Collecting Data: 21-30

A researcher planning a survey of heads of households in New York has census lists for each of 62 counties in the state. The procedure will be to obtain a simple random sample of heads of households from each of the counties rather than grouping all the census lists together and obtaining a sample from the entire group. Which of the following is not a true statement about the resulting stratified sample?

• It is more susceptible to bias than would be a simple random sample.

• It is easier and more cost-effective than a simple random sample.

• It gives comparative information that a simple random sample wouldn't give.

• It recognizes that opinions of heads of household in rural NY communities may differ from those in urban communities.

• All other statements are true.

Answer explanation

Stratified samples are often easier and more cost-effective to obtain and also make comparative data more available. In this case, responses can be compared in and among various counties. Rural and urban counties are less varied within each county than the population as a whole, and stratified sampling recognize this. There is no reason to suspect any more bias in this stratified sample than would be present in a simple random sample.

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CCSS.HSS.IC.B.3

Sampling variability (also called sampling error) occurs

• when interviewers make mistakes resulting in bias.

• when interviewers use judgment instead of random choice in picking the sample.

• when samples are too small.

• because a sample statistic is used to estimate a population parameter.

• in all of the other cases.

Answer explanation

Different samples give different sample statistics, all of which are estimates for the same population parameter. So error, called sampling variability or sampling error, is naturally present.

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CCSS.HSS.IC.B.4

Which of the following is most important in minimizing the placebo effect?

• Replication and randomization

• Replication and blinding

• Randomization and blinding

• Randomization and a control

• Blinding and a control

Answer explanation

Use of a control group and blinding as to which subjects are in the control group are the best tools to minimize the possibility of confounding due to the placebo effect. Replication and randomization are important marks of good experimental design, but they do not impact the placebo effect as does the use of a control and blinding.

A bank wishes to survey its customers. The decision is made to randomly pick ten customers who have just checking accounts, ten customers who have just savings accounts, and ten customers who have both checking and savings accounts. This procedure is an example of which type of sampling?

• Cluster

• Convenience

• Simple Random

• Stratified

• Systematic

Answer explanation

In stratified sampling, the population is divided into homogeneous groups called strata, and random samples of persons from all strata are chosen. In this example, the bank stratified by type of account holding into three strata.

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CCSS.HSS.IC.B.3

Which of the following is a true statement?

• If bias is present in a sampling procedure, it can be overcome by dramatically increasing the sample size.

• There is no such thing as a "bad sample."

• Sampling techniques that use probability techniques effectively eliminate bias.

• Sampling techniques that allow the surveyor to choose participants with care and precision go a long way to control bias.

• In choosing a sample size, actual sample size is more important than the fraction of the population that is surveyed.

Answer explanation

If there is bias, taking a larger sample just magnifies the bias. If there is enough bias, the sample can be worthless. Even when the subjects are chosen randomly, there can be bias due, for example, to nonresponse or to the wording of the questions. Allowing surveyors to choose participants usually fails to result in representative samples because there are too many unknowns. Most important is not the fraction of the population but, rather, the actual sample size.

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CCSS.7.SP.A.1

CCSS.HSS.IC.A.1

To find out a town's average family size, a researcher interviews a random sample of parents arriving at a pediatrician's office. The average family size in the final 100-family sample is 3.48. Is this estimate probably too low or too high?

• Too low because of undercoverage bias

• Too low because convenience sample underestimate average results

• Too high because of undercoverage bias

• Too high because convenience samples overestimate average results

• Too high because voluntary response samples overestimate average results

Answer explanation

The procedure misses all or nearly all childless families.

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CCSS.HSS.IC.B.3

Which of the following is a true statement about blocking?

• Blocking is to experiment design as stratification is to sampling design.

• By controlling certain variables, blocking can make conclusions more specific.

• The paired (matched pairs) comparison design is a special case of blocking.

• Blocking is a useful procedure when there are certain attributes, not under study, that may affect the outcomes.

• All of the other statements are true about blocking.

Answer explanation

Blocking in experiment design first divides the subjects into representative groups called blocks, just as stratification in sampling design first divides the population into representative groups called strata. This procedure can control certain variables by bringing them directly into the picture, and thus conclusions are more specific. The paired (matched pairs) comparison design is a special case of blocking in which each pair can be considered a block. When we can't control for certain attributes that may affect the outcomes, blocking may allow us to more clearly see true differences caused by the treatments.

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CCSS.HSS.IC.B.3

Two antidepressants are to be compared in the treatment of elderly patients in a nursing home. Each patient has his or her own room, some with spectacular views of the ocean. The experimental design is to create homogeneous blocks with respect to window view. How should randomization be used for a randomized block design?

• Within each block, randomly pick half the patients to receive each antidepressant.

• Randomly pick half of all patients to receive each antidepressant, but then analyze the results separately by blocks.

• Randomly chose which blocks will receive which antidepressant.

• Randomly choose half the blocks to receive each antidepressant for a given time period; then for the same time period, switch the medication in each block and compare the results.

• For ethical reasons, allow patients to choose which medication they prefer taking, but then randomly assign patients to the blocks.

Answer explanation

In a randomized block design, we assign subjects to treatments at random within each of the homogeneous blocks. In effect, to reduce variability, we run parallel experiments on the blocks.

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CCSS.HSS.IC.B.3

What is bias in conducting surveys?

• An example of sampling error

• Lack of a control group

• Confounding variables

• Difficulty in concluding cause and effect

• A tendency to favor the selection of certain members of a population.

Answer explanation

Poorly designed sampling techniques result in bias, that is, in a tendency to favor the selection of certain members of a population. For example, door-to-door surveys ignore the homeless, radio call-in programs give too much emphasis to persons with strong opinions, and interviews at shopping malls typically give the opinions of a very select sample of the population.

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CCSS.HSS.IC.B.3

A human resource department plans to survey 100 of the 3,000 employees in the firm. An alphabetical list of the employees is available, a random number between 1 and 30 is picked and the sample consists of the person that far down the list together with every 30th person after that. This procedure is an example of which type of sampling?

• Cluster

• Convenience

• Simple Random

• Stratified

• Systematic

Answer explanation

Systematic sampling involves listing the population in some order (alphabetically in this example), choosing a random point to start, and then picking every kth person (every 30 person in this example) from the list. This gives a reasonable sample as long as the original order of the list is not in any way related to the variables under consideration.

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CCSS.HSS.IC.B.3