# Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. Sampling: Surveys and How to Ask Questions Chapter 4.

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Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. Sampling: Surveys and How to Ask Questions Chapter 4

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 2 4.1The Beauty of Sampling Sample Survey: a subgroup of a large population questioned on set of topics. Special type of observational study. Less costly and less time than a census. With proper methods, a sample of 1500 can almost certainly gauge the percentage in the entire population who have a certain trait or opinion to within 3%.

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 3 The Margin of Error The sample proportion and the population proportion with a certain trait or opinion differ by less than the margin of error in at least 95% of all random samples. Conservative margin of error: For proportions: For percents: Add and subtract margin of error to create an approximate 95% confidence interval.

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 4 Example 4.1 The Importance of Religion for Adult Americans Poll of n = 1003 adult Americans: “How important would you say religion is in your own life?” Very important65% Fairly important23% Not very important12% No opinion0% Conservative margin of error is 3%: Approx. 95% confidence interval for the percent of all adult Americans who say religion is very important: 65%  3% or 62% to 68%

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 5 Interpreting Confidence Interval The interval 62% to 68% may or may not capture the percent of adult Americans who considered religion to be very important in their lives. But, in the long run this procedure will produce intervals that capture the unknown population values about 95% of the time => called the 95% confidence level.

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 6 Advantages of a Sample Survey over a Census Sometimes a Census Isn’t Possible when measurements destroy units Speed especially if population is large Accuracy devote resources to getting accurate sample results

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 7 Bias: How Surveys Can Go Wrong Results based on a survey are biased if method used to obtain those results would consistently produce values that are either too high or too low. Selection bias occurs if method for selecting participants produces sample that does not represent the population of interest. Nonresponse bias occurs when a representative sample is chosen but a subset cannot be contacted or doesn’t respond. Response bias occurs when participants respond differently from how they truly feel.

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 8 4.2Simple Random Sampling and Randomization Probability Sampling Plan: everyone in population has specified chance of making it into the sample. Simple Random Sample: every conceivable group of units of the required size has the same chance of being the selected sample.

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 9 Choosing a Simple Random Sample You Need: 1.List of the units in the population. 2.Source of random numbers. Portion of a Table of Random Digits:

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 10 Simple Random Sample of Students Class of 270 students. Want a simple random sample of 10 students. 1.Number the units: Students numbered 001 to 270. 2.Choose a starting point: Row 3, 2 nd column (10484…) 3.Read off consecutive numbers: (3-digit labels here) 104, 842, 461, 613, 466, 416, 180, 855, 118, 314, 577, 002, 896, … 4.If number corresponds to a label, select that unit. If not, skip it. Continue until desired sample size obtained.

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 11 Simple Random Sample of Students 5.Step 4 very inefficient. Can give each unit in population multiple labels. e.g. use 001 to 270 then 301 to 570, 601 to 870 so the second 3-digit number of 842 would correspond to unit with label 842 – 600 = 242. Using method in Step 4 selected units would be: 104, 180, 118, 002, etc. Using method in Step 5 selected units would be found more efficiently as: 104, 242, 161, 013, 166, 116, 180, 255, 118, 014.

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 12 Example 4.4 Representing the Heights of British Women Simple random sample of 10 from 199 British women. 1.Assign an ID number from 001 to 199 to each woman. 2.Use random digits to randomly select ten numbers between 001 to 199, sample the heights of the women with those IDs. Sample 1: Using statistical package Minitab IDs: 176, 10, 1, 40, 85, 162, 46, 69, 77, 154 Heights: 60.6, 63.4, 62.6, 65.7, 69.3, 68.7, 61.8, 64.6, 60.8, 59.9; mean = 63.7 inches Sample 2: Using Table (Row 5, Col 3; multiple labels approach) IDs: 41, 93, 167, 33, 157, 131, 110, 180, 185, 196 Heights: 59.4, 66.5, 63.8, 62.6, 65.0, 60.2, 67.3, 59.8, 67.7, 61.8; mean = 63.4 inches

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 13 Using a Table of Random Digits in a Randomized Experiment Randomization plays a key role in designing experiments to compare treatments. Completely randomized design = all units are randomly assigned to treatment conditions. Matched-pairs / Randomized Block design = randomize order treatments are assigned within pair/block.

