3. The Practice of Statistics, 5th Edition 3
DISTINGUISH between an observational study and an experiment.
EXPLAIN the concept of confounding.
IDENTIFY the experimental units, explanatory and response variables,
and treatments in an experiment.
EXPLAIN the purpose of comparison, random assignment, control, and
replication in an experiment.
DESCRIBE a completely randomized design for an experiment.
DESCRIBE the placebo effect and the purpose of blinding in an
experiment.
INTERPRET the meaning of statistically significant in the context of an
experiment.
EXPLAIN the purpose of blocking in an experiment.
DESCRIBE a randomized block design or a matched pairs design for
an experiment.
4. An observational study observes individuals and measures
variables of interest but does not attempt to influence the
responses.
An experiment deliberately imposes some treatment on
individuals to measure their responses.
When our goal is to understand cause and effect, experiments are the
only source of fully convincing data.
The distinction between observational study and experiment is one of
the most important concepts in statistics.
5. Observational studies of the effect of an explanatory variable on a
response variable often fail because of confounding between the
explanatory variable and one or more other variables.
Well-designed experiments take steps to prevent confounding.
Confounding occurs when two variables are associated in
such a way that their effects on a response variable cannot be
distinguished from each other.
AP Tip: If you are asked to identify a possible confounding variable,
you must:
1. Explain how it is associated with the explanatory variable.
2. explain how it affects the response variable.
6. 1. Does reducing screen brightness increase battery life in laptop computers? To
find out, researchers obtained 30 new laptops of the same brand. They chose
15 of the computers at random and adjusted their screens to the brightest
setting. The other 15 laptop screens were left at the default setting—moderate
brightness. Researchers then measured how long each machine’s battery
lasted. Was this an observational study or an experiment? Justify your
answer.
Experiment, because a treatment (brightness of
screen) was imposed on the laptops.
7. