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1.2 Sampling
LEARNING GOAL
Understand the importance of choosing a representative sample and become familiar with several common methods of sampling.
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Definition
A census is the collection of data from every member of a population.
Definition
A representative sample is a sample in which the relevant characteristics of the sample members are generally the same as the characteristics of the population.
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EXAMPLE 1 A Representative Sample for Heights
Suppose you want to determine the mean height of all students at your school. Which is more likely to be a representative sample for this study: the men’s basketball team or the students in your statistics class?
Solution:
The men’s basketball team is not a representative sample for a study of height, both because it consists only of men and because basketball players tend to be taller than average. The mean height of the students in your statistics class is much more likely to be close to the mean height of all students, so the members of your class make a more representative sample than the members of the man’s basketball team.
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Bias
Definition
A statistical study suffers from bias if its design or conduct tends to favor certain results.
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EXAMPLE 2 Why Use Nielsen?
Nielsen Media Research earns money by charging television stations and networks for its services. For example, NBC pays Nielsen to provide ratings for its television shows. Why doesn’t NBC simply do its own ratings, instead of paying a company like Nielsen to do them?
Solution:
The cost of advertising on a television show depends on the show’s ratings. The higher the ratings, the more the network can charge for advertising—which means NBC would have a clear bias if it conducted its own ratings. Advertisers therefore would not trust ratings that NBC produced on its own.
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TIME OUT TO THINK
The fact the NBC pays Nielsen for its services might seem to give Nielsen a financial incentive to make NBC look good in the ratings. How does the fact that Nielsen also provides ratings for other networks help prevent it from being biased toward NBC?
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Sampling Methods
Simple Random Samples
A random sample is one in which every member of the population has an equal chance of being selected to be part of the sample.
With simple random sampling every possible sample of a particular size has an equal chance of being selected.
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TIME OUT TO THINK
Look for the random number key on a calculator. What happens when you push it? How could you use the random number key to select a sample of 100 students?
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EXAMPLE 3 Telephone Book Sampling
You want to conduct an opinion poll in which the population as all the residents in a town. Could you choose a simple random sample by selecting names from the local telephone book?
Solution:
A sample drawn from a telephone book is not a simple random sample of the town population because phone books invariably are missing a lot of names, and any one whose name is missing has no chance of being selected. For example, the phone book will be missing names when two or more people share the same phone number but have only one listing, when people choose to have an unlisted phone number or to rely exclusively on a cell phone, or when people (such as the homeless) don’t have a telephone.
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Sampling Methods
Simple Random Samples
Systematic Sampling
A type of sampling in which we use a system such as choosing every 50th member of a population.
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EXAMPLE 5 When Systematic Sampling Fails
You are conducting a survey of students in a co-ed dormitory in which males are assigned to odd-numbered rooms and females are assigned to even-numbered rooms. Can you obtain a representative sample when you choose every 10th room?
Solution:
No. If you start with an odd-numbered room, every 10th room will also be odd-numbered (such as room numbers 3, 13, 23,…). Similarly, if you start with an even numbered room, every 10th room will also be even-numbered. You will therefore obtain a sample consisting of either all males or all females, neither of which is representative of the co-ed population.
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TIME OUT TO THINK
Suppose you chose every 5th room, rather than every 10th room, in Example 5. Would the sample then be representative?
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Sampling Methods
Simple Random Samples
Systematic Sampling
Convenience Samples
The sample is chosen for convenience rather than by a more sophisticated procedure.
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EXAMPLE 6 Salsa Taste Test
A supermarket wants to decide whether to carry a new brand of salsa, so it offers free tastes at a stand in the store and asks people what they think. What type of sampling is being used? Is the sample likely to be representative of the population of all shoppers?
Solution:
The sample of shoppers stopping for a taste of the salsa is a convenience sample because these people happen to be in the store and are willing to try the new product. (This type of convenience sample, in which people choose whether or not to be part of the sample, is also called a self-selected sample.)
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EXAMPLE 6 Salsa Taste Test
Solution: cont.
The sample is unlikely to be representative of the population of all shoppers, because different types of people may shop at different times (for example, stay-at-home parents are more likely to shop at mid-day than are working parents) and only people who like salsa are likely to participate.
The data may still be useful, however, because the opinions of people who like salsa are probably the most important ones in this case.
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Sampling Methods
Simple Random Samples
Systematic Sampling
Convenience Samples
Cluster Samples
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Cluster sampling involves the selection of all members in randomly selected groups, or clusters.
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EXAMPLE 7 Gasoline Prices
You want to know the mean price of gasoline at gas stations located within a mile of rental car locations at airports. Explain who you might use cluster sampling in this case.
Solution:
You could randomly select a few airports around the country. For theses airports, you would check the gasoline price at every gas station within a mile of the rental car location.
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Sampling Methods
Simple Random Samples
Systematic Sampling
Convenience Samples
Cluster Samples
Stratified Samples
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Stratified sampling involves randomly selecting members from each stratum.
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EXAMPLE 8 Unemployment Data
The U.S. Labor Department surveys 60,000 households each month to copile its unemployment reprot. To select these households, the Department first groups cities and counties into about 2000 geographic areas. It then ramdomly selects households to survey within these geographic areas.
How is this an example of stratified sampling?
What are the strata?
Why is stratified sampling important in this case?
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EXAMPLE 8 Unemployment Data
Solution:
The unemployment survey is an example of stratified sampling because it first breaks the population into subgroups.
Stratified sampling is important in this case because unemployment rates in rural Kansas may be very different from those in Silicon Valley
By using stratified sampling, the Labor Department ensures that its sample fairly represents all geographic regions.
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Summary of Sampling Methods
Keep in mind the following three key ideas:
A study can be successful only if the sample is representative of the population.
A biased sample is unlikely to be a representative sample.
Even a well-chosen sample may still turn out to be unrepresentative just because of bad luck in the actual drawing of the sample.
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Common Sampling Methods
Simple random sampling: We choose a sample of items in such a way that every sample of the same size has an equal chance of being selected.
Systematic sampling: We use a simple system to choose the sample, such as selecting every 10th or every 50th member of the population.
Convenience sampling: We use a sample that happens to be convenient to select.
Cluster sampling: We first divide the population into groups, or clusters, and select some of these clusters at random. We then obtain the sample by choosing all the members within each of the selected clusters.
Stratified sampling: We use this method when we are concerned about differences among subgroups, or strata, within a population. We first identify the strata and then draw a random sample within each stratum. The total sample consists of all the samples from the individual strata.
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Simple Random Sampling:
Every sample of the same size has an equal chance of being selected. Computers are often used to generate random numbers.
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Systematic Sampling:
Select every kth member.
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Convenience Sampling:
Use results that are readily available.
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Cluster Sampling:
Divide the population into clusters, randomly select some of those clusters, then choose all members of the selected clusters.
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Stratified Sampling:
Partition the population into at least two strata, then draw a sample from each.
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The End
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