sample selection process while maintaining the probabilistic nature of the resulting sample. When applied effectively, stratification can also increase the efficiency of a sample by localizing the selection process within subgroups comprised of similar units. In contrast, simple random samples can require a larger size to achieve a comparable level of precision. Effective sample stratification requires three basic elements:

Availability of reliable frame data for all units for creation of sampling strata.
Optimal allocation of the total sample across all strata.
Efficient selection of sampling units within each stratum.

Despite the above attractive features of stratification, it is important to be cognizant of the potential drawbacks of this sampling methodology when it is applied ineffectively or for the wrong reasons. As such, the following cautionary points are noteworthy when considering the pros and cons of stratification:

Effective Stratification

Critical to the creation of effective strata, for any of the three reasons numerated earlier, is the availability of reliable data for all units on the sampling frame. Construction of poor strata, those comprised of heterogenous (dissimilar) units, due to poor frame data can backfire and obliterate all benefits of stratification. Effective sampling strata must include homogeneous (similar) units that are mutually exclusive (have no overlap) and collectively exhaustive (cover the entire frame).

Design Effect

When by design certain units of the population are selected at higher or lower rates, such departures from equal probability of selection method (EPSEM) must be corrected by application of design weighs that reflect selection probabilities. Since unequal weights reduce the effective sample size of a survey, as measured by the following statistic, it is important for stratification to be employed judiciously and for the right reasons. This means excessive departure from an EPSEM design via superfluous stratification can severely reduce the efficiency of a sample.

*_{Departure from an EPSEM design requires design weighting as seen in the image above.}*

Optimal Sample Allocation

In addition to construction of effective sampling strata, the total sample must be optimally allocated across the resulting strata. While proportional allocation is statistically most optimal, disproportional allocation should be justified by the analytical and cost saving needs of a survey. Again, it is important to remember that any departure from a proportional allocation of the sample across strata will have precision costs vis-à-vis the incurred design effect.

Selection of Sampling Units

The final stage of sample selection occurs within each stratum. While an EPSEM option can minimize the sampling error margins associated with the resulting survey estimates, intentional departure from this option should have valid reasons. Unequal selection probabilities, which can have perfectly justifiable reasons, will further decrease the effective sample size of a survey. Lastly, it is imperative to ensure that all eligible units would have known and nonzero (not necessarily equal) chance of selection to preserve the probabilistic nature of the employed sample.