Chapter 13

SAMPLING

Sampling is the process of selecting a number of individuals for a study in such a way that they represent the larger group from which they were selected. A sample comprises the individuals, items, or even selected from a larger group referred to as a population. The purpose of sampling is to gain information about the population baby using the sample. Rarely do studies gather data from the entire population. In fact, not only is it generally not feasible to study the  whole population, it is also not necessary. If the population, it is also not necessary. If the population of interest is large or geographically scattered, study of it would not be feasible or would be prohibitively  costly and time consuming. If a sample is well-selected, research results based on it will be generalizable to the population. The degree to which the sample represents the population is the degree to which  results for one are applicable to the other. The first step in sampling is to define the population. The population is  the group of interest to the researcher, the group to which she or he would like the results of the study to be generalizable. Generalizability is the extent to which the results of one study can be applied to other populations or situations.

Selecting a Random Sample 

Selecting a sample is  a very  important step in conducting a research study. The “goodness” of the sample determines the meaningfulness and generalizability of the results. A good sample is one that is representative of the population form which it was selected. There are several appropriate techniques for selecting a sample. Certain techniques are more appropriate for certain situations; the techniques provide different levels of assurance of sample representativeness. However, as with populations, we sometimes have to compromise the ideal for the real and do what is feasible. This is true for educational as well as for other areas or research. We can’t always have what we want.   

        Regardless of the technique used, the steps in sampling are essentially the same: identify the population, determine the required sample size, and select the sample. There are four basic random sampling techniques or procedures:

• Simple random sampling
• Stratified sampling
• Cluster sampling
• Systematic sampling

They are referred to as probability sampling techniques because it is possible for the researcher to specify the probability, or chance, that each member of a defined population will be selected for the sample. These sampling techniques are all based on randomness in the selection of the sample.

Simple Random Sampling

Random sampling is the process of selecting a sample in such a way that all individuals in the defined population have an equal and independent chance of being selected for the sample. Randomness is sampling  takes the selection of the sample completely out of  the researcher’s control by letting a random, or chance, procedure select the sample. In other words, every individual has the same probability of being selected and selection of one individual in no way affects selection of another individual. You may recall in physical education class the teacher occasionally formed teams by having the class line up and count off by twos—one-two-one-two, and so on. With this method, you could never be on the same team as the person next to you. This selection process was not random, because whether you were on one team or another was determined by where you were in line and the team for which the person next to you was on. If selection of teams had been random, you would have had an equal (50-50) chance of being on either team, regardless of the team status of the person next to you.

        Random sampling is the best single way to obtain a representative sample. Although no technique, not even random sampling, guarantees a representative sample, the probability of achieving one is higher for this procedure than for any other. In most cases, the differences between the sample and the population are small.

Steps in Simple Random Sampling

In general, random sampling involves defining the population, identifying each member of the population, and selecting individuals for the sample on a completely chance basis. One way to do this is to write each individual’s name on a separate slip of paper, place all the slips in a hat or other container, shake the container, and select slips from the container until the desired number of individuals is selected. This procedure is not exactly satisfactory if a population has 1,ooo or more members. One would need a very large hat—and a strong writing hand! A  much more members satisfactory approach is to use a table of random members (also called a table of random digits). Using a table of random numbers to select a sample involves the following specific steps:

1. Identify and define  the population.
2. Determine the desired sample size.
3. List all members of the population.
4. Assign all individuals on the list a consecutive  number from zero  to the required number, for example, 000 to 249 or 00 to 89. each individual must have the same number of digits as each other individual.
5. Select an arbitrary number in the table of random numbers. (close your eyes and point!).
6. For the selected number , look at only the number of digits assigned to each population member. For example, if a population has 800 members, you only need to use the last 3 digits of the numbers; if a population has 90 members, you only need to use the last 2 digits.
7. If the number corresponds to the number  assigned to any of the individuals in the population, then that individual is in the sample. For example, if a population had 500 members and the number selected was 375, the individual assigned 375 would be in the sample; if a population had only 300 members, then 375 would be ignored.
8. Go to the next number in the column and repeat step 7 until the desired number of individuals has been selected for the sample.

        Once the sample has been selected, it may be used as is for survey or correlational studies or randomly subdivided into two or more groups for use in experimental or causal-comparative studies. If there will be only two subgroups, the full sample may be divided by flipping a coin—heads one group, tails the other.

Stratified Sampling

Stratified sampling is the process of selecting a sample in such a way that identified subgroups in the population are represented in the sample in the same proportion that they exist in the population. It can also be used to select equal-sized sample from each of a number of subgroups if subgroup comparisons are desired.

          Alternatively, equal-sized samples would be most useful if you wanted to compare the performance of different subgroups. Suppose, for example, that you were interested  in comparing the achievement of students of different ability levels (high, average, and low) being taught by two methods of mathematics instruction (teacher and computer). Simply selecting a random sample of students and assigning one-half of the sample to each of the two  methods would not (as you know!) guarantee equal representation of each of the ability levels in each method. If fact, just by chance, one of the methods might not have any students from one of the three ability levels. However, randomly selecting students separately for the three ability levels and then assigning half of each ability level to each of the methods would guarantee equal representation of each ability level in each method. The purpose of stratified sampling is to guarantee desired representation of relevant subgroups within the sample.

Steps in Equal-Sized Groups Stratified Sampling

The steps in stratified sampling are similar to those in random sampling except that selection is from subgroups in the population rather than the population as a whole. In other words, random sampling is done more than once; it is done for each subgroup. Stratified sampling involves the following steps:

1. Identify and define the population.
2. Determine desired sample size.
3.  Identify the variable and subgroups (strata) for which you want to guarantee appropriate, equal representation.
4. Classify all members of the population as members of one of the identified subgroups.
5. Randomly select (using a table of random numbers) an “appropriate” number of individuals from each of the subgroups, appropriate in this case meaning an equal umber of individuals.

