Chapter 13 Samples and Surveys Copyright © 2011 Pearson Education, Inc 13.1 Two Surprising Properties of Sampling How is the winning car model of J.D Power and Associates Initial Quality Award determined? By focusing on a subset of the whole group (a sample) By making sure that items are selected randomly from the larger group of 36 Copyright © 2011 Pearson Education, Inc 13.1 Two Surprising Properties of Sampling Definitions Population: the entire collection of interest Sample: subset of the population Survey: posing questions to a sample to learn about the population Representative: samples that reflect the mix in the entire population Bias: systematic error in selecting the sample of 36 Copyright © 2011 Pearson Education, Inc 13.1 Two Surprising Properties of Sampling The two surprises are: The best way to get a representative sample is to pick members of the population at random Larger populations not require larger samples of 36 Copyright © 2011 Pearson Education, Inc 13.1 Two Surprising Properties of Sampling Randomization A randomly selected sample is representative of the whole population Randomization ensures that on average a sample mimics the population of 36 Copyright © 2011 Pearson Education, Inc 13.1 Two Surprising Properties of Sampling Comparison of Two Random Samples from a Population of 3.5 Million Customers of 36 Copyright © 2011 Pearson Education, Inc 13.1 Two Surprising Properties of Sampling Randomization Produces samples whose averages resemble those in the population (avoids bias) Enables us to infer characteristics of the population from a sample of 36 Copyright © 2011 Pearson Education, Inc 13.1 Two Surprising Properties of Sampling Infamous Case: The Literary Digest The Literary Digest predicted defeat for Franklin D Roosevelt in the 1936 presidential election They selected their sample from a list of telephone numbers (telephones were a luxury during the Great Depression) Roosevelt’s supporters tended to be poor and were underrepresented in the sample of 36 Copyright © 2011 Pearson Education, Inc 13.1 Two Surprising Properties of Sampling This sample size is an almost infinitesimal portion of the population, yet the survey reveals attitudes of the entire population to within ± 3% 10 of 36 Copyright © 2011 Pearson Education, Inc 4M Example 13.1: EXIT SURVEYS Message On the basis of the survey, the owner will be able to find out why shoppers are leaving without buying 22 of 36 Copyright © 2011 Pearson Education, Inc 13.3 ALTERNATIVE SAMPLING METHODS Stratified Samples Divide the sampling frame into homogeneous groups, called strata Use simple random sample to select items from each strata 23 of 36 Copyright © 2011 Pearson Education, Inc 13.3 ALTERNATIVE SAMPLING METHODS Cluster Samples Divide a geographic region into clusters Randomly select clusters Randomly choose items within selected clusters 24 of 36 Copyright © 2011 Pearson Education, Inc 4M Example 13.2: ESTIMATING THE RISE OF PRICES Motivation What goes into determining the consumer price index (CPI), the official measure of inflation? 25 of 36 Copyright © 2011 Pearson Education, Inc 4M Example 13.2: Method ESTIMATING THE RISE OF PRICES The Bureau of Labor Statistics (BLS) uses a survey to estimate inflation The target population consists of the costs of every consumer transaction in urban areas during a specific month 26 of 36 Copyright © 2011 Pearson Education, Inc 4M Example 13.2: ESTIMATING Mechanics THE RISE OF PRICES The BLS has a list of urban areas and a list of people living in each, but does not have a list of every sales transaction So the BLS divides items sold into 211 categories and estimates the change in price for each category in every area 27 of 36 Copyright © 2011 Pearson Education, Inc 4M Example 13.2: ESTIMATING THE RISE OF PRICES Message The urban consumer price index is an estimate of inflation base on a complex, clustered sample in selected metropolitan areas 28 of 36 Copyright © 2011 Pearson Education, Inc 13.3 ALTERNATIVE SAMPLING METHODS Census A comprehensive survey of the entire population Cost and time constraints generally prohibit carrying out a census; in some cases a census is not feasible 29 of 36 Copyright © 2011 Pearson Education, Inc 13.3 ALTERNATIVE SAMPLING METHODS Voluntary Response A sample consisting of individuals who volunteer when given the opportunity to participate in a survey These samples are biased toward those with strong opinions 30 of 36 Copyright © 2011 Pearson Education, Inc 13.3 ALTERNATIVE SAMPLING METHODS Convenience Samples A sampling method that selects individuals who are readily available Although easy to obtain, these samples are rarely representative 31 of 36 Copyright © 2011 Pearson Education, Inc 13.4 CHECKLIST FOR SURVEYS Questions to Consider What was the sampling frame? Is the sample a simple random sample? What is the rate of nonresponse? How was the question worded? Did the interviewer affect the results? Does survivor bias affect the survey? 32 of 36 Copyright © 2011 Pearson Education, Inc 13.4 CHECKLIST FOR SURVEYS How Wording of the Question Affects Results 33 of 36 Copyright © 2011 Pearson Education, Inc Best Practices Randomize Plan carefully Match the sampling frame to the target population 34 of 36 Copyright © 2011 Pearson Education, Inc Best Practices (Continued) Keep focused Reduce the amount of nonresponse Pretest your survey 35 of 36 Copyright © 2011 Pearson Education, Inc Pitfalls Don’t conceal flaws in your sample Do not lead the witness Do not confuse a sample statistic for the population parameter Do not accept results because they agree with what you expect 36 of 36 Copyright © 2011 Pearson Education, Inc .. .Chapter 13 Samples and Surveys Copyright © 2011 Pearson Education, Inc 13. 1 Two Surprising Properties of Sampling How is the winning car model of J.D Power and Associates Initial... 36 Copyright © 2011 Pearson Education, Inc 13. 2 VARIATION Notation for Statistics and Parameters 15 of 36 Copyright © 2011 Pearson Education, Inc 13. 2 VARIATION Sampling Variation Is the variability... © 2011 Pearson Education, Inc 13. 1 Two Surprising Properties of Sampling Randomization A randomly selected sample is representative of the whole population Randomization ensures that on average