4.1 The Beauty of Sampling

Chapter 4

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.

Sampling: Surveys and How to Ask Questions

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%.

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Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc.

Example 4.1 The Importance of Religion

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:

Very important Fairly important Not very important No opinion

65% 23% 12% 0%

Approx. 95% confidence interval for the percent of all adult Americans who say religion is very important: 65% ± 3% or 62% to 68%

Add and subtract margin of error to create an approximate 95% confidence interval. 3

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Advantages of a Sample Survey over a Census

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.

for Adult Americans Poll of n = 1003 adult Americans: “How important would you say religion is in your own life?”

Conservative margin of error is 3%:

For percents:

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Sometimes a Census Isn’t Possible when measurements destroy units

Speed especially if population is large

Accuracy devote resources to getting accurate sample results

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4.2 Simple Random Sampling and Randomization

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.

Probability Sampling Plan: everyone in population has specified chance of making it into the sample.

Selection bias occurs if method for selecting participants produces sample that does not represent the population of interest.

Simple Random Sample: every conceivable group of units of the required size has the same chance of being the selected sample.

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.

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Choosing a Simple Random Sample

Class of 270 students. Want a simple random sample of 10 students. 1.  Number the units: Students numbered 001 to 270 – place in one column. 2.  Generate random numbers: in an adjacent column, generate uniform random numbers (Calc – Random Data – Uniform …). 3.  Sort: both columns by random numbers. 4.  Choose: the top ten students are those selected in the sample. 5.  Save your results! 9

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Example 4.5 Assigning Children

Using a Table of Random Digits in a Randomized Experiment

to Lift Weights

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.

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Simple Random Sample of Students

You Need: 1.  List of the units in the population. 2.  Source of random numbers : Minitab or random number tables (book).

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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 random numbers to assign children to groups: - assign labels to each child -  assign a random number to each child -  sort by random numbers -  first 15 go to group 1, next 16 to group 2, last 12 to group 3 Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc.

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4.3 Other Sampling Methods

Stratified Random Sampling

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.

Divide population of units into groups (called strata) and take a simple random sample from each of the strata.

Shaded squares show a simple random sample of 30 rooms.

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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.

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Cluster Sampling

Systematic Sampling

Divide population of units into groups (called clusters), take a random sample of clusters and measure only those items in these clusters.

Order the population of units in some way, select one of the first k units at random and then every kth unit thereafter. College survey: Order list of rooms starting at top floor of 1st undergrad dorm. Pick one of the first 11 rooms at random => room 3, then pick every 11th room after that.

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.

Note: often a good alternative to random sampling but can lead to a biased sample.

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.

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Random-Digit Dialing

Multistage Sampling

Method approximates a simple random sample of all households in the United States that have telephones.

Using a combination of the sampling methods, at various stages.

1.  2. 

3.  4. 

List all possible exchanges (= area code + next 3 digits). Take a sample of exchanges (chance of being sampled based on white pages proportion of households with a specific exchange). Take a random sample of banks (= next 2 digits) within each sampled exchange. Randomly generate the last two digits from 00 to 99.

Example: •  • 

• 

Once a phone number determined, make multiple attempts to reach someone at that household. Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc.

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• 

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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.

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Example 4.7

Example 4.8

The Nationwide Personal Transportation Survey

A Los Angeles Times National Poll

“… 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

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.

Times

Multistage Sample:

Times Poll

•  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.

•  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 nonlisted numbers could be contacted.

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4.4 Difficulties and Disasters in Sampling

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.

Using wrong sampling frame Not reaching individuals selected Self-selected sample Convenience/Haphazard sample

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Not Reaching the Individuals Selected

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“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

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.

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Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc.

Nonresponse or Volunteer Response

Failing to contact or measure the individuals who were selected in the sampling plan leads to nonresponse bias. •  •  •  • 

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Using the Wrong Sampling Frame

Some problems occur even when a sampling plan has been well designed. •  •  •  • 

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•  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. Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc.

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Example 4.9

Which Scientists Trashed the Public?

Disasters in Sampling Responses from a self-selected group, convenience sample or haphazard sample rarely representative of any larger group.

“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)

Example 4.10

•  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. Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc.

A Meaningless Poll

“Do you support the President’s economic plan?” Results from TV quickie poll and proper study:

Science Poll

Those dissatisfied more likely to respond to TV poll and it did not give the “not sure” option. 25

Case Study 4.1 The Infamous Literary

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Case Study 4.1 The Infamous Literary

Digest Poll of 1936

Digest Poll of 1936

Election of 1936: Democratic incumbent Franklin D. Roosevelt and Republican Alf Landon

Election of 1936: Democratic incumbent Franklin D. Roosevelt and Republican Alf Landon

Literary Digest Poll:

Gallup 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.

•  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%.

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4.5 How to Ask Survey Questions

Possible Sources of Response Bias in Surveys (cont)

Possible Sources of Response Bias in Surveys

•  Asking the Uninformed: People do not like to

•  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. Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc.

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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. Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc.

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Possible Sources of Response Bias in Surveys (cont)

•  Be Sure You Understand What Was Measured:

•  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.

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?

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Case Study 4.2 No Opinion of Your Own?

•  Open or Closed Questions: Should Choices Be Given?

Let Politics Decide

Open question = respondents allowed to answer in own words.

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.

Closed question = given list of alternatives, usually offer choice of “other” and can fill in blank.

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.

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.

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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. Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc.

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