In stratified sampling, the N population units are grouped into L strata, independent samples are selected from within each stratum, and unbiased estimation is achieved as a weighted average of stratum-specific estimates. Strata may be natural—pool, riffle, and run habitat unit types in a small stream—or strata may be constructed to ensure that some units from specific groups of population units will always be included in the sample. Within strata, any unbiased method of selection can be used. If SRS is used within strata, this is a stratified SRS design. Allocation of the total stratified sample of size n across the L strata can affect sampling variance of stratified estimators. Optimal allocation theory shows that optimal stratum-specific sample sizes depend on relative numbers of units in strata, and stratum-specific costs per unit of sampling and variances of y values. An ANOVA sums of squares partition can be used to show that a proportionally allocated stratified SRS strategy will outperform selection of a single SRS with mean-per-unit estimation whenever the average variation within strata is less than the finite population variance. Therefore, it is desirable to minimize variation within strata and maximize the variation in stratum means. For a variety of reasons, post-stratification, in which one large SRS is stratified after the sample has been selected, may often be a good alternative to selection of a (pre-) stratified sample.
Estimation of Sensitive Attributes Using a Stratified Kuk Randomization Device
