EDUR 7130
Educational Research On-Line

Sampling

Definition and Purpose of Sampling

Sampling is the process of choosing a group of subjects who, hopefully, represent well the population from which the group was selected. The primary purpose of sampling is to learn about the population from information obtained from the sampled subjects. In short, one would like to make inferences from the sample to the population. Samples are used primarily because populations are almost impossible to work with, especially in education. For example, rather than research all 3rd graders in the US, one would take a sample of 3rd graders in the nearby school.

Definition of Population

Researchers are usually interested in making general statements about something. For example, if one is researching an instructional strategy, like cooperative learning, one would like to be able to say that cooperative learning has a given effect on achievement for all students within given parameters. These given parameters are what defines the population. Or, stated differently, populations have distinguishing characteristics—attributes that identify one group of subjects from another. For example, if the population is defined as U.S. 3rd graders, then the distinguishing characteristics are: U.S. student, 3rd grade student. So we know instantly, for example, that 4th grade students or Canadian students are not part of the population.

The problem with a population like U.S. 3rd graders is that the group is so large, it is difficult to work with practically. So if a researcher wanted to perform an experiment to learn whether cooperative learning benefits 3rd graders, it would be impractical and too expensive to use all U.S. 3rd graders in the study. This is where sampling helps. Sampling allows one to select a small subset of a population to use for a study. Hopefully, the sample will be representative of the population, so anything learn in the study from the sample will also work, or hold for the population as well.

When samples are selected, one generally wants to make inferences, or generalizations, from the sample to the population. So whatever is learned about the sample will apply to the population. For this to occur, that is for accurate generalizations to occur, it is necessary that the sample be representative of the population, i.e., the sample should resemble accurately the population. For instance, in the US the racial mix in the population is approximately 72% White, 13% Black, 12% Hispanic, and about 3% everyone else. So if a sample was selected from the US, hopefully these percentages would hold in the sample. If the percentages varied greatly, say for example 50% of the sample was Black, then it is likely that any information learned from the sample will not hold for the population.

Populations may be classified into two types, target and accessible. The target population is the group one wishes to generalize to or make inferences about. The accessible population is the group from which subjects are selected; this is the population from which one can realistically sample from. Note that in some cases the target and accessible populations are the same, but in others they are not. For example, my target population may be US 3rd graders, but I can realistically expect to sample 3rd graders only from my school district. So 3rd graders in my school district would be the accessible population. There is always the possibility that my accessible population is not representative of the target population.

Methods for Selecting Samples

To sample, one must identify the population, determine the sample size needed (how many people to include in the sample), and then decide how to select the sample. Identifying the population is one of the first steps in research, and is often done once a research topic is selected. For example, if I wanted to see how competency testing influences students to dropout of school, my population is defined without any effort from me because only high school students are subject to competency testing.

When reading research reports and articles, one will almost always see reported the size of the sample used in the study. In most cases sample size is denoted by the symbol N. For example, in one of my studies I had a sample size of 98 students, thus N = 98. In most cases researchers want sample sizes that are large as possible because the larger the sample, the greater the likelihood that the sample represents the population and the more information that can be obtained from the sampled people. Remember this: Larger samples, if possible to obtain, are always better.

There are two general methods for selecting samples, probability and non-probability. In probability sampling (a) one can calculate the probability, or chance, that a given person will be selected for inclusion in the sample. That is, one can actually determine the likelihood of a particular subject being selected for the sample. For example, if there are 15 people in the class and we are to select 1 person as our sample, then each person has a 1/15 chance of being selected for the sample. In addition, to (a) above, probability sampling methods are characterized by (b) the systematic application of randomization in the selection process. This simply means that people are selected from the population in a manner that is systematically arbitrary and unpredictable.

