14 1 Chapter 14 Sampling and Simulation By

14 -1 Chapter 14 Sampling and Simulation By Dr. Ateq Ahmed Al-Ghamedi

14 -2 Outline l l 14 -1 Introduction 14 -2 Common Sampling Techniques 14 -3 Surveys and Questionnaire Design 14 -4 Simulation Techniques © The Mc. Graw-Hill Companies, Inc. , 2000

14 -3 Outline l 14 -5 The Monte Carlo Method © The Mc. Graw-Hill Companies, Inc. , 2000

14 -4 Objectives l l l 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. © The Mc. Graw-Hill Companies, Inc. , 2000

14 -5 1 -1 Introduction l Instead of studying a real-life situation, which may be costly or dangerous, researchers create similar situations in a laboratory or with a computer. © The Mc. Graw-Hill Companies, Inc. , 2000

14 -6 1 -1 Introduction (cont’d. ) l By studying the simulation, the researcher can gain the necessary information about the real-life situation in a less expensive or safer manner. © The Mc. Graw-Hill Companies, Inc. , 2000

14 -7 14 -2 Common Sampling Techniques l l 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. © The Mc. Graw-Hill Companies, Inc. , 2000

14 -8 14 -2 Common Sampling Techniques (Cont’d. ) l Samples are said to be biased samples when some type of systematic error has been made in the selection of the subjects. © The Mc. Graw-Hill Companies, Inc. , 2000

14 -9 14 -2 Random Sampling l l 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. © The Mc. Graw-Hill Companies, Inc. , 2000

14 -10 14 -2 Incorrect Sampling Methods l l “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. © The Mc. Graw-Hill Companies, Inc. , 2000

14 -11 14 -2 Random Numbers l l 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. © The Mc. Graw-Hill Companies, Inc. , 2000

14 -12 14 -2 Systematic Sample l l A systematic sample is obtained by numbering each element in the population and then selecting every 3 rd or 5 th or 10 th, etc. , number from the population to be included in the sample. This is done after the first number is selected at random. © The Mc. Graw-Hill Companies, Inc. , 2000

14 -13 14 -2 Stratified Sample l 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. © The Mc. Graw-Hill Companies, Inc. , 2000

14 -14 14 -2 Cluster Sample l 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. © The Mc. Graw-Hill Companies, Inc. , 2000

14 -2 Advantages for Cluster 14 -15 Sampling l 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 Mc. Graw-Hill Companies, Inc. , 2000

14 -2 Disadvantages for Cluster Sampling 14 -16 l 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. © The Mc. Graw-Hill Companies, Inc. , 2000

14 -17 14 -2 Other Sampling Methods l l 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. © The Mc. Graw-Hill Companies, Inc. , 2000

14 -26 14 -4 Simulation Techniques l l 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 reallife problems. © The Mc. Graw-Hill Companies, Inc. , 2000

14 -5 The Monte Carlo Method 14 -27 l l 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. © The Mc. Graw-Hill Companies, Inc. , 2000

14 -28 14 -5 The Monte Carlo Method (cont’d. ) l Step 1 l Step 2 l Step 3 List all possible outcomes of the experiment. Determine the probability of each outcome. Set up a correspondence between the outcomes of the experiment and the random numbers. © The Mc. Graw-Hill Companies, Inc. , 2000

14 -29 14 -5 The Monte Carlo Method (cont’d. ) l Step 4 l Step 5 l Step 6 Select random numbers from a table and conduct the experiment. Repeat the experiment and tally the outcomes. Compute any statistics and state the conclusions. © The Mc. Graw-Hill Companies, Inc. , 2000

14 -30 14 -5 Examples 14 -4 to 14 -8 l l See the book pages 728 -730. Two dice are rolled 50, 500, and 10000 times. Using simulation techniques plot the output of the sum ? © The Mc. Graw-Hill Companies, Inc. , 2000

14 -31 How many times the totals occurred when throwing two dice 50 times 12 10 Frequence 8 6 Series 1 4 2 0 1 2 3 4 5 6 7 8 9 10 11 12 Total © The Mc. Graw-Hill Companies, Inc. , 2000

14 -32 How many times the totals occurred when throwing two dice 500 times 90 80 70 60 50 40 30 20 10 0 1 2 3 4 5 6 7 8 9 10 11 12 © The Mc. Graw-Hill Companies, Inc. , 2000

14 -33 How many times the totals occurred when throwing two dice 10000 times 1800 1600 1400 1200 1000 800 600 400 200 0 1 2 3 4 5 6 7 8 9 10 11 12 © The Mc. Graw-Hill Companies, Inc. , 2000