copyright © 2011 pearson education, inc. samples and surveys chapter 13

Copyright © 2011 Pearson Education, Inc.

Samples and Surveys

Chapter 13

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


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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


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The two surprises are:

The best way to get a representative sample is to pick members of the population at random.

Larger populations do not require larger samples.


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Randomization

A randomly selected sample is representative of the whole population.

Randomization ensures that on average a sample mimics the population.


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Comparison of Two Random Samples from a Population of 3.5 Million Customers.


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Randomization

Produces samples whose averages resemble those in the population (avoids bias).

Enables us to infer characteristics of the population from a sample.


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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.


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This sample size is an almost infinitesimal portion of the population, yet the survey reveals attitudes of the entire population to within ± 3%


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Simple Random Sample (SRS)

A sample of n items chosen by a method that has an equal chance of picking any sample of size n from the population.

Is the standard to which all other sampling methods are compared.


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Simple Random Sample (SRS)

Sampling Frame: a list of items from which to select a random sample.

Systematic Sampling: method for selecting items from a sampling frame that follows a regular pattern (e.g., every 10th item).


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Identifying the Sampling Frame

If there is no fixed population of outcomes, no sampling frame exists (e.g., output from a production process).

The list available may differ from the list desired (e.g., voter registration lists identify people who can vote, not those who will).


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13.2 VARIATION

Estimating Parameters

Parameter: a characteristic of the population (e.g., µ)

Statistic: an observed characteristic of a sample (e.g., )

Estimate: using a statistic to approximate a parameter


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y

13.2 VARIATION

Notation for Statistics and Parameters


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13.2 VARIATION

Sampling Variation

Is the variability in the value of a statistic from sample to sample.

The price we pay for working with a sample rather than the population.


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13.2 VARIATION

Sampling Variation in Sample Means


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13.2 VARIATION

Sampling Variation in Sample Proportions


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4M Example 13.1: EXIT SURVEYS

Motivation

Why do customers leave a busy clothing store in the mall without making a purchase?


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Method

A survey is necessary. The owner decides to survey 50 weekend customers. The ideal sampling frame would list every customer who did not make a purchase over the weekend. Such a list does not exist.


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Mechanics

Interview every 10th customer who departs the store on the weekend. Based on typical customer flow, a sample of size 60 is expected. Ask customers why they didn’t make a purchase.


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Message

On the basis of the survey, the owner will be able to find out why shoppers are leaving without buying.


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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


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Cluster Samples

Divide a geographic region into clusters

Randomly select clusters

Randomly choose items within selected clusters


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4M Example 13.2: ESTIMATING THE RISE OF PRICES

Motivation

What goes into determining the consumer price index (CPI), the official measure of inflation?


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Method

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.


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Mechanics

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.


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Message

The urban consumer price index is an estimate of inflation base on a complex, clustered sample in selected metropolitan areas.


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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.


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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.


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Convenience Samples

A sampling method that selects individuals who are readily available.

Although easy to obtain, these samples are rarely representative.


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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?


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13.4 CHECKLIST FOR SURVEYS

How Wording of the Question Affects Results


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Best Practices

Randomize.

Plan carefully.

Match the sampling frame to the target population.


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Best Practices (Continued)

Keep focused.

Reduce the amount of nonresponse.

Pretest your survey.


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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.


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copyright © 2011 pearson education, inc. samples and surveys chapter 13

Documents

sample copyright

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systematic sampling

representative sample

selected sample

sampling methods

sample size

population representative