How can something be selected in a systematically arbitrary way? Most of you are familiar with the analogy of drawing names from a hat. Randomized selection can be done in a systematic method, and represents entirely an arbitrary selection procedure. For example, placing names in a hat, mixing the names, then blinding drawing names from the hat represents a systematic procedure (names in hat, mixing names, then blinding drawing name) that arbitrarily selects (since the drawing is blind, we don't know which name will be selected and all names have the same chance of selection).

Such a systematically arbitrary method for selecting subjects from a population is used in all probability sampling techniques, and this procedure is referred to as randomized selection. The most common and well known form of randomized selection is Simple Random Sampling, which is described below.

Types of Probability Sampling Techniques

(1) Simple Random Sampling (SRS)

With SRS, one attempts to select people for the sample in a manner that ensures that all people in the population of interest have an equal and independent chance of being selected. That is, one person's chance of being selected is the same as someone else's chance of being selected. So, equal means everyone has the same chance, and independent means that selecting one person does not preclude the selection of someone else.

Blindly drawing names from a hat is an example of SRS. In educational research, typically people are randomly selected using random numbers. Random numbers can be generated in a variety of methods, and the most frequently used is computer programs. Before computers, researchers typically consulted a table of random numbers, and these can still be found in most educational research texts, but to facilitate discussion, a table of random numbers is provided below.

Table of random numbers.

 Rows Columns 1 2 3 4 5 1 09149 04999 77422 25992 27372 2 94157 43252 83266 47196 94045 3 10075 34237 46293 46178 50110 4 78907 37586 50940 88094 28209 5 02548 10236 02541 85471 59614 6 12159 56987 95424 06458 21578 7 82843 43383 32561 62108 46076

How would this table be used? Suppose we had a population of 20 people, and we assign a unique, consecutive number to each person. Table 1 below illustrates this.

Table 1. Individuals in a Population and Their Unique Identification Number

 Unique Number Person Unique Number Person 1 Bill 11 Bonnie 2 Bertha 12 Bathsheba 3 Barney 13 Barbara 4 Betty 14 Brunhilda 5 Brian 15 Boris 6 Bryan 16 Basil 7 Brent 17 Brooke 8 Brenda 18 Bevis 9 Brett 19 Bryanna 10 Blinda 20 Burt

Let us suppose we wish to select, randomly, 5 of these 20 to serve as the sample. To use the table of random numbers, we would start somewhere and then move either up or down through the table in a consistent fashion. If the table provides a two-digit number that is between 01 and 20, then that person is selected for the sample. To illustrate, we will start on the first row and the first column on the Table of Random Numbers above, and we use the first two columns (first two digits) for the two-digit numbers. The numbers in the table, reading down the column, are:

09, 94, 10, 78, 02, 12, 82

then we can move over two spaced (still in Column 1) and use the next two digits:

14, 15, 07, 90, 54, 15, 84

and follow the same pattern until we obtain the sample size desired. So in this example, the random numbers are:

09, 94, 10, 78, 02, 12, 82, 14, 15, 07, 90, 54, 15, 84

The first five unique and usable numbers that we obtain from the table are in bold and underlined. So the people selected for our sample include

09 Brett
10 Blinda
02 Bertha
12 Bathsheba
14 Brunhilda

When researchers use random selection, like SRS, for a study, this will typically be identified in the "Participants" section of the research paper (see Format of a Research Paper for more details on "Participants"). In most cases researchers will report the use of randomized selection by stating clearly that it was used. For example, research my write something like: Students were randomly selected from three classes for participation in shock treatment observations.

A closely related sampling technique is randomized selection in which not all individuals have an equal chance of selection. With this type of sampling, everyone has an independent chance of being selected, but they may not have an equal chance of being selected. Using the name in a hat analogy, one person may have their name in the hat twice while all others have their name in the hat once. While the chances of selection are not equal for all people, the chance of selection may still be independent since selection will be random.

See your text's discussion of random sampling to learn of the steps involved in selecting via a randomized process.

