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Random Sampling: Playing It Safe by Taking Chances

Random Sampling: Playing It Safe by Taking Chances. Statistics: From Data to Decision Watkins, Scheaffer , and Cobb 12 th Grade. Introduction.

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Random Sampling: Playing It Safe by Taking Chances

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  1. Random Sampling: Playing It Safe by Taking Chances Statistics: From Data to Decision Watkins, Scheaffer, and Cobb 12th Grade

  2. Introduction • In this unit, you will learn about methods of inference. We will discuss the five most common types of random sampling and why they are used. After this presentation you will be able to distinguish them and know if there was a selection bias in the selection process. You will also be able to apply the concepts to real life problems as well as make up your own examples of random sampling types.

  3. Population vs. Sample • In statistics, the set of people or objects that you want to know about is called the population. Each element of the population is called unit. The population size is given by the number of units (N). A census occurs when we collect data of the entire population. • Because it is very difficult to record data of all units in a population, we usually take a sample to study it. The sample size is the number of units in the sample (n). • To get unbiased data, samples are usually selected randomly.

  4. Why do we use random sampling? • Randomization is not a unsystematic procedure. It requires careful implementation to avoid biasing the analysis. In surveys, the sample selected from a population needs to be a good representative of the population. Taking a random sample is generally what is done to satisfy this requirement. In observational studies, the sample needs to be representative of the population as a whole to enable generalization from sample to population. The best way to satisfy this is to use random selection in choosing the sample.

  5. Types of Random Sampling Simple Random Stratified Random Cluster Random Two-Stage Cluster Random Systematic Random Stratified Random Textbook Exercise

  6. Simple Random Sample • In simple random sampling (sometimes called just random sampling), all possible samples of a given size are equally likely to be selected. For example, if the sample size is n = 5, then every possible group of five units has the same chance of being chosen for the sample. • The main benefit of simple random sampling is that it guarantees that the sample chosen is representative of the population. This ensures that the statistical conclusions will be valid. Go Back to Types of Sampling

  7. Steps in Choosing Simple Random Sample • Start with a list of all N units in the population • Number the units in the list from 1 to N • Use a random digit table or generator to choose numbers from 1 to N, one at a time, until you have as many units as you need.

  8. Stratified Random Sample • In stratified random sampling, the population is divided into groups called strata and from each stratum a simple random sample is drawn. • Suppose a farmer wishes to work out the average milk yield of each cow type in his herd which consists of four kinds of cows. He could divide up his herd into the four sub-groups and take samples from these. Go Back to Types of Sampling

  9. Steps in Choosing Stratified Random Sample • Divide the units of the population into non-overlapping subgroups. • Take a simple random sample from each subgroup.

  10. Cluster Sample • In cluster random sampling, we select a simple random sample of clusters of units (such as classrooms of students) rather than individual units (students) • To see how well students in the 9th grade are doing in math in Ohio, we could randomly pick as our clusters a few 9th grade classrooms from different schools throughout the state and give all the students a standardized test. Go Back to Types of Sampling

  11. Steps in Choosing Cluster Sample • Create a list of all the clusters in your population. • Take a simple random sample of clusters. • Obtain data on each individual in each clusters in your simple random sampling

  12. Two-Stage Cluster Sample • In two-stage cluster random sampling, we take a random sample of clusters and afterwards we take a sample from each of those clusters. • Going back to the previous example, instead of giving all students from the 9th grade classrooms standardized tests, we would pick randomly a few students in each of those classrooms to take the test. Go Back to Types of Sampling

  13. Steps in Choosing Two-Stage Cluster Sample • Create a list of all the clusters in your population, and then take a simple random sample of clusters. • Create a list of all the individuals in each cluster already selected, and then take a simple random sampling from each cluster.

  14. Systematic Samples with Random Start • In systematic sampling with random start, a sample is selected by taking every nth member of the population, starting at a random point. • To get a quick sample of the students in a class to do homework problems on the board, a teacher can first number the students by the chairs they are sitting . She would after pick a random number, let’s say 2. Then, she would say that every 5th student would be in the sample. The picture below shows how this system would look like. Go Back to Types of Sampling

  15. Steps in Choosing Systematic Samples with Random Start • By a method such as counting off, divide your population into groups of the size you want for your sample. • Use a chance method to choose one of the groups for your sample.

  16. Can you remember the definitions? • Go back to the Types of Random Sampling slide to see if you remember the difference between the five different types of sampling. Click in each type to see if you are correct!

  17. Matching Pictures Game • Systematic Samples with Random Start • Simple Random Sample • Cluster Samples • Stratified Random Samples • Two-Stage Cluster Sample

  18. Sampling Bias • Sampling bias is a consistent error that arises due to the sample selection. For example, a survey of high school students to measure teenage use of illegal drugs will be a biased sample because it does not include home schooled students or dropouts. • A sample is also biased if certain members are underrepresented or overrepresented relative to others in the population. For example, distributing a questionnaire at the end of a 3-day conference is likely to include more people who are committed to the conference so their views would be overrepresented. • Sampling bias can occur any time your sample is not a random sample. If it is not random, some individuals are more likely than others to be chosen. Always think very carefully about which individuals are being favored and how they differ.

  19. Exercise #1 • Each of the 29 NBA teams has 12 players. A sample of 58 players is to be chosen as follows. Each team will be asked to place 12 cards with their players' names into a hat and randomly draw out two names. The two names from each team will be combined to make up the sample. Will this method result in a simple random sample of the 348 basketball players? • No, because not every group of 58 players has the same chance of being selected.

  20. Exercise #2 • To survey the opinions of bleacher fans at Wrigley Field, a surveyor plans to select every one hundredth fan entering the bleachers one afternoon. Will this result in a simple random sample of Cub fans who sit in the bleachers? • No, because not every sample of the intended size has an equal chance of being selected.

  21. Textbook Exercise a. Not an SRS b. Not an SRS. The sample size is random, depending on the outcome of the randomly selected digit c. This is cluster sampling. Not all possible groups of 5 students are equally likely to be included in the sample. d. This is an SRS. Each possible group of 6 students is equally likely to be included in the sample. e. This is stratified random sampling. Not all possible groups of 6 students are equally likely to be included in the sample. f. Not an SRS. The sample size is not fixed in advance of drawing the sample.

  22. Can you think of some examples of Random Sampling?

  23. Additional Resources (Hyperlinks) • “Sampling Methods”(2005). Research Methods Workshops. Wadsworth CENGAGE Learning. Web • “AP Statistics Tutorial: Survey Sampling Methods” (2012). Stat Trek. Web • “Choosing a Sampling Method” (2012). Changing Minds. Web • Westfall, L. “Sampling Methods” (2009). The Westfall Team. Web • “Sampling” (July, 2002). Social Science Computing Cooperative. Web

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