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This chapter covers common sampling techniques, surveys and questionnaire design, and simulation techniques. It explores the various methods for obtaining unbiased samples and demonstrates how simulation can be used to study real-life situations in a safe and cost-effective manner.
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14-1 Chapter 14 Sampling and Simulation By Dr. Ateq Ahmed Al-Ghamedi
Outline 14-2 • 14-1 Introduction • 14-2 Common Sampling Techniques • 14-3 Surveys and Questionnaire Design • 14-4 Simulation Techniques
Outline 14-3 • 14-5 The Monte Carlo Method
Objectives 14-4 • 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.
1-1 Introduction 14-5 • Instead of studying a real-life situation, which may be costly or dangerous, researchers create similar situations in a laboratory or with a computer.
1-1 Introduction (cont’d.) 14-6 • By studying the simulation, the researcher can gain the necessary information about the real-life situation in a less expensive or safer manner.
14-2 Common Sampling Techniques 14-7 • 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.
14-2 Common Sampling Techniques (Cont’d.) 14-8 • Samples are said to be biased sampleswhen some type of systematic error has been made in the selection of the subjects.
14-2 Random Sampling 14-9 • 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.
14-2 Incorrect Sampling Methods 14-10 • “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.
14-2 Random Numbers 14-11 • 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.
14-2 Systematic Sample 14-12 • A systematic sampleis 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.
14-2 Stratified Sample 14-13 • A stratified sampleis obtained by dividing the population into subgroups, called strata, according to various homogeneous characteristics and then selecting members from each stratum for the sample.
14-2 Cluster Sample 14-14 • A cluster sampleis obtained by selecting a preexisting or natural group, called a cluster, and using the members in the cluster for the sample.
14-2 Advantages for Cluster Sampling 14-15 • 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.
14-2 Disadvantages for Cluster Sampling 14-16 • 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.
14-2 Other Sampling Methods 14-17 • 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.
14-4 Simulation Techniques 14-26 • A simulation techniqueuses 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.
14-5 The Monte Carlo Method 14-27 • 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.
14-5 The Monte Carlo Method (cont’d.) 14-28 • Step 1 List all possible outcomes of the experiment. • Step 2 Determine the probability of each outcome. • Step 3 Set up a correspondence between the outcomes of the experiment and the random numbers.
14-5 The Monte Carlo Method (cont’d.) 14-29 • Step 4 Select random numbers from a table and conduct the experiment. • Step 5 Repeat the experiment and tally the outcomes. • Step 6 Compute any statistics and state the conclusions.
14-5 Examples 14-4 to 14-8 14-30 • See the book pages 728-730. • Two dice are rolled 50, 500, and 10000 times. Using simulation techniques plot the output of the sum ?
