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

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

The strata

The population

One stratum

The population

One stratum

Anotherstratum

The population

A simple random samplefrom this stratum

The population

A simple randomsample fromthis stratum

A simple random samplefrom this stratum

The population

Simple random samples from all strata

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

The clusters

The population

One cluster

The population

One cluster

Anothercluster

The population

A random sampleof clustersSelect all of these

And all of these

The population

The cluster random sample

Example

Now suppose thatAndy, 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 samplingFrom 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).

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

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