Chapter Eleven Sampling Foundations. Copyright © Houghton Mifflin Company. All rights reserved.11 | 2 Chapter Objectives Define and distinguish between.

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<ul><li>Slide 1</li></ul><p>Chapter Eleven Sampling Foundations Slide 2 Copyright Houghton Mifflin Company. All rights reserved.11 | 2 Chapter Objectives Define and distinguish between sampling and census studies Discuss when to use a probability versus a nonprobability sampling method and implement the different methods Explain sampling error and sampling distribution Construct confidence intervals for population means and proportions List the factors to consider in determining sample size, and compute the required sample size to achieve a specific degree of precision at a desired confidence level Slide 3 Copyright Houghton Mifflin Company. All rights reserved.11 | 3 Gallup Poll on Sampling: China 12,500 counties, cities, and urban districts were divided into 50 strata based on their geographic location, degree of economic development, and proportion of non-agricultural population One primary sampling unit (PSU), consisting of either a county or a city, was selected from each stratum based on probability proportional to population size Within each PSU, the populations of all neighborhoods and villages were compiled. From this listing, four neighborhoods or villages were selected proportional to size. From each of these four neighborhoods or villages, five households were selected at random Slide 4 Copyright Houghton Mifflin Company. All rights reserved.11 | 4 Gallup Poll on Sampling: China (Contd) One respondent was selected from each of the selected households, ensuring proper representation in the sample of all age groups by both genders The respondent to be interviewed is then selected according to a prescribed systematic procedure If the designated respondent was not at home, or could not be reached, a second or, if needed, a third adult family member was selected systematically from among the household members remaining on the list If contact with the designated respondent could not be made after a total of three separate visits to the household, an interview with a respondent in a substitute household in the same locality was permitted Two substitute households were kept in reserve for each five assigned households in the interviewing area Slide 5 Copyright Houghton Mifflin Company. All rights reserved.11 | 5 Gallup Poll on Sampling: China (Contd) By following this methodology and correcting for any rural/urban sampling issues the Gallup China polls are statistically accurate to within + or 2% Slide 6 Copyright Houghton Mifflin Company. All rights reserved.11 | 6 National Poll Sample Size Harris Poll A weekly study that monitors the reactions of the American public to a variety of economic, political, and social issues Sample Size Based on a nationally representative telephone survey of 1,000 adults age 18 or over Slide 7 Copyright Houghton Mifflin Company. All rights reserved.11 | 7 AC Nielsen Scantrack Index Offers valuable scanner-based sales and brand share data on a regular basis to manufacturers of a wide variety of consumer products such as food, drugs, and cosmetics Sample Size Sales and brand share estimates are gathered weekly from a representative sample of more than 4,800 stores representing over 800 retailers in 50 major markets Slide 8 Copyright Houghton Mifflin Company. All rights reserved.11 | 8 Sampling vs. Census Studies A census study draws inferences from the entire body of units of interest (the population) A sample study draws inferences from a sample drawn from the population Slide 9 Copyright Houghton Mifflin Company. All rights reserved.11 | 9 Advantages of Sampling Low Cost Reduced time Slide 10 Copyright Houghton Mifflin Company. All rights reserved.11 | 10 Sampling and Nonsampling Errors Sampling error: The difference between a statistic value that is generated through a sampling procedure and the parameter value, which can be determined only through a census study Nonsampling error: Any error in a research study other than sampling error (which arises purely because a sample, rather than the entire population, is studied) Slide 11 Copyright Houghton Mifflin Company. All rights reserved.11 | 11 Minimizing Sampling Errors Increase the sample size Use a statistically efficient sampling plan Make the sample as representative of the population as possible Slide 12 Copyright Houghton Mifflin Company. All rights reserved.11 | 12 Types of Nonsampling Errors Nonsampling Error Any error other than sampling error Sampling Frame Error Sampling frame not being representative of ideal population Nonresponse Error Final sample not representative of planned sample Data Error Distortions in collected data and mistakes in data coding, analysis, or interpretation Slide 13 Copyright Houghton Mifflin Company. All rights reserved.11 | 13 Potential Causes of Sampling Frame Errors Incomplete sampling frame over-represents some population segments and