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 14 Example 4.5 Assigning Children to Lift Weights In Case Study 3.2, 43 children randomly assigned – the first 15 to Group 1, the next 16 to Group 2, and the remaining 12 to Group 3. Using table to assign children to groups: Label children from 01 to 43, and then 51 to 93. Starting at Row 7: 16, 33, 24, 01, 39, 14 (64 – 50), 20 (70 – 50), (14 skip), 13 (63 – 50), 05 (55 – 50), 12 (62 – 50), 34, 02, (20 skip), 11, (47 skip), 25, 27 (77 – 50).

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 15 4.3Other Sampling Methods Not always practical to take a simple random sample, can be difficult to get a numbered list of all units. Example: College administration would like to survey a sample of students living in dormitories. Shaded squares show a simple random sample of 30 rooms.

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 16 Stratified Random Sampling Divide population of units into groups (called strata) and take a simple random sample from each of the strata. College survey: Two strata = undergrad and graduate dorms. Take a simple random sample of 15 rooms from each of the strata for a total of 30 rooms. Ideal: stratify so little variability in responses within each of the strata.

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 17 Cluster Sampling Divide population of units into groups (called clusters), take a random sample of clusters and measure only those items in these clusters. College survey: Each floor of each dorm is a cluster. Take a random sample of 5 floors and all rooms on those floors are surveyed. Advantage: need only a list of the clusters instead of a list of all individuals.

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 18 Systematic Sampling Order the population of units in some way, select one of the first k units at random and then every k th unit thereafter. College survey: Order list of rooms starting at top floor of 1 st undergrad dorm. Pick one of the first 11 rooms at random => room 3, then pick every 11 th room after that. Note: often a good alternative to random sampling but can lead to a biased sample.

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 19 Random-Digit Dialing Method approximates a simple random sample of all households in the United States that have telephones. 1.List all possible exchanges (= area code + next 3 digits). 2.Take a sample of exchanges (chance of being sampled based on white pages proportion of households with a specific exchange). 3.Take a random sample of banks (= next 2 digits) within each sampled exchange. 4.Randomly generate the last two digits from 00 to 99. Once a phone number determined, make multiple attempts to reach someone at that household.

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 20 Multistage Sampling Using a combination of the sampling methods, at various stages. Example: Stratify the population by region of the country. For each region, stratify by urban, suburban, and rural and take a random sample of communities within those strata. Divide the selected communities into city blocks as clusters, and sample some blocks. Everyone on the block or within the fixed area may then be sampled.

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 21 Example 4.7 The Nationwide Personal Transportation Survey Nationwide Personal Transportation Survey: taken every 5 years by the U.S. Department of Transportation. 1995 Survey = 21,000 households. Interviews conducted by telephone using a computer-assisted telephone interviewing (CATI) system. Multistage Sample: U.S. households were stratified by region of country, size of metropolitan area, and whether there is a subway system. Households were then selected by random-digit dialing. Everyone in a selected household was included => each household was a cluster.

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 22 Example 4.8 A Los Angeles Times National Poll Times Poll 1,249 adults nationwide by telephone. Over a two-day period in February 1999. Telephone numbers chosen from all exchanges in nation. Random-digit dialing techniques used so listed and non- listed numbers could be contacted. “… half of Americans polled said they view Jan. 1, 2000, as ‘just another New Year’s Day’ … About one in 10 report that they are stockpiling goods.” Los Angeles Times

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 23 4.4Difficulties and Disasters in Sampling Using wrong sampling frame Not reaching individuals selected Self-selected sample Convenience/Haphazard sample Some problems occur even when a sampling plan has been well designed.

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 24 Using the Wrong Sampling Frame The sampling frame is the list of units from which the sample is selected. This list may or may not be the same as the list of all units in the desired “target” population. Example: using telephone directory to survey general population excludes those who move often, those with unlisted home numbers, and those who cannot afford a telephone. Solution: use random-digit dialing.

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 25 Not Reaching the Individuals Selected Failing to contact or measure the individuals who were selected in the sampling plan leads to nonresponse bias. Telephone surveys tend to reach more women. Some people are rarely home. Others screen calls or may refuse to answer. Quickie polls: almost impossible to get a random sample in one night.

