Sampling Techniques (from AP Stats text)
(1) Voluntary Response Sample - consists of people who choose to be part of a sample by responding to a general appeal.
Example 1 (Trenholm): If Channel 7 conducts a phone-in survey concerning gay marriage (or some other controversial
topic), the people who phone in make up the voluntary response sample.
Advantages to using this method:
Disadvantages to using this method:
(2) Convenience Sampling - involves choosing the most convenient individuals from the population for your sample.
Example 2 (BPS): Manufacturers and advertising agencies often use interviews at shopping malls to gather information
about the habits of consumers and effectiveness of advertisements. Discuss the pros and cons of obtaining data using
mall interviewing.
Advantages to using this method:
Disadvantages to using this method:
Note: The two sampling methods listed above are biased. One method used to create an unbiased sample is described
below.
(3) Simple Random Sample (SRS) - a sample of size n selected in such a way that every
set of n individuals
has an equal chance of being selected for the sample.
This is an extremely important concept (as you can probably tell from the size of the print I used). Let’s make sure that
we understand what the definition says and what it doesn’t say.
Methods used to obtain a simple random sample:
1. “Names in a hat"
2. Dice, coins, cards
3. Random numbers table
4. Random number generator (TI calculator or computer)
Advantages to using this method:
Disadvantages to using this method:
Sometimes, we would like to ensure that all subgroups of a population are represented in a sample. For example, if you are
selecting a sample of students from the school, you may want to select a certain number of freshmen, sophomores, juniors
and seniors. In situations like this, you need to select an SRS from each of these subgroups (called strata) of the population.
This method is called stratified random sampling and described below.
(4) Stratified Random Sampling (steps involved in the process).
i. Divide the population into groups of similar individuals, called strata.
ii. Choose a separate SRS from each strata.
iii. Combine all of those individuals chosen from all of the stratus to make up the full sample.
Note of importance: A stratified random sample IS NOT a simple random sample.
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Advantages to using this method:
Disadvantages to using this method:
(5) Multistage Sample Design - we’ll describe this process with an example used in your book.
Suppose we wanted to interview 500 households in the United States about their favorite television programs. The
following stages could be used to select a sample:
i
Select a number (or numbers) between 1 and 50. This will tell us which state(s) we will be using.
ii Select a sample of towns at random from each state selected in step (i).
iii Select a sample of blocks at random from each town.
iv Select a sample of households at random from each block.
Advantages to using this method:
Disadvantages to using this method:
(6) Systematic sample - we’ll also describe this process with an example.
Example (Trenholm): Suppose you want to inspect packages of potato chips coming off the Lays factory assembly line.
A systematic sample would involve inspecting, for example, every 25th bag coming off line.
Advantages to using this method:
Disadvantages to using this method:
(7) Cluster Sample - an SRS from a set of all designated clusters.
Example (Trenholm): Suppose you want to examine 10th grade MCAS scores from various high schools in
Massachusetts. Instead of compiling a list of all individual students who took the 10th grade MCAS, it might be easier
to select several high schools (which contain groups or clusters of students) an examine scores from students in these
schools.
Advantages to using this method:
Disadvantages to using this method:
Sampling Techniques Additional Problems (from Statistics in Action)
1. Suppose you want to know what percentage of the U.S. households have children under the age of 13 living at home. Each
weekday from 9 to 5, your polltakers call households in your sample. Every time they reach a person in one of the homes,
they ask “ Do you have children under the age of 13 living in your household?” Eventually you give up on the households
that cannot be reached.
a.
Will your estimate of the percentage of U.S. households with children under the age of 13 probably be too low, too
high or about right?
b.
How does this example help explain why polltakers are likely to call at dinnertime?
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2. Make up two versions of a question about a controversial issue (gun control, abortion, gay marriage, the war in Iraq, etc.)
with one version designed to get a higher percentage in favor, the other designed to get a higher percentage opposed .
Test your questions on a sample of 20 people.
Do this as a separate writing assignment.
3. Suppose you want to know the average response to the question “ Do you like math?" on a scale from 1 “ Not at all," to 7
"Definitely,” for all students in your school. If you use your statistics class as a convenience sample, what sort of bias, if any,
would be likely? Be specific. In particular, tell whether you expect the sample average to be higher or lower than the
population average, and why.
4. You want to estimate the average number of states that people living in the United States have visited. If you asked only
those at least 40 years old, would you expect the estimate to be too high or too low? What kind of bias might you expect if
you select from only those living in Rhode Island?
5. “Television today is more offensive than ever, say the overwhelming majority - 92% - of readers who took part in the USA
Weekend’s third survey measuring attitudes toward the small screen.“ More than 21,600 people responded to this write-in
survey.
a.
Do you trust the results of the survey? Why or why not?
b.
What percentage of the entire U.S. television-watching public do you think would say that “today’s shows are more
offensive than ever”: more than 92%, quite a bit less than 92%, or just about 92%? Why do you think that?
6. For a study on smoking habits, you want to know the proportion of adult males in the United States who are nonsmokers,
who are cigarette smokers, and who are pipe of cigar smokers. Tell why it makes more sense to use a sample than to try to
check every individual. What types of bias might appear when you attempt to collect this information?
7. You want to take a sample of students in your school to estimate the average amount they spent on their last haircut.
Which sampling method do you think would work best: a simple random sample, a stratified random sample with two strata,
male and female, or a stratified random sample with class levels as strata.
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8. You are called upon to advise a local movie theater on designing a sampling plan for a survey of students in your school to
gain information about recent movies. The theater has time and money to interview about 50 students. What design would
you use?
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