Other Sampling Methods Lecture 8 Sections 2.6 – 2.7 Tue, Jan 29, 2008

Stratified Random Sampling Stratified random sample

Stratified Random Sampling Normally the members within each stratum share a common characteristic that they do not share with members of the other strata. That is, each stratum is homogeneous.  Male vs. female.  Resident vs. non-resident.

Stratified Random Sampling The population

Stratified Random Sampling The population The strata

Stratified Random Sampling The population One stratum

Stratified Random Sampling The population One stratum Another stratum

Stratified Random Sampling The population A simple random sample from this stratum

Stratified Random Sampling The population A simple random sample from this stratum A simple random sample from this stratum

Stratified Random Sampling The population Simple random samples from all strata

Stratified Random Sampling The population The stratified random sample

Example Let the population consist of males Andy, Bob, Charlie, Don, Ed, Fred, Greg, and Hank and females Pam, Queeny, Rachel, Susie, Terri, Uzi, Valerie, and Wendy. Choose a stratified sample of size n = 8, where the strata are the two sexes. Is the sample representative with regard to sex?

Why Stratified Samples? If we know the proportion of the population that each group comprises, then we increase our chances of getting a representative sample by using a stratified sample.

Strata vs. Populations We may be genuinely interested in the differences among the strata.  For example, pollsters studying elections routinely categorize their samples by gender, and ethnic group, party affiliation, etc. However, in that case, the strata are better viewed as distinct populations.

Cluster Sampling

Note that it is the clusters that are selected at random, not the individuals. It is hoped that each cluster by itself is representative of the population, i.e., each cluster is heterogeneous.

Cluster Random Sampling The population

Cluster Random Sampling The population The clusters

Cluster Random Sampling The population One cluster

Cluster Random Sampling The population One cluster Another cluster

Cluster Random Sampling The population A random sample of clusters Select all of these And all of these

Cluster Random Sampling The population The cluster random sample

Example Now suppose that  Andy, Bob, Pam, and Queeny live in Fredericksburg.  Charlie, Don, Rachel, and Susie live in Richmond.  Ed, Fred, Terri, and Uzi live in Charlottesville.  Greg, Hank, Valerie, and Wendy live in Roanoke.

Example Use cluster sampling to choose a sample of size n = 8, where the clusters are the cities. Is the sample representative with regard to sex? Is the sample representative with regard to geographic location?

Stratified Sampling vs. Cluster Sampling In stratified sampling  From all of the strata we take randomly selected individuals. In cluster sampling  From randomly selected clusters we take all of the individuals.

Stratified Sampling vs. Cluster Sampling It is done this way because In stratified sampling, the members of a stratum have some characteristic in common (homogeneous). In cluster sampling, the members of each cluster are believed to resemble the entire population (heterogeneous).