1. 5.10: Stratification after Selection of Sample – Post Stratification
Situations can arise in which we cannot place sampling units into their correct strata until after the sample has been selected.
If wish to stratify by gender and we obtain
the sample by telephone survey, respondents
cannot be placed in male or female stratum
until after they have been contacted.
An auditor may wish to stratify accounts by whether they are wholesale or retail, but this information may not be available until after the account has been selected for the sample.

2. 5.10: Post Stratification - 2
Sample of n people selected in a poll; can be divided into n1 men and n2 women after the sample has been interviewed.
Note that n1 and n2 are random b/c they can change from sample to sample even though n is fixed.

3. 5.10 Post Stratification - 3
Since n1, n2,… nL are random, post stratification is not exactly a stratified random sample according to the definition:
A stratified random sample is one obtained by separating the population elements into non-overlapping groups, called strata, and then selecting a simple random sample from each stratum.

4. 5.10: Post Stratification - 4
If Ni/N is known (at least approximately) and if ni ≥ 20 for each stratum, then post stratification is nearly as accurate as stratified random sampling with proportional allocation.
post stratification very common for household and population surveys
Census data provide number of persons, households per area, by age, etc.

5. 5.10 Post Stratification - 5
Post stratification appropriate when a SRS is not properly balanced according to major groupings of the population.
Men
Women
Population is about 50/50 men/women, men underrepresented in sample
Note that Ni/N is known to a good degree of approximation, even though N1, N2, N not known.

6. 5.10 Post Stratification - 6
Recall that ni are random

7. 5.10 Post Stratification - 7 If we had stratified in advance
Penalty for not stratifying in advance