The Advantage and Disadvantage of Implicitly Stratified Sampling

Explicitly stratified sampling (ESS) and implicitly stratified sampling (ISS) are well-established alternative methods for controlling the distribution of a survey sample in terms of variables that define the strata. If these variables are correlated with survey estimates, the estimates will benefit from improved precision. With ESS, unbiased estimation of the standard errors of survey estimates is possible, provided that sampling strata membership is identified on the survey dataset. With ISS this is not possible and usual practice is to invoke an approximation that tends to result in systematic over-estimation of standard errors. This can be perceived as a disadvantage of ISS. However, this article demonstrates, both theoretically and through a simulation study, that true standard errors can be smaller with ISS and argues that this advantage may be more important than the ability to obtain unbiased estimates of the standard errors. The simulation findings also suggest that the extent of over-estimation with the usual approximate variance estimator may be modest.