(2) Stratified Random Sampling

Suppose one is interested in selecting a sample from a given population, but thinks that it is important to consider some characteristics of the individual when studying the sample. For example, a very simple descriptive study is to select people and ask them if they have watched at least 5 minutes worth of a fishing program in the last year. Do you think it is likely that the percentage of people who have watched 5 minutes of a fishing program during the last year varies between men and women? Who is more likely to watch fishing, men or women? For this study, random sampling may not be the best procedure for selecting the sample. Why? With a random sample, is there any guarantee that both men and women will be selected? If the selection process is truly random, then it is possible that only men or only women could be selected. If this occurred, then we could not answer the question of whether there is a difference in watching habits between men and women.

Stratified random sampling is a sampling procedure that overcomes this potential problem with SRS. With stratified random sampling, the population is first divided into strata (unique groups, e.g., men and women), and then SRS be done from each and every stratum identified. Continuing with our example, the population would first be divided into two groups, men and women. Next, a sample would be selected only from men, then a sample would be selected only from women. By selecting two samples, one from each group, we are guaranteed to have a sample of both men and women.

As noted above, the groups used to build the stratified sampling scheme represent a variable thought to be important in the study. Thus, strata are usually derived from some variable thought to be important to the study. For example, in the investigation of possible test item bias on a minimum competency test, one would want to stratify the sample by the variable race such that the following strata will result: White, Black, Hispanic, Asian, American Indian, etc. In selecting the sample, one would use a SRS from each and every group identified. By randomly selecting people from each group, one ensures that each group will be represented in the sample.

Two types of stratified random sampling exists, proportional and non-proportional (or equal sized). With proportional sampling, one selects sample sizes for each strata according to the proportional representation in the population for each strata. For instance, with the above example one might select 75 Whites since Whites are approximately 75% of the U.S. population. Similarly, about 12 Blacks will be selected and 10 Hispanics since they make-up about 12% and 10% of the U.S. population respectively.

With non-proportional sampling, one usually selects equal sized samples for each of the strata. Thus, 50 Whites, 50 Blacks, 50 Hispanics will be selected. Non-proportional stratified sampling is used when one is interested in having samples large enough to allow generalizations to each of the subgroups (strata), while proportional sampling is used when one wishes to generalize to the total population.

To illustrate the difference in interpretations that can be drawn from the two types of stratified sampling, consider the following. Suppose there is an issue in which strong differences in opinion exist among Blacks, Hispanics, and Whites. Further, suppose that 100% of Blacks and Whites support the issue, but that 0% of the Hispanics support the issue. Table 2 shows the percentage of support in the population.

Table 2: Percentage of Support in Population by Black, Hispanic, and White Classifications

 Race Percent Supporting Percent Not Supporting Percent of Population Black 100 0 13 Hispanic 0 100 12 White 100 0 75

Note from Table 2 that the population is 75% White, 13% Black, and 12% Hispanic. If a proportional stratified sample were selected, the numbers of Blacks, Hispanics, and Whites selected will be in proportion to the percentage representation in the population. So if 100 people were selected, 75 would be White, 13 Black, and 12 Hispanic. In this case, the results of the survey would show that 75 + 13 = 88 or 88% of the people surveyed support the issue, while 12% of the people (Hispanics only) do not support the issue. This figures agree with what is found in Table 2, and is the correct interpretation for the population as a whole. So, using a stratified sample, one may generalized from the sample to the population.

Now if we were to use a non-proportional stratified sample, we might take equal sized samples of 33 per group. Thus, 33 Blacks, 33 Hispanics, and 33 Whites would be selected. In this sample, we could not generalize to the population as a whole since the percentages by racial category are not equal to the percentages in the population. For example, using this sample, we would mistakenly claim that 33 + 33 = 66 or about 66% of the people (Blacks and Whites) agree with the issue while 33% (Hispanics) do not agree with the issue. As this shows, drawing generalizations to the population from a non-proportional stratified sample may present misleading information.