Cluster Sampling

Cluster sampling randomly selects groups, not individuals. All the members of  selected groups have similar characteristic. For example, instead of randomly selecting from all fifth graders in a large school district, you could randomly select fifth-grade classrooms and use all the students in each classroom. Cluster sampling is most useful when the population is very large or spread out over a wide geographic area. Sometimes it is the only feasible method of selecting a sample. It is not always possible, for example, to obtain or compile a list of all members of the population, as is required by simple random sampling and stratified sampling. Also, educational researchers frequently cannot select and assign individual participants, as they may like. For example, if your population were 10th-grrade biology students, it is very unlikely that you would obtain administrative approval to randomly select and remove a selected view students form different classrooms for your study. You would have a much better chance of securing permission to use several intact classrooms.

Steps in Cluster Sampling

The steps in cluster sampling  are not  very different from those involved in random sampling. The major difference, of course, is that random selection of groups (clusters) is involved, not individuals. Cluster sampling involves the following steps:

1. Identify and define the population.
2. Determine the  desired sample size.
3. Identify and define a logical cluster.
4. List all clusters (or obtain a list) that make up the population of clusters.
5. Estimate the average number of population members per cluster.
6. Determine the number of cluster needed by dividing the sample size by the estimated size of a cluster.
7. Randomly select the needed number of clusters (using a table of random numbers).
8. Include in your study all population members in each selected cluster.

         Cluster sampling can be done in stages, involving selection of clusters within clusters. For example, a district in a state, then schools in the district, and then classrooms in the schools could be randomly selected to sample classrooms for a study. This process is called multistage sampling.

An Example of Cluster Sampling

Let us see how our superintendent would get a sample of teachers if cluster sampling were used. We will follow the steps previously listed:

1. The population is all 5,000 teachers in the superintendent’s school system.
2. the desired sample size is 500.
3. A logical cluster is a school.
4. The superintendent has a list of all the schools in the district; there are 100 schools.
5. Although the schools vary in the number of teachers per school, there is an average of 50 teachers per school.
6. The number of clusters (schools) to be selected equals the desired sample size, 500, divided by the average size of a cluster, 50. thus, the number of schools needed is 500 ÷ 50 = 10.
7. Therefore, 10 of the 100 schools are randomly selected by assigning a number to each school and using a table of random numbers.
8. All the teachers in each of the 10  schools are in the sample (10 schools, 50 teachers per school on average, equals the desired sample size).

          Thus, the interviewer could conduct interviews at 10 schools and interview all teachers in the school instead of traveling to a possible 100 schools. The advantages of cluster sampling are evident. As with most things, however, nothing is all good.

Systematic Sampling

Systematic sampling is not used very often, but it is appropriate in certain situations, and in some instances it is the only feasible way to select a sample. Systematic sampling is sampling in which individuals are selected from a list by taking every Kth name. so what’s a “Kth” name?  That depends on what K is. If K = 4, selection involves taking every 4th name, if K = 10, every 10th name, and so forth. What K actually equals depends on the size of the list and desired sample size. The major difference between systematic sampling and the other types of sampling so far discussed is that all  member of the population do not have an independent chance of being selected for the sample. Once the first name is selected, all the rest  of the individuals to be included in the sample are automatically determined.

Steps in Systematic Sampling

Systematic sampling involves the following steps:

1. Identify and define the population.
2. Determine the desired  sample size.
3. Obtain a list of the population.
4. Determine what K is equal to by dividing the size of the population by the desired sample size.
5. Start at some random place in the population list. Close your eyes and stick your finger on a name.
6. Starting at that point, take every Kth name on the list until the desired sample size is reached.
7. I f the end of the list is reached before the desired sample is reached, go back to the top of the list.

Now let us see how our superintendent would use systematic sampling.

An Example of Systematic Sampling

If our superintendent used systematic sampling, the process would be as follows:

1. The population is all 5,000 teachers in the superintendent’s school system.
2. the desired sample is 500.
3. The superintendent has a directory that lists all teachers in the system in alphabetical order. The list is not randomly ordered, but it is the best available.
4. K is equal to the size of the population, 5,000, divided by the desired sample size, 500. thus K = (5,000 ÷ 500) = 10.
5. Some random name in the list  of teachers is selected.
6. From that point, every following 10th name is automatically in the sample. For example, if the teacher selected instep 5 were the 3rd name on the list, then the sample would include the 13th name, the 23rd, the 23rd, the 43rd, and so forth.

Avoiding Sampling Error and Bias.

Selecting random  samples does not guarantee that they will be representative of the population. Sampling error, which is beyond the control of the researcher, is a reality of random sampling.

Things to remember …

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Sample vs. Population

Two key terms that you must be familiar with are “sample” and “population.” The population is all individuals of interest to the researcher. For example, a researcher may be interested in studying anxiety among lawyers; in this example, the population is all lawyers. For obvious reasons, researchers are typically unable to study the entire population. In this case it would be difficult, if not impossible, to study anxiety among all lawyers. Therefore, researchers typically study a subset of the population, and that subset is called a sample. Because researchers may not be able to study the entire population of interest, it is important that the sample be representative of the population from which it was selected. For example, the sample of lawyers the researcher studies should be similar to the population of lawyers. If the population of lawyers is composed mainly of White men over the age of 35, studying a sample of lawyers composed mainly of Black women under the age of 30 would obviously be problematic because the sample is not representative of the population. Studying a representative sample permits the researcher to draw valid inferences about the population. In other words, when a researcher uses a representative sample, if something is true of the sample, it is likely also true of the population.