underrepresents others Sampling frame contains irrelevant units Slide 14 Copyright Houghton Mifflin Company. All rights reserved.11 | 14 Minimizing Sampling Frame Errors Start with a complete sampling frame Modify the sampling frame to make it representative of the ideal population using plus-one dialing in telephone surveys Slide 15 Copyright Houghton Mifflin Company. All rights reserved.11 | 15 Potential Causes of Nonresponse Errors Mail surveys/Internet surveys Certain types of sample units being more likely to respond than others Telephone and personal interview surveys Person not-at home problem and respondent refusal problem Slide 16 Copyright Houghton Mifflin Company. All rights reserved.11 | 16 Minimizing Nonresponse Errors Mail surveys: increase response rates through the use of incentives, follow-up mailings, etc. Caution: increase in response rate per se may not reduce non-response error Telephone and personal interview surveys: make call-backs and spread out the time blocks during which interviews are conducted Slide 17 Copyright Houghton Mifflin Company. All rights reserved.11 | 17 Potential Causes of Data Errors Respondents reluctance/inability to give accurate answers Ill-trained interviewers Unscrupulous interviewers Poorly designed questionnaire Mistakes in coding data Erroneous analysis Incorrect/ inappropriate interpretation of results Slide 18 Copyright Houghton Mifflin Company. All rights reserved.11 | 18 Exhibit 11.1 Types and Potential Causes of Nonsampling Errors Slide 19 Copyright Houghton Mifflin Company. All rights reserved.11 | 19 When Census Studies Are Appropriate The feasibility condition Whenever a population is relatively small or can be accessed easily The necessity condition When the population units are extremely varied and each population unit is likely to be very different from all the other units Slide 20 Copyright Houghton Mifflin Company. All rights reserved.11 | 20 Probability and Nonprobability Sampling Probability sampling is an objective procedure in which the probability of selection is known in advance for each population unit Nonprobability sampling is a subjective procedure in which the probability of selection for each population unit is unknown beforehand Slide 21 Copyright Houghton Mifflin Company. All rights reserved.11 | 21 Exhibit 11.3 Classification of Sampling Methods Slide 22 Copyright Houghton Mifflin Company. All rights reserved.11 | 22 Probability Sampling Methods Simple Random Sampling Stratified Random Sampling Cluster Sampling Slide 23 Copyright Houghton Mifflin Company. All rights reserved.11 | 23 Gallup Poll: USA Identify and describe the population that a given poll is attempting to represent Choose or design a method that will enable Gallup to sample the target population randomly Random Digit Dialing (RDD): a procedure that creates a list of all possible household phone numbers in America and then selects a sub-set of numbers from that list for Gallup to call Slide 24 Copyright Houghton Mifflin Company. All rights reserved.11 | 24 Simple Random Sampling Every possible sample of a certain size within a population has a known and equal probability of being chosen as the study sample Slide 25 Copyright Houghton Mifflin Company. All rights reserved.11 | 25 Stratified Random Sampling Two Types of Stratified Random Sampling Proportionate Stratified Random Sampling Disproportionate Stratified Random Sampling Slide 26 Copyright Houghton Mifflin Company. All rights reserved.11 | 26 Proportionate Stratified Random Sampling Sample consists of units selected from each population stratum in proportion to the total number of units in the stratum Slide 27 Copyright Houghton Mifflin Company. All rights reserved.11 | 27 Kirkwood University- Proportionate Stratified Random Sampling Administrators of Kirkwood University wanted to determine the attitudes of their students toward various aspects of the university They selected a proportionate stratified random sample of 500 students for conducting the attitude survey Slide 28 Copyright Houghton Mifflin Company. All rights reserved.11 | 28 Table 11.2 Proportionate Allocation of Total Sample of Kirkwood University Students Slide 29 Copyright Houghton Mifflin Company. All rights reserved.11 | 29 Disproportionate Stratified Random Sampling Sample consists of units selected from each population stratum according to how varied the units are within the stratum Slide 30 Copyright Houghton Mifflin Company. All rights reserved.11 | 30 Exhibit 11.4 Disproportionate Stratified Random Sampling Used by A.C. Nielsen Company Copyright ACNielsen Company. Reprinted by permission. Slide 31 Copyright Houghton Mifflin Company. All rights reserved.11 | 31 Cluster Sampling Clusters of population units are selected at random and then all or some units in the chosen clusters are studied Slide 32 Copyright Houghton Mifflin Company. All rights reserved.11 | 32 Systematic Sampling Steps An organized procedure, selecting a sample from a list containing all the population units Steps: 1)Determine the