The reason one may use a non-proportional stratified sample is to allow one to make generalizations not the the overall population, but rather to the specific subgroups. In a proportional stratified sample, there may not be enough people in some subgroups to allow for accurate description of how subpopulations think about an issue (e.g., only 12 selected for Hispanics), but with non-proportional stratified sampling, one may selected a larger number of people from each subgroup with the intention of generalizing only to the subgroups, not to the population as a whole.

(3) Cluster Sampling

Cluster sampling is the random selection of groups or clusters from among a larger number of groups or clusters in the population. Note that not all clusters or groups will be represented in this sampling procedure. For example, one may be interested in learning how teachers react to a new state-wide policy. One method for selecting teachers to interview would be to first identify each school in the state, then to randomly select a given number of schools (say 10), and to interview the teachers in the school. This would be a cluster sample. Note that with cluster samples, one does not attempt to randomly select individuals first, rather groups or clusters are randomly selected first. The key with cluster sampling is to determine what is first being selected. If groups of individuals are selected, first, then cluster sampling is being used. In the example just given, one could randomly select ten schools (cluster sampling), then follow that by randomly selecting a few teachers from each school that was selected. So with cluster sampling, one first randomly selects groups, then one selects individuals from the groups. This second stage, the selection of individuals, may be done randomly or non-randomly (like using all people available in the school).

(4) Systematic Sampling

Systematic sampling is perhaps the easiest sampling procedure to identify and use. One simply forms a list of subjects, randomly picks a subject near the top (beginning) of the list, and then picks every nth or kth subject from list. Some argue that systematic sampling is not a probability sampling technique (which is correct), but the results obtained from systematic sampling usually approximate well SRS.

What does it mean to pick every nth or kth subject from the list? If we had a list of 100 people and each person had a unique number assigned to them (like in Table 1 above) with the numbers ranging from 1 to 100, and we wanted to select 4 people for the sample, we would first randomly select one person with a number between 1 and 25. Assume number 19 is selected. To complete the sample selection, we would then skip every 25th person, so we would select, starting with person 19, person 44, person 69, and person 94.

Using the sample example, assume we wished to select 10 people out of 100. We would randomly select one person with a number between 1 and 10, then we would skip every 10th person. If the first person selected was number 3, then we would select, skipping every 10th, person 13, 23, 33, 43, 53, 63, 73, 83, and 93 for a total sample size of 10 people.

Types of Non-probability Sampling Techniques

First, in non-probability sampling one cannot calculate the probability of selection for a given subject—that is, one cannot determine the likelihood of a particular subject being selected for inclusion in the sample. The reason that calculation is not possible stems from the fact that non-probability sampling does not require the use of a list of subjects from which random selection occurs. Second, non-probability sampling procedures are usually characterized by a lack of a systematically randomized form of selection. Usually non-probability sampling procedures use a form of convenience selection--using whoever is available--so randomized selection does not often play a role.

(1) Convenience Sampling

Convenience sampling is the selection of subjects based upon convenience, ease of use, or accessibility—such as the use of volunteers. The selection process with convenience sampling is void of any form of a systematic application of randomized selection.

In educational research, the most common example of convenience sampling is the use of classroom students for a study. For example, a research may wish to perform an experiment to determine if cooperative learning provides better achievement outcomes than lecture. If the researcher is teaching two courses, then is it convenient to use one class with cooperative learning and the other with lecture. Since students were not randomly selected to be included in the study (or class), this represents convenience sampling.

As another example, a researcher may ask students in his class to volunteer to participate in a study. This too represents convenience sampling since students were not randomly selected.

(2) Judgment (or Purposive) Sampling

Judgment sampling is similar to convenience sampling except that subjects are selected based upon the researcher’s judgment as to their representatives of the population. What the researcher deems important about the population is used to shape the researcher’s judgment as to who should be included in the sample. An important drawback of this type of sampling is that the researcher’s judgment may be in error thus rendering the sample unrepresentative of the population. As with other non-probability sampling techniques, judgment sampling is void of any form of systematic selection procedures based upon a randomized selection process.

