Other Sampling Methods Lecture 7 Sections 2.6 – 2.8 Tue, Jan 31, 2006

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

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 random sample from this stratum

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

Stratified Random Sampling The population Random samples from all strata

Stratified Random Sampling The population The stratified random sample

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. 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. 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. 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. However, in that case, the strata are better viewed as distinct populations.

Example Use the Excel file Use the Excel file HSC Prof Tenures Stratified.xls. HSC Prof Tenures Stratified.xls. HSC Prof Tenures Stratified.xls HSC Prof Tenures Stratified.xls Use the two strata Male and Female. Use the two strata Male and Female. Select 5 males and 5 females. Select 5 males and 5 females. Compute Compute Male average years and proportion  15. Male average years and proportion  15. Female average years and proportion  15. Female average years and proportion  15. Compute the overall average and proportion. Compute the overall average and proportion.

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. 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. 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., heterogeneous. It is hoped that each cluster by itself is representative of the population, i.e., heterogeneous.

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

Systematic Sampling 1-in-k systematic sampling 1-in-k systematic sampling Label the members of the population 1 through N. Label the members of the population 1 through N. Select one member at random from the first k. Select one member at random from the first k. Select every k-th member from there on. Select every k-th member from there on. The size of the sample will be approximately N/k. The size of the sample will be approximately N/k. Therefore, if we want sample size n, we should choose k to be approximately N/n. Therefore, if we want sample size n, we should choose k to be approximately N/n.

Example Use the file HSC Prof Tenures.xls. Use the file HSC Prof Tenures.xls.HSC Prof Tenures.xlsHSC Prof Tenures.xls Use systematic sampling to choose a sample of size 10. Use systematic sampling to choose a sample of size 10. What should k be? What should k be? Find the average number of years. Find the average number of years. Find the proportion  15. Find the proportion  15.