PROBABILITY SAMPLING We are going to discuss four different types of probability samples: simple random, systematic, stratified, and cluster or area sampling. Simple random samples are defined as those for which (a) the probabilities of selection are equal for all elements, and (b) sampling is done in one stage with elements of the sample selected independently of one another in contrast to more complex samples where the selection is done in two or more stages and where clusters rather than individual elements are chosen. Suppose you wanted to interview a random sample of the players who participated in a recent baseball game. You have a list of the players for the two teams.
First, assign a number to each player on the list as already done above. Next, decide how many players you intend to interview. Let's say you want to choose six players for your sample. Using a table of random numbers, an example of which is at the end of this report (Note: Most statistics textbooks include tables of random numbers. Tables can also be self-generated through the use of computer software.), you are going to need six two-digit numbers ranging from 01 to 28. Add a zero in front of the single-digit numbers to make it possible to choose systematically. Then you may begin anywhere in the table and can proceed in any direction, noting down two digits at a time as you come to them, until you have six such pairs. Let us begin with the last-two digits in the second column from the left at the top of the table and proceed down the column. The first six numbers we come to that fall between 01 and 28 will be the numbers of the players to be interviewed. The numbers randomly selected are 11, 07, 05, 16, 28, 01. Now, refer to the list of players to see who is in the sample.
You now have a simple random sample of players from the game. However, you may feel your sample is lopsided. You have a genuine random sample, but you have more players from one team than the other. The population consists of two teams equal in size, having fourteen players each. If you decide that you want the teams to be equally represented in your sample, you can arrange it by randomly sampling from each team separately, using a technique called stratified random sampling. To generate a stratified random sample, begin by renumbering the Underdogs from 1 to 14. Then go again to the table of random numbers and select three numbers for each team, using the same method as before. Now, however, you must eliminate any number over fourteen. If you begin in the same place as before, you get 11, 07, and 05 for the Stat-Team, or Bob, Linda A. and Ethel. Continuing to select numbers gives you 01, 13, and 11 for the Underdogs, or Bertha, Joe and Trish. Note that if a number previously selected for the Stat-Team also comes up for the Underdogs, that would be acceptable; the groups are being sampled separately, and duplication of a number does not mean an individual will be interviewed twice. Another way to sample from a list is called systematic sampling. It consists of selecting at predetermined intervals. In our baseball teams example number the names as before from 1 to 28. Next, decide on the sample size, also as before. For this example, let's use seven as a sample size. Continuing with the example, you would, therefore, want seven names out of 28 or every fourth name. However, you cannot arbitrarily begin with the first player and take 1, 5, 9, 13, 17, 21, 25; that would give you a biased, rather than a random, sample. To eliminate bias, use any method of random selection, randomly choosing a number from 1 to 4 (since you are choosing every fourth name) and beginning with that number. The table of random numbers can be easily used for this purpose. Let's say the number randomly selected as our starting point is three. This gives you 3, 7 (3+4), 11 (7+4), 15 (11+4), and so forth. Your systematic sample consists of Darlene, Linda A., Bob, Bertha, Arminta, Dawn and Joe. When the population to be sampled is too large for simple random sampling because the process would be time consuming and expensive, then cluster or area sampling is a way to sample randomly in progressively smaller populations. Suppose you need a random sample of general hospitals in the United States. If you simply list all general hospitals and select a sample using one of the techniques we have discussed, you would find yourself with a cumbersome sample, especially if you intend to visit each general hospital in your sample. To gather a cluster or area sample, first list all states and territories in the United States, and then select a random sample, as we have done above. Let's assume you have randomly chosen five states: Colorado, Indiana, Florida, Pennsylvania and Oregon. You have now completed the first stage of your multistage or cluster sampling. Next, list the general hospitals in each of the five states chosen in the first stage. Again you select a random sample of general hospitals from each of the states. This sample would contain your ultimate subjects. Whatever sampling technique you choose make certain that all variations in your chosen population have a chance to be represented in the sample. If you can succeed in this, you will avoid bias and will be able to generalize from the sample to the population. In practice, often the techniques described above are combined in a complex sampling design. Again, we recommend you consult someone very familiar with sampling techniques to assist you in obtaining a truly representative sample and also in determining your sample size. RANDOM NUMBER TABLE
|
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
