1. © Copyright McGraw-Hill 2004 14-1 CHAPTER 14 Sampling and Simulation

2. © Copyright McGraw-Hill 2004 14-2 Objectives Demonstrate a knowledge of the four basic sampling methods. Recognize faulty questions on a survey and other factors that can bias responses. Solve problems using simulation techniques.

3. © Copyright McGraw-Hill 2004 14-3 Introduction Instead of studying a real-life situation, which may be costly or dangerous, researchers create similar situations in a laboratory or with a computer. By studying the simulation, the researcher can gain the necessary information about the real-life situation in a less expensive or safer manner.

4. © Copyright McGraw-Hill 2004 14-4 Biased and Unbiased Samples For a sample to be a random sample, every member of the population must have an equal chance of being selected. When a sample is chosen at random from a population, it is said to be an unbiased sample. Samples are said to be biased samples when some type of systematic error has been made in the selection of the subjects.

5. © Copyright McGraw-Hill 2004 14-5 Random Sampling A random sample is obtained by using methods such as random numbers, which can be generated from calculators, computers, or tables. In random sampling, the basic requirement is that for a sample of size n, all possible samples of this size must have an equal chance of being selected from the population.

6. © Copyright McGraw-Hill 2004 14-6 Incorrect Sampling Methods “the person on the street”—Selecting people haphazardly on the street does not meet the requirement for simple random sampling. Many people will be at home or work and, therefore, do not have a chance of being selected. “radio polls”—This sample is not random because, of the people who heard the program, only those who feel strongly for or against the issue will respond.

7. © Copyright McGraw-Hill 2004 14-7 Random Numbers The theory behind random numbers is that each digit, 0 through 9, has an equal probability of occurring. To obtain a sample by using random numbers, number the elements of the population sequentially and then select each person by using random numbers.

8. © Copyright McGraw-Hill 2004 14-8 Systematic Sample A systematic sample is obtained by numbering each element in the population and then selecting every 3rd or 5th or 10th, etc., number from the population to be included in the sample. This is done after the first number is selected at random.

9. © Copyright McGraw-Hill 2004 14-9 Stratified Sample A stratified sample is obtained by dividing the population into subgroups, called strata, according to various homogeneous characteristics and then selecting members from each stratum for the sample.

10. © Copyright McGraw-Hill 2004 14-10 Cluster Sample A cluster sample is obtained by selecting a preexisting or natural group, called a cluster, and using the members in the cluster for the sample.

11. © Copyright McGraw-Hill 2004 14-11 Advantages for Cluster Sampling There are three advantages to using a cluster sample instead of other types of samples: 1.A cluster sample can reduce costs. 2.It can simplify fieldwork. 3.It is convenient. The major disadvantage of cluster sampling is that the elements in a cluster many not have the same variations in characteristics as those selected individually from a population.

12. © Copyright McGraw-Hill 2004 14-12 Other Sampling Methods Sequence sampling, used in quality control, samples successive units taken from production lines to ensure that the products meet certain standards. In multistage sampling, the researcher uses a combination of sampling methods.

13. © Copyright McGraw-Hill 2004 14-13 Other Sampling Methods (cont’d.) In double sampling, a very large population is given a questionnaire to determine those who meet the qualifications for a study. After the questionnaires are reviewed, a second smaller population is defined. The sample is selected from this group.

14. © Copyright McGraw-Hill 2004 14-14 Conducting a Sample Survey Step 1Decide what information is needed. Step 2Determine how the data will be collected (phone interview, mail survey, etc.). Step 3Select the information-gathering instrument or design the questionnaire if one is not available. Step 4Set up a sampling list, if possible.

15. © Copyright McGraw-Hill 2004 14-15 Conducting a Sample Survey (cont’d.) Step 5Select the best method for obtaining the sample (random, systematic, stratified, cluster, or other). Step 6Conduct the survey and collect data. Step 7 Tabulate the data. Step 8Conduct the statistical analysis.

16. © Copyright McGraw-Hill 2004 14-16 Surveys A survey is conducted when a sample of individuals is asked to respond to questions about a particular subject. The two types of surveys are interviewer- administered and self-administered.

17. © Copyright McGraw-Hill 2004 14-17 Interview and Self-administered Surveys Interviewer-administered surveys require a person to ask the questions. The interview can be conducted face-to-face in an office, on a street, in the mall, or via telephone. Self-administered surveys can be done by mail or in a group setting such as a classroom.

18. © Copyright McGraw-Hill 2004 14-18 Common Questionnaire Mistakes Asking biased questions—by asking questions in a certain way, the researcher can lead the respondents to answer in the way he or she wants them to. Using confusing words—the participant misinterprets the meaning of the words and answers the question in a biased way.

19. © Copyright McGraw-Hill 2004 14-19 Common Questionnaire Mistakes (cont’d.) Asking double-barreled questions—sometimes questions contain compound sentences that require the participant to respond to two questions at the same time. Using double negatives in questions—double negatives can be confusing to the respondents.

20. © Copyright McGraw-Hill 2004 14-20 Common Questionnaire Mistakes (cont’d.) Ordering questions improperly—by arranging the questions in a certain order, the researcher can lead participants to respond in a way that he or she may otherwise not have done.

21. © Copyright McGraw-Hill 2004 14-21 Simulation Techniques A simulation technique uses a probability experiment to mimic a real-life situation. Mathematical simulation techniques use probability and random numbers to create conditions similar to those of real-life problems.

22. © Copyright McGraw-Hill 2004 14-22 Monte Carlo Method The Monte Carlo method is a simulation technique using random numbers. These techniques are used in business and industry to solve problems that are extremely difficult or involve a large number of variables.

23. © Copyright McGraw-Hill 2004 14-23 Monte Carlo Method (cont’d.) Step 1List all possible outcomes of the experiment. Step 2Determine the probability of each outcome. Step 3Set up a correspondence between the outcomes of the experiment and the random numbers.

24. © Copyright McGraw-Hill 2004 14-24 Monte Carlo Method (cont’d.) Step 4Select random numbers from a table and conduct the experiment. Step 5Repeat the experiment and tally the outcomes. Step 6Compute any statistics and state the conclusions.

25. © Copyright McGraw-Hill 2004 14-25 Summary The four most common methods researchers use to obtain samples are random, systematic, stratified, and cluster sampling methods. In random sampling, some type of random method (usually random numbers) is used to obtain the sample. In systematic sampling, the researcher selects every k th person or item after selecting the first one at random.

26. © Copyright McGraw-Hill 2004 14-26 Summary (cont’d.) In stratified sampling, the population is divided into subgroups according to various characteristics, and elements are then selected at random from the subgroups. In cluster sampling, the researcher selects an intact group to use as a sample. Multistage sampling, a combination of sampling methods, is used when the population is large to obtain a subgroup of the population.

27. © Copyright McGraw-Hill 2004 14-27 Summary (cont’d.) Researchers must use caution when conducting surveys and designing questionnaires, otherwise conclusions obtained from these will be inaccurate. Most sampling methods use random numbers, which can be used to simulate many real-life problems or situations.

28. © Copyright McGraw-Hill 2004 14-28 Summary (cont’d.) The basic method of simulation is known as the Monte Carlo method. The purpose of simulation is to duplicate situations that are too dangerous, too costly, or too time-consuming to study in real life. Most simulation techniques can be done on the computer or calculator.

29. © Copyright McGraw-Hill 2004 14-29 Conclusions Sampling and simulation are two techniques that enable researchers to gain information that might otherwise be unobtainable.