(3) Quota sampling

Quota sampling is essentially a judgment sample in which specified numbers of subjects meeting select criteria are chosen. For example, an interviewer may be instructed to survey the first 20 Black males who exit the student union.

Note that non-probability sampling is more likely to introduce bias into the sample. Bias is anything that systematically reduces the representativeness of the sample, i.e., reduces the chance that the sample will adequately represent, or reflect, the population. The less representative the sample, the less likely that the sample results will generalize to the population. Thus, the less representative the sample, the less generalizable the sample to the population. So, when one speaks of a biased sample, what they are referring to is the a that does not look like the population and the reason it does not look like the population can be explained by a problem with how the sample was selected.

For example, if one were interested in learning how residents of a city viewed a new law, interviewing shoppers at 2:30 in the afternoon at the local mall on a weekday may produce a biased sample because most employed individuals will not be shopping at that time.

Determining Sample Size (N)

Determining sample size involves knowledge of statistical inference, which statistical procedure will be used to analyze the data, effect size, and how the these work in combination. The methods for determining sample size discussed in your texts are simplified and may not be the most accurate. To get a more accurate accounting of sample size determination, please see one of the following texts:

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Erlbaum.

Kish, L. (1965). Survey sampling. New York: Wiley.

Lipsey, M. W. (1990). Design sensitivity: Statistical power for experimental research. Newbury Park, CA: Sage.

As pointed out above, when selecting a sample, it is usually best to select a sample that is as large as possible. The reason is that larger samples are usually more representative of the population because larger samples provide more information than smaller samples.

Practice Exercise for Sampling

Instructions:
Answer the questions listed below each example. Note that each example represents one of the following sampling procedures: random, stratified, cluster, systematic, and convenience. For the purposes of this exercise, simply label all non-probability sampling examples as convenience sampling.

1. A number is assigned to fifty people, the numbers are placed in a basket, and a judge blindly draws ten numbers from the basket.

What type of sampling was used?

2. A psychology professor requires his introductory psychology class to participate in an experiment.

What type of sampling was used?

3. A principal, interested in determining the opinion parents hold toward a new busing policy, decides to select three sets of parents from each grade level in the school and asks them to fill out a questionnaire.

What type of sampling should be used?

4. A reporter, interested in conducting interviews about the President’s foreign policy, picks the first three people who look as if they keep informed of the news.

What type of sampling was used?

5. A principal, interested in determining teacher satisfaction with a new school policy, decides to select three of the twelve grades represented in the school, and to interview all the teachers within those three grades selected.

What type of sampling should be used?

6. A principal, interested in determining teacher satisfaction with a new school policy, decides to select three of the twelve grades represented in the school, and to interview three randomly selected teachers from each grade level selected.

What type of sampling should be used?

7. The same principal, interested in determining teacher satisfaction with a new school policy, decides to select three teachers from each grade level for an interview.

What type of sampling should be used?

8. The same principal, interested in how teachers feel about the new library, asks the secretary to type a list which includes all teachers in the school. The principal takes the list, assigns numbers to the list, and looks in the newspaper for the daily lotto numbers. The lotto numbers corresponding to the numbers beside the teachers’ names will determine who will be selected.

What type of sampling was used?

9. Using the same list described above, the principal decides to interview every tenth teacher.

What type of sampling was used?

10. Nick Henry, interested in what the faculty have to say about research support, randomly selects five departments and interviews all faculty members in the departments selected.

What type of sampling was used?

11. A researcher, studying the effects of shampoo on rats’ diets, assigns numbers to 20 rats. The researcher then places these numbers in a box; however, the researcher places each female rat’s number in the box 10 times and only places the male rats’ number in the box once. The researcher then blindly selects one number for the experiment.

What type of sampling was used?

12. A researcher places the names of 150 subjects in a box, mixes them thoroughly, and then draws out the names of 25 individuals to interview.

What type of sampling was used?