sampling interval, number of units in the population k = ------------------------------------------ number of units desired in the sample Slide 33 Copyright Houghton Mifflin Company. All rights reserved.11 | 33 Systematic Sampling Steps (Contd) 2) Choose randomly one unit between the first and kth units in the population list 3) The randomly chosen unit and every kth unit thereafter are designated as part of the sample Slide 34 Copyright Houghton Mifflin Company. All rights reserved.11 | 34 Practical Considerations: Probability Sampling Methods Probability sampling techniques are generally used by large commercial marketing research firms that maintain national samples or panels that can be readily accessed for conducting periodic research surveys Slide 35 Copyright Houghton Mifflin Company. All rights reserved.11 | 35 Nonprobability Sampling Methods Convenience Sampling Judgment Sampling Quota sampling Slide 36 Copyright Houghton Mifflin Company. All rights reserved.11 | 36 Convenience Sampling Researcher's convenience forms the basis for selecting a sample of units The administrators of a college have announced a sharp increase in tuition fees for the next year. A TV reporter covering this news item is shown standing on campus talking to several students, one at a time, about their reactions to the proposed tuition fee increase. TV Reporter says: While some of the students feel that the 10 percent fee hike is justified, most of them consider it to be unfair. Slide 37 Copyright Houghton Mifflin Company. All rights reserved.11 | 37 Judgment Sampling A procedure in which a researcher exerts some effort in selecting a sample that he or she believes is most appropriate for a study Example The administrators of a college have announced a sharp increase in tuition fees for the next year A judgment sample of student officers may be more representative than a convenience sample of students The researcher should be knowledgeable about the ideal population for a study Slide 38 Copyright Houghton Mifflin Company. All rights reserved.11 | 38 Quota Sampling Involves sampling a quota of units to be selected from each population cell based on the judgment of the researchers and/or decision makers Steps 1)Divide the population into segments (referred to as cells) based on certain control characteristics 2)Determine the quota of units for each cell (quotas are determined by the researchers and/or decision makers) 3)Instruct the interviewers to fill the quotas assigned to the cells Slide 39 Copyright Houghton Mifflin Company. All rights reserved.11 | 39 Parameter &amp; Statistic Parameter The actual, or true, population mean value or population proportion for any variable income, product ownership Statistic An estimate of a parameter from sample data Slide 40 Copyright Houghton Mifflin Company. All rights reserved.11 | 40 Sampling Error Sampling Error = Parameter Value - Statistic Value Difference between a statistic value that is generated through a sampling procedure and the parameter value, which can be determined only through a census study Slide 41 Copyright Houghton Mifflin Company. All rights reserved.11 | 41 Sampling Distribution Representation of the sample statistic values obtained from every conceivable sample of a certain size chosen from a population by using a specified sampling procedure along with the relative frequency of occurrence of those statistic values Slide 42 Copyright Houghton Mifflin Company. All rights reserved.11 | 42 XX SXSX Sampling Distribution Slide 43 Copyright Houghton Mifflin Company. All rights reserved.11 | 43 50010 4509 4008 3507 3006 2505 2004 1503 1002 501 Annual expenditure for eating out ($) Family Number Table 11.4 Expenditures for Eating Out for a Hypothetical Population Slide 44 Copyright Houghton Mifflin Company. All rights reserved.11 | 44 4759,10 3755,10;6,9;7,8 2751,10;2,9;3,8;4,7;5,6 1751,6;2,5;3,4 75 1,2 Sample Mean Values ($) Samples of Two Families Table 11.5 Partial List of Possible Samples and Sample Means Slide 45 Copyright Houghton Mifflin Company. All rights reserved.11 | 45 Exhibit 11.5 Sampling Distribution (Bar Chart) for Simple Random Samples of Two Units Slide 46 Copyright Houghton Mifflin Company. All rights reserved.11 | 46 Exhibit 11.6 Sampling Distribution Shown as a Histogram Slide 47 Copyright Houghton Mifflin Company. All rights reserved.11 | 47 Central Limit Theorem When the sample size is sufficiently large, the sampling distribution associated with the sampling procedure display the properties of a normal distribution. Slide 48 Copyright Houghton Mifflin Company. All rights reserved.11 | 48 Confidence Estimation for Interval Data n = number of units in the sample X = sample mean value S x = s / n S = standard deviation Slide 49 Copyright Houghton Mifflin Company. All rights reserved.11 | 49 Given n = 100, x = 1,278 units, and s = 399 units To Construct 95 percent confidence interval s 399 s x = --- = ----- = 39.9 units n 100 The 95 percent confidence interv...</p>

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