Sampling: Surveys and How to Ask Questions

Chapter 4

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The Beauty of SamplingSample 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%.

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The Margin of Error: The Accuracy of Sample Surveys

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 =

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

€

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n×100%

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The Margin of Error: The Accuracy of Sample Surveys

A confidence interval is an interval of values computed from sample data that is likely to include the true population value.

€

1

n×100%

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Example: 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 important 65%Fairly important 23%Not very important 12%No opinion 0%

Conservative margin of error is 3%: 03.01003

1=

Approx. 95% confidence interval for the percent of all adult Americans who say religion is very important:

65% 3% or 62% to 68%

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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.

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Confidence LevelConfidence Level describes the chance (probability) that an interval actually contains the true population valueMost of the time (quantified by the confidence level) intervals computed in this way will capture the truth about the population, but occasionally they will not. In any given instance, the interval either captures the truth or it does not, but we will never know which is the case. Therefore, our confidence is the procedure (it works most of the time) and the confidence level (or level of confidence) is the percent of time we expect it to work.

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Advantages of a Sample Survey over a Census

Sometimes a Census Isn’t Possible when measurements destroy units

Speedespecially if population is large

Accuracydevote resources to getting accurate sample results

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Bias: How Surveys Can Go WrongResults 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.

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Simple 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.

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Choosing a Simple Random SampleYou Need:1. List of the units in the population.2. Source of random numbers.

ROW 0 00157 37071 79553 31062 42411 79371 25506 69135 1 38354 03533 95514 03091 75324 40182 17302 64224 2 59785 46030 63753 53067 79710 52555 72307 10223 3 27475 10484 24616 13466 41618 08551 18314 57700 4 28966 35427 09495 11567 56534 60365 02736 32700 5 98879 34072 04189 31672 33357 53191 09807 85796 6 50735 87442 16057 02883 22656 44133 90599 91793 7 16332 40139 64701 46355 62340 22011 47257 74877 8 83845 41159 67120 56273 67519 93389 83590 12944 9 12522 20743 28607 63013 60346 71005 90348 86615

Portion of a Table of Random Digits:

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Simple Random Sample of StudentsClass of 270 students. Want a simple random sample of 10 students.

ROW 0 00157 37071 79553 31062 42411 79371 25506 69135 1 38354 03533 95514 03091 75324 40182 17302 64224 2 59785 46030 63753 53067 79710 52555 72307 10223 3 27475 10484 24616 13466 41618 08551 18314 57700 4 28966 35427 09495 11567 56534 60365 02736 32700 5 98879 34072 04189 31672 33357 53191 09807 85796 6 50735 87442 16057 02883 22656 44133 90599 91793 7 16332 40139 64701 46355 62340 22011 47257 74877 8 83845 41159 67120 56273 67519 93389 83590 12944 9 12522 20743 28607 63013 60346 71005 90348 86615

1. Number the units: Students numbered 001 to 270.2. Choose a starting point: Row 3, 2nd 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.

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Simple Random Sample of Students5. Step 4 very inefficient.

Can give each unit in population multiple labels.e.g. use 001 to 270 then 301 to 570, 601 to 870so 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.

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Using a Table of Random Digitsin 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.

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Other Sampling MethodsNot 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.

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Stratified Random SamplingDivide 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.

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Cluster SamplingDivide 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.

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Systematic SamplingOrder 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.

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

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Difficulties 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.

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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.

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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.

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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

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

Example 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.

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Example: 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.

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How 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

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• 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)

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• 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)

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• 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?

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• 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.

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Example: 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.

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Example: 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.