Other Effective Sampling Methods

Transcription

1 Other Effective Sampling Methods MATH 130, Elements of Statistics I J. Robert Buchanan Department of Mathematics Fall 2018

2 Stratified Sampling Definition A stratified sample is obtained by separating the population into non-overlapping groups called strata and then obtaining a simple random sample from each stratum. The individuals within each stratum should be similar in some way.

3 Example (1 of 2) The president of DePaul University wants to conduct a survey to determine the community s opinion regarding campus safety. The president divides the DePaul community into three groups: resident students (number 6, 204), nonresident (commuting) students (number 13, 304), and faculty and staff (number 2, 401). The president wants to obtain a sample of size 100, with the number of individuals selected from each stratum weighted by the population size.

4 Example (2 of 2) Resident students make up 6204/21, 909 = 28% of DePaul University, nonresident students account for 61%, and faculty and staff constitute 11% of the sample. A sample of size 100 requires a stratified sample of 0.28(100) = 28 resident students, 0.61(100) = 61 nonresident students, and 0.11(100) = 11 faculty and staff. To obtain the stratified sample, conduct a simple random sample within each group. That is, obtain a simple random sample of 28 resident students (from the 6204 resident students), a simple random sample of 61 nonresident students, and a simple random sample of 11 staff.

5 Systematic Sampling Definition A systematic sample is obtained by selecting every k th individual from the population. The first individual selected corresponds to a random number between 1 and k.

6 Example The manager of Kroger Food Stores wants to measure the satisfaction of the store s customers. The manager chooses to use systematic sampling to obtain a sample of 40 customers. The manager decides to obtain a systematic sample by surveying every 7th customer. He randomly determines a number between 1 and 7, say 5. He then surveys the 5th customer exiting the store and every 7th customer thereafter, until he has a sample of 40 customers. The survey will include customers 5, 12, 19,..., 278.

7 Cluster Sampling Definition A cluster sample is obtained by selecting all the individuals within a randomly selected collection or group of individuals.

8 Example A sociologist wants to gather data regarding household income within the city of Boston and decides to use cluster sampling. The city of Boston can be set up so that each city block is a cluster. Once the city blocks have been identified, we obtain a simple random sample of the city blocks and survey all households on the blocks selected. Suppose there are 10, 493 city blocks in Boston. 1. The sociologist must number the blocks from 1 to 10, If the sociologist has enough time and money to survey 20 clusters (city blocks), the sociologist should obtain a simple random sample of 20 numbers between 1 and 10, 493 and survey all households from the clusters selected. Remark: Cluster sampling is a good choice in this example because it reduces the travel time to households that is likely to occur with both simple random sampling and stratified sampling.

9 Convenience Sampling Definition A convenience sample is a sample in which the individuals are easily obtained. Remarks: Often a convenience sample is obtained via self-reporting or voluntary response. Studies that use convenience sampling generally have results that are suspect. The results should be looked on with extreme skepticism.

10 Multistage Sampling (1 of 2) Large-scale surveys obtain samples using a combination of the previous sampling techniques. Nielsen Media Research randomly selects households and monitors the television programs these households are watching through a People Meter. The meter is an electronic box placed on each TV within the household. The People Meter measures what program is being watched and who is watching it.

11 Multistage Sampling (2 of 2) Nielsen selects the households with the use of a two-stage sampling process. Stage 1: Using U.S. Census data, Nielsen divides the country into geographic areas (strata). The strata are typically city blocks in urban areas and geographic regions in rural areas. About 6000 strata are randomly selected. Stage 2: Nielsen sends representatives to the selected strata and lists the households within the strata. The households are then randomly selected through a simple random sample.