Other Sampling Methods

Transcription

1 Other Sampling Methods Taking a simple random sample may not always be the best approach to sampling. The following are a few other sampling methods, all of which are good substitutes for simple random sampling in most situations. In fact, they often have advantages over simple random sampling. Examples : Suppose you were interested in investigating the link between the family of origin and income and your particular interest is in comparing incomes of Hispanic and Non-Hispanic respondents. For statistical reasons, you decide that you need at least 1,000 non-hispanics and 1,000 Hispanics. Hispanics comprise around 6 or 7% of the population. If you take a simple random sample of all races that would be large enough to get you 1,000 Hispanics, the sample size would be near 15,000, which would be far more expensive than a method that yields a sample of 2,000. One strategy that would be more cost-effective would be to split the population into Hispanics and non-hispanics, then take a simple random sample within each portion (Hispanic and non-hispanic) Let's suppose your sampling frame is a large city's telephone book that has 2,000,000 entries. To take asrs, you need to associate each entry with a number and choose n= 200 numbers from N= 2,000,000. This could be quite an ordeal. Instead, you decide to take a random start between 1 and N/n= 20,000 and then take every 20,000th name, etc Suppose you wanted to study dance club and bar employees in NYC with a sample of n = 600. Yet there is no list of these employees from which to draw a simple random sample. Suppose you obtained a list of all bars/clubs in NYC. One way to get this would be to randomly sample 300 bars and then randomly sample 2 employees within each bars/club. This is an example of cluster sampling. Here the unit of analysis (employee) is different from the primary sampling unit (the bar/club).

2 Stratified random sampling: A stratified random sample is collected by first dividing the population of individuals into groups (strata) and then taking a simple random sample from each group. For example, public opinion pollsters often take separate samples from each region of the country so they can spot regional differences as well as measure national trends. One advantage of using stratified random sampling over simple random sampling is that it allows us to gather separate information about each stratum. In 2008, the United States Senate had 47 Republicans, 51 Democrats, and 2 Independents. The president wants to have a luncheon with 4 Republicans, 4 Democrats and 1 Other. Obtain a stratified sample in order to select members who will attend the luncheon To obtain the stratified sample, conduct a simple random sample within each group. That is, obtain a simple random sample of 4 Republicans (from the 47), a simple random sample of 4 Democrats (from the 51), and a simple random sample of 1 Other from the 100. Be sure to use a different seed for each stratum.

3 Systematic Sampling: Suppose you had a list of 5,000 names and telephone numbers from which you wanted to select a sample of 100. This means you would want to select 1 out of every 50 people on the list. The first idea that might occur to you is to simply choose every 50 th name on the list. If you did so, you would be using a systematic sampling plan. To take a systematic sample, divide the list into as many consecutive segments as you need, randomly choose a starting point in the first segment, then sample at that point in each segment. In the above example, you would randomly choose a starting point in the first 50 names, then sample every 50 th name after that. When you were finished, you would have selected one person from each of 100 segments, equally spaced throughout the list. Example A survey of every 10 th customer who shops at a particular store. Steps involved in Systematic Sampling : Step 1: Determine the population size, N. Step 2: Determine the sample size desired, n. Step 3: Compute N/n and round down to the nearest integer. This value is k. Step 4: Randomly select a number between 1 and k. Call this number p. Step 5: The sample will consist of the following individuals: p, p + k, p + 2k,, p + (n 1)k Problem with systematic sampling is that it can sometimes lead to a biased sample. Example Suppose you were doing a survey of potential noise problems in a highrise college dormitory. Further, suppose a list of residents was provided, arranged by room number, with 20 rooms per floor and two people per room. If you were to take a systematic random sample of, say, every 40 th person on the list, you would get people who lived in the same location on every floor and thus a biased sampling of opinions about noise problems.

4 Cluster Sampling. Cluster sampling is often confused with stratified sampling, but it is actually a radically different concept. To take a cluster sample, divide the population into groups, called clusters, but rather than sampling within each group, we select a simple random sample of clusters and measure all individuals in those clusters. Example Suppose we wanted to sample students living in the dormitories at a college. If the college had 15 dorms and each dorm had six floors, we could consider the 90 floors to be 90 clusters of units. We could then randomly select the desired number of floors and measure everyone on those floors. It would probably be much cheaper and more convenient than obtain a simple random sample of all dormitory residents. One advantage of cluster sampling is that you only need a list of clusters, instead of a list of all individuals.

5 Stratified Sampling and Cluster Sampling are different. Stratified sampling works best when a heterogeneous population is split into fairly homogeneous groups. Under these conditions, stratification generally produces more precise estimates of the population percents than estimates that would be found from a simple random sample. It is important to note that, unlike with the strata in stratified sampling, the clusters should be microcosms, rather than subsections, of the population. Each cluster should be heterogeneous. Additionally, the statistical analysis used with cluster sampling is not only different, but also more complicated than that used with stratified sampling.

6 A convenience sample is one in which the individuals in the sample are easily obtained. Example : Phone polls, Internet polls, Surveys at shopping malls One needs to be extremely skeptical about the results from such sampling. Multistage Sampling : In practice, most large-scale surveys obtain samples using a combination of the techniques just presented. As an example of multistage sampling, consider Nielsen Media Research. Nielsen 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. 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. Nielsen sells the information obtained to television stations and companies. These results are used to help determine prices for commercials.