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UT Knoxville STAT 201 - Chapter 12

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Chapter12 Presentation 1213Copyright © 2009 Pearson Education, Inc.11Chapter12 Presentation Copyright © 2009 Pearson Education, Inc.Chapter 12Sample SurveysChapter12 Presentation 1213Copyright © 2009 Pearson Education, Inc.2Sampling - Outline1 - Understand a Population (i.e., all the units of interest) 2 – Sampling Biases3 – Randomized SamplesChapter12 Presentation 1213Copyright © 2009 Pearson Education, Inc.3Populations• The concept of a population is key to this entire course. • Having a well defined population helps researchers select better samples.• When doing statistics, we typically want to understand certain aspects of a population.– Examples: • Cholesterol level of Male Native Americans• Income of Banking Executives• GPA of UT students that own laptopsChapter12 Presentation 1213Copyright © 2009 Pearson Education, Inc.4The Population • We want to learn details about the population.– We summarize this by saying that we want to learn about a population parameter.– A population parameter can be a:• Mean• Variance• Percentile• Percent• or some other function of the population distribution.Chapter12 Presentation 1213Copyright © 2009 Pearson Education, Inc.5The Sample• To learn about the population parameterswe usually take a sample.• Given the data from a sample, we can compute sample statistics.Chapter12 Presentation 1213Copyright © 2009 Pearson Education, Inc.6Notation• We typically use Greek letters to denote parameters and Latin letters to denote statistics.Chapter12 Presentation 1213Copyright © 2009 Pearson Education, Inc.7How Large of a Sample?• How large a random sample do we need for the sample to be reasonably representative of the population?• It’s the size of the sample, not the size of the population, that makes the difference in sampling.Chapter12 Presentation 1213Copyright © 2009 Pearson Education, Inc.8How Large of a Sample? (Cont.)• To estimate the proportion of the population in Knox County that approves of Obama’s health care plan with a margin of error of 3% we need a sample slightly bigger than 1000.• To estimate the proportion of the population in the U.S. that approves of Obama’s health care plan with a margin of error of 3% we need a sample slightly bigger than 1000.• The fraction of the population that you’ve sampled doesn’t matter. It’s the samplesize itself (and how the sample is selected) that’s important.Chapter12 Presentation 1213Copyright © 2009 Pearson Education, Inc.9Collecting the Sample: Sampling Frame• The sampling frame is a list or collection of individuals from which the sample is drawn.• When the list or collection of individuals misses part of the population we say that the sampling frame is biased.Chapter12 Presentation 1213Copyright © 2009 Pearson Education, Inc.10Collecting the Sample• We want to collect the sample that gives us an unbiasedpicture of the population.• This chapter describes sampling strategies that avoid bias and produce accurate results.• Good samples are called Representative.• First let’s review what can go wrong if we don’t have a representative sample.Chapter12 Presentation 1213Copyright © 2009 Pearson Education, Inc.11Voluntary Response Sampling• A large group is invited to respond. • All those that respond are counted.• Voluntary response bias - the sample only includes people with a strong interest in the topic.Chapter12 Presentation 1213Copyright © 2009 Pearson Education, Inc.12Ex. Voluntary Response Bias• Statistics 201 samples students opinions on a range of issues and uses the data for a class project.• If students aren’t required (or strongly encouraged) to respond, what effect might it have on the responses?• Who will respond?• How might their opinions or behaviors differ from other students in the class?Chapter12 Presentation 1213Copyright © 2009 Pearson Education, Inc.13Convenience Sampling• Suppose that we only collect samples from population members that are convenient?• Ex. A recent internet survey found that ___% of the population had internet access.Chapter12 Presentation 1213Copyright © 2009 Pearson Education, Inc.14Sample Biases• Undercoverage – some portion of the population is not sampled or has smaller representation than in the original population.– Example: US Census forms are sent to all residences in America. What segment of the US population is “undercovered”?Chapter12 Presentation 1213Copyright © 2009 Pearson Education, Inc.15Sample Biases (cont.)• Nonresponse – those that don’t respond to the sample differ in their opinions from those that do.– Example: Telephone surveys. Have you ever hung up on a person doing a phone survey? Are your opinions (and others that hang up) different from those that don’t?Chapter12 Presentation 1213Copyright © 2009 Pearson Education, Inc.16Sample Biases (cont.)• Response Bias – question wording, interviewer behavior can affect answers.– Example: “Are you a racist?” will get you a “no” response almost 100% of the time.Chapter12 Presentation 1213Copyright © 2009 Pearson Education, Inc.17Sampling Bias: Swine Flu• The recent outbreak of Swine Flu in Mexico terrified the world because of the seemingly high death rate.• CNN regularly reported on the proportion of hospitalized patients that died.• Later research showed a much lower mortality rate.Chapter12 Presentation 1213Copyright © 2009 Pearson Education, Inc.18• Population?• Parameter of Interest?• Sampling Frame?• Sample?• Sampling Method?Sampling Bias: Swine FluChapter12 Presentation 1213Copyright © 2009 Pearson Education, Inc.19Sampling DesignsWe will explore each of these designs:• Simple Random Sample• Systematic Sample• Stratified Random Sample• Cluster Sample• Multistage SampleChapter12 Presentation 1213Copyright © 2009 Pearson Education, Inc.20Simple Random Sample• Elements of the population are enumerated (like a lottery, where each element of the population gets a ticket with a unique number on it).• Each member of the population has the same probability of being selected.• When to use it? When you have easy access to the entire population, e.g. the registrar taking a sample of UT students.Chapter12 Presentation 1213Copyright © 2009 Pearson Education, Inc.21Systematic Sample• Each element of the population is enumerated and every k-th element of the population is sampled (beginning at a randomly


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UT Knoxville STAT 201 - Chapter 12

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