Other Sampling Methods

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Presentation transcript:

Other Sampling Methods Lecture 7 Sections 2.6, 2.8 Wed, Sep 13, 2006

Stratified Random Sampling Stratified random sample – A sample selected by First, dividing the population into mutually exclusive groups, or strata, Then, taking a simple random sample from each stratum. Normally the members within each stratum share a common characteristic that they do not share with members of the other strata, i.e., each stratum is homogeneous. For example, male vs. female.

Stratified Random Sampling The population

Stratified Random Sampling The strata The population

Stratified Random Sampling One stratum The population

Stratified Random Sampling One stratum Another stratum The population

Stratified Random Sampling A random sample from this stratum The population

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

Stratified Random Sampling Random samples from all strata The population

Stratified Random Sampling The stratified random sample The population

Example Let the population be Alberto, Beryl, Chris, Debby, Ernesto, Florence, Gordon, and Helene. Choose a stratified sample of size n = 4, 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 Cluster Sampling – The units of the population are grouped into clusters. One or more clusters are selected. All members of the selected clusters are in the sample. 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 clusters The population

Cluster Random Sampling One cluster The population

Cluster Random Sampling One cluster Another cluster The population

Cluster Random Sampling A random sample of clusters The population

Cluster Random Sampling The cluster random sample The population

Example Let the population be Alberto, Beryl, Chris, Debby, Ernesto, Florence, Gordon, and Helene. Suppose Alberto, Beryl, Chris, and Debby live in Richmond and that Ernesto, Florence, Gordon, and Helene live in Lynchburg. Use cluster sampling to choose a sample of size n = 4, where the clusters are the two cities. Is the sample representative with regard to sex?

Stratified Sampling vs. Cluster Sampling In stratified sampling The members of a stratum have some characteristic in common (homogeneous). From all of the strata we take randomly selected individuals. In cluster sampling The members of each cluster are intended to resemble the entire population (heterogeneous). From randomly selected clusters we take all of the individuals.

Variability In stratified sampling, the variability within the strata should be less than the variability between strata. (homogeneous strata) In cluster sampling, the variability between the clusters should be less than the variability within clusters. (heterogeneous clusters)