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 26 Nonresponse or Volunteer Response The lower the response rate, the less the results can be generalized to the population as a whole. Response to survey is voluntary. Those who respond likely to have stronger opinions than those who don’t. Surveys often use reminders, follow up calls to decrease nonresponse rate. “In 1993 the GSS (General Social Survey) achieved its highest response rate ever, 82.4%. This is five percentage points higher than our average over the last four years.” GSS News, Sept 1993

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 27 Example 4.9 Which Scientists Trashed the Public? Science Poll 1400 professionals (in science and in journalism). Only 34% response rate among scientists. Typical respondent was white, male physical scientist over age of 50 doing basic research. Respondents represent a narrow subset of scientists => inappropriate to generalize to all scientists. “82% (of scientists) trashed the media, agreeing with the statement ‘The media do not understand statistics well enough to explain new findings.’ ” Science (Mervis, 1998)

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 28 Disasters in Sampling Responses from a self-selected group, convenience sample or haphazard sample rarely representative of any larger group. Example 4.10 A Meaningless Poll “Do you support the President’s economic plan?” Results from TV quickie poll and proper study: Those dissatisfied more likely to respond to TV poll and it did not give the “not sure” option.

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 29 Case Study 4.1 The Infamous Literary Digest Poll of 1936 Election of 1936: Democratic incumbent Franklin D. Roosevelt and Republican Alf Landon Literary Digest Poll: Sent questionnaires to 10 million people from magazine subscriber lists, phone directories, car owners, who were more likely wealthy and unhappy with Roosevelt. Only 2.3 million responses for 23% response rate. Those with strong feelings, the Landon supporters wanting a change, were more likely to respond. (Incorrectly) Predicted a 3-to-2 victory for Landon.

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 30 Case Study 4.1 The Infamous Literary Digest Poll of 1936 Election of 1936: Democratic incumbent Franklin D. Roosevelt and Republican Alf Landon Gallup Poll: George Gallup just founded the American Institute of Public Opinion in 1935. Surveyed a random sample of 50,000 people from list of registered voters. Also took a random sample of 3000 people from the Digest lists. (Correctly) Predicted Roosevelt the winner. Also predicted the (wrong) results of the Literary Digest poll within 1%.

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 31 4.5How to Ask Survey Questions Deliberate bias: The wording of a question can deliberately bias the responses toward a desired answer. Unintentional bias: Questions can be worded such that the meaning is misinterpreted by a large percentage of the respondents. Desire to Please: Respondents have a desire to please the person who is asking the question. Tend to understate response to an undesirable social habit/opinion. Possible Sources of Response Bias in Surveys

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 32 Asking the Uninformed: People do not like to admit that they don’t know what you are talking about when you ask them a question. Unnecessary Complexity: If questions are to be understood, they must be kept simple. Some questions ask more than one question at once. Ordering of Questions: If one question requires respondents to think about something that they may not have otherwise considered, then the order in which questions are presented can change the results. Possible Sources of Response Bias in Surveys (cont)

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 33 Confidentiality and Anonymity: People will often answer questions differently based on the degree to which they believe they are anonymous. Easier to ensure confidentiality, promise not to release identifying information, than anonymity, researcher does not know the identity of the respondents. Possible Sources of Response Bias in Surveys (cont)

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 34 Be Sure You Understand What Was Measured: Words can have different meanings. Important to get a precise definition of what was actually asked or measured. E.g. Who is really unemployed? Some Concepts Are Hard to Precisely Define: E.g. How to measure intelligence? Measuring Attitudes and Emotions: E.g. How to measure self-esteem and happiness?

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 35 Open or Closed Questions: Should Choices Be Given? Open question = respondents allowed to answer in own words. Closed question = given list of alternatives, usually offer choice of “other” and can fill in blank. If closed are preferred, they should first be presented as open questions (in a pilot survey) for establishing list of choices. Results can be difficult to summarize with open questions.

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 36 Case Study 4.2 No Opinion of Your Own? Let Politics Decide 1978 Poll, Cincinnati, Ohio: people asked whether they “favored or opposed repealing the 1975 Public Affairs Act.” No such act, about one-third expressed opinion. 1995 Washington Post Poll: 1000 randomly selected people asked “Some people say the 1975 Public Affairs Act should be repealed. Do you agree or disagree that it should be repealed?” 43% expressed opinion, 24% agreeing should be repealed.

Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. 37 Case Study 4.2 No Opinion of Your Own? Let Politics Decide (cont) Second 1995 Washington Post Poll: polled two separate groups of 500 randomly selected adults. Group 1: “President Clinton [a Democrat] said that the 1975 Public Affairs Act should be repealed. Do you agree or disagree?” Of those expressing an opinion: 36% of the Democrats agreed should be repealed, 16% of the Republicans agreed should be repealed. Group 2: “The Republicans in Congress said that the 1975 Public Affairs Act should be repealed. Do you agree or disagree?” Of those expressing an opinion: 36% of the Republicans agreed should be repealed, 19% of the Democrats agreed should be repealed.