In traditional sampling theory, we occasionally encounter the problem of assigning the sampling units to their correct strata or sub-groups until after the sample is taken. Consider, for example, a survey of ever-married women in a city to estimate the average number of children ever born (CEB) to them.
Since CEB is correlated with the duration of the marriage, the researcher desires to stratify the women by their duration of the marriage and then gather information on the CEB.
A compiled list of all women together with their CEB is available in a recent census report.
Still, unfortunately, the report does not provide any information on the duration of the marriage. A random sample stratified according to the duration, therefore, cannot be implemented. In such a case, one can ‘stratify after selection’ or ‘poststratify.’
A random sample of all ever-married women is selected, and each woman’s duration of the marriage is ascertained at the interview stage. The resultant sample can then be grouped for each duration of marriage after the sample is interviewed and the mean CEB computed for each duration category.
Consider a second example.
Suppose a bank auditor wants to stratify accounts according to whether the accounts are current or savings, but he may not have this information until after an account is actually verified after selection. This is what we call, post-stratification, or stratification after selection.
With this technique, knowledge of the population distribution of some supplementary variable (or variables) as in the above examples is used in the analysis to improve the precision of the sample estimates.