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# Sample Surveys Study Guide (page 3)

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Updated on Oct 5, 2011

## Stratified Random Sampling

Sometimes, the population has natural groups, called strata. As an illustration, when estimating the literacy rate for the nation, estimates of the literacy rate for each state may be useful in assessing state and regional differences. A stratified random sample is one in which the population is first divided into groups (strata) and then a simple random sample is taken within each stratum. Estimates are made for each stratum and then combined to obtain the population estimate. Because the sizes of strata usually vary, a weighted average of the stratum estimates, with weights proportional to the strata sizes (not a simple average), is used to estimate the population parameter.

## Cluster Sampling

Although cluster sampling is often confused with stratified random sampling, it is very different. In cluster sampling, a population is divided into groups, called clusters, a random sample of clusters is selected, and only units in those clusters are measured. In most applications of stratified random sampling, the population is divided into a few large strata and a simple random sample is selected from each stratum. In contrast, in most applications of cluster sampling, the population is divided into many small clusters, a sample of clusters is randomly selected, and every unit in the cluster is measured.

Cluster sampling is often used because it is easier and more cost effective than other alternatives. For example, suppose we want to sample the households in a large city, using door-to-door interviews. It may be very expensive to construct a list of all households, select n addresses at random, and visit each selected household. A cluster sample in which blocks within the city are randomly selected and all households within each selected block are interviewed may be more cost effective. Once a block is selected, the interviewer can conduct several interviews before moving to the next block, reducing the time needed to obtain interviews from the same number of households. However, households within the same block may tend to be more alike than households in different blocks. This tendency of units in the same cluster to be more alike than units in different clusters must be addressed in the analysis. Such approaches are available in books on sampling.

## Systematic Sampling

Suppose that you have a sample frame consisting of a list of 5,000 names and want to draw a sample of 100. To use a systematic sampling plan, we would divide the list into 100 consecutive segments of size = 50, choose a random point in the first segment, and include that unit in the study and every unit at the same point in all segments. Upon completion, the sample would consist of 100 units equally spaced throughout the list. Systematic sampling is also used in many natural resource studies. Here, a grid of points is randomly placed over the region. To randomize, one point, say a corner point, is randomly assigned a location within a small area, and the whole grid is set relative to the random placement of that point.

Systematic sampling can be a good alternative to simple random sampling. If the sample units are randomly listed in the sample frame, the systematic sample is usually treated as a simple random sample. Care must be taken as systematic random sampling could lead to biases. The potential biases associated with treating a systematic sample as a simple random sample when using a grid have been discussed in the natural resources literature.

## Multistage Sampling

Many large surveys use a combination of the methods we have discussed. As an illustration, a large national survey may first stratify by regions of the country. Within each regional stratum, we might then stratify by state. Within each state, we could stratify by urban, suburban, and rural areas. We could then randomly select communities within each of the urban, suburban, and rural strata. Finally, we could randomly select blocks or fixed areas within each selected community and interview everyone within that fixed area. A multistage sampling plan is one that combines methods as illustrated here.

## Random-Digit Dialing

Most of the national polling organizations and many of the government surveys in the United States now use a sampling plan called random-digit dialing. This method approximates a random sample of all households in the region of interest that have telephones. To initiate a random-digit dialing plan, the polling organization must first get a list of all telephone exchanges in the region of interest. A telephone exchange consists of the area code and the next three digits. Using the numbers listed in the white pages, the proportion of all households in the region with that specific exchange can be approximated. That proportion is used to determine the chance that the telephone exchange is randomly selected for inclusion in the sample. Next, the same process is followed to randomly select banks within each exchange. A telephone bank consists of the next two numbers. Finally, the last two digits are randomly selected from 00 to 99. Although the process is quite involved, it has been computerized, and random telephone numbers can be generated rapidly.

Once a telephone number has been generated, pollsters should make multiple attempts to reach someone at that household if no one responds initially. They may ask to speak to a male or an adult because females and children are more likely to answer the phone, potentially biasing the results because they are overrepresented in the sample.

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