13. A science teacher is interested in how students feel about a new textbook. She also intends to compare the achievement of students using the more traditional book with those using the new book. Based upon past experience, she believes sex may also have an effect on achievement, so it is important that she gets an adequate sample for both males and females.

What type of sampling should be used?

14. A researcher is interested in how North Carolina teachers feel about a new state mandated policy. The names of all teachers are obtained and listed alphabetically. Next, the researcher assigns numbers to the list so everyone has a distinct number. Using a table of random numbers, the researcher then selects 25 teachers to survey.

What type of sampling was used?

15. The principal of a large middle school with over 1000 students wants to know how students feel about the new menu in the school cafeteria. She obtains the names of all students and has them listed alphabetically. Unique numbers are assigned to every student on the list. Next, she places the numbers one through ten in a hat and randomly selects one. She chose the number nine, so she decides to pick every student whose number ends in nine, e.g., 9, 19, 29, 39, etc.

What type of sampling was used?

16. A state superintendent is interested in how teachers feel about merit pay. There are 10,000 teachers in all the elementary and secondary schools in the district, and there are 83 schools district-wide. To facilitate surveying, the superintendent decides to select randomly a few schools and to send surveys to the teachers within those selected schools.

What type of sampling was used?

17. To find out how students feel about food service in the student union at GSU, the manager stands outside the main door of the cafeteria one Monday morning and interviews the first fifty students who walk out of the cafeteria.

What type of sampling was used?

18. A high school counselor interviews all students who come to him for counseling about their career plans.

What type of sampling was used?

19. A news reporter for a local television station asks passersby on a downtown street corner their opinions about plans to build a new baseball stadium in a nearby suburb.

What type of sampling was used?

20. A university professor compares student reactions to two different textbooks in her statistics classes.

What type of sampling was used?

21. An eighth-grade teacher chooses the two students with the highest GPA in her class, the two whose GPA falls in the middle of the class, and the two with the lowest GPA to learn how her class feels about including a discussion of current events as a regular part of classroom activity. Similar samples in the past have represented the viewpoints of the total class quite accurately.

What type of sampling was used?

1. A number is assigned to fifty people, the numbers are placed in a basket, and a judge blindly draws ten numbers from the basket.

What type of sampling was used?

• This best illustrates SRS (simple random sampling).

2. A psychology professor requires his introductory psychology class to participate in an experiment.

What type of sampling was used?

• Convenience sampling (no randomized selection indicated here).

3. A principal, interested in determining the opinion parents hold toward a new busing policy, decides to select three sets of parents from each grade level in the school and asks them to fill out a questionnaire.

What type of sampling should be used?

• Stratified -- grade level is the stratification variable and parents should be randomly selected from each and every grade level.

4. A reporter, interested in conducting interviews about the President’s foreign policy, picks the first three people who walk by on the street.

What type of sampling was used?

• Convenience--no form of randomized selection from an identified population was used.

5. A principal, interested in determining teacher satisfaction with a new school policy, decides to select three of the twelve grades represented in the school, and to interview all the teachers within those three grades selected.

What type of sampling should be used?

• Cluster sampling should be used; in this case, each grade level represents a cluster of teachers, and only a limited number of clusters (grades) will be selected.

6. A principal, interested in determining teacher satisfaction with a new school policy, decides to select three of the twelve grades represented in the school, and to interview three randomly selected teachers from each grade level selected.

What type of sampling should be used?

• Cluster sampling should be used. This example illustrates the two-stage process often found in cluster sampling. First, a number of grade levels will be selected (three), then in the second stage teachers will be randomly selected from those grade levels selected in stage one. This is a common procedure in cluster sampling.

7. The same principal, interested in determining teacher satisfaction with a new school policy, decides to select three teachers from each grade level for an interview.

What type of sampling should be used?

• Stratified should be used. In this case, teachers will be selected from each and every grade level.

8. The same principal, interested in how teachers feel about the new library, asks the secretary to type a list that includes all teachers in the school. The principal takes the list, assigns numbers to the list, and looks in the newspaper for the daily lotto numbers. The lotto numbers corresponding to the numbers beside the teachers’ names will determine who will be selected.

What type of sampling was used?

• Random sampling (SRS). Lotto numbers are selected randomly, so any teacher's number selected base on lotto drawing will represent a SRS.

9. Using the same list described above, the principal decides to interview every tenth teacher.

What type of sampling was used?

• Systematic sampling; every nth (10th) teacher selected.

10. The president of GSU, interested in what the faculty have to say about research support, randomly selects five departments out of the 30 on campus and interviews all faculty members in the departments selected.

What type of sampling was used?

• Cluster sampling used; a few departments out of 30 were randomly selected.

11. A researcher, studying the effects of shampoo on rats’ diets, assigns numbers to 20 rats. The researcher then places these numbers in a box; however, the researcher places each female rat’s number in the box 10 times and only places the male rats’ number in the box once. The researcher then blindly selects one number for the experiment.

What type of sampling was used?

• This is random sampling, but with unequal probabilities of selection.

12. A researcher places the names of 150 subjects in a box, mixes them thoroughly, and then draws out the names of 25 individuals to interview.

What type of sampling was used?

• SRS.

13. A science teacher is interested in how students feel about a new textbook. She also intends to compare the achievement of students using the more traditional book with those using the new book. Based upon past experience, she believes sex may also have an effect on achievement, so it is important that she gets an adequate sample for both males and females.

What type of sampling should be used?

• Stratified random sampling would be the best strategy here to ensure adequate representation of women and men.

14. A researcher is interested in how North Carolina teachers feel about a new state mandated policy. The names of all teachers are obtained and listed alphabetically. Next, the researcher assigns numbers to the list so everyone has a distinct number. Using a table of random numbers, the researcher then selects 25 teachers to survey.

What type of sampling was used?

• SRS.

15. The principal of a large middle school with over 1000 students wants to know how students feel about the new menu in the school cafeteria. She obtains the names of all students and has them listed alphabetically. Unique numbers are assigned to every student on the list. Next, she places the numbers one through ten in a hat and randomly selects one. She chose the number nine, so she decides to pick every student whose number ends in four, e.g., 4, 14, 24, 34, etc.

What type of sampling was used?

• Systematic sampling, skipping every 10th person.

16. A state superintendent is interested in how teachers feel about merit pay. There are 10,000 teachers in all the elementary and secondary schools in the district, and there are 83 schools district-wide. To facilitate surveying, the superintendent decides to select randomly a few schools and to send surveys to the teachers within those selected schools.

What type of sampling was used?

• Cluster sampling. In the first stage, a few schools out of 83 were randomly selected, and in the second stage all teachers in those few schools selected in the first stage were sent surveys.

17. To find out how students view food service in the student union at GSU, the manager stands outside the main door of the cafeteria one Monday morning and interviews the first fifty students who walk out of the cafeteria.

What type of sampling was used?

• Convenience. There is no indication of a randomized selection process here.

18. A high school counselor interviews all students who come to him for counseling about their career plans.

What type of sampling was used?

• Convenience. There is no indication of a randomized selection process here.

19. A news reporter for a local television station asks passersby on a downtown street corner their opinions about plans to build a new baseball stadium in a nearby suburb.

What type of sampling was used?

• Convenience. There is no indication of a randomized selection process here.

20. A university professor compares student reactions to two different textbooks in her statistics classes.

What type of sampling was used?

• Convenience. There is no indication of a randomized selection process here.

21. An eighth-grade teacher chooses the two students with the highest GPA in her class, the two whose GPA falls in the middle of the class, and the two with the lowest GPA to learn how her class feels about including a discussion of current events as a regular part of classroom activity. Similar samples in the past have represented the viewpoints of the total class quite accurately, although none of the students were selected using a randomized selection procedure.

What type of sampling was used?

• Convenience (more specifically, judegement or quota sampling). Since randomized selection procedures were not used, this cannot be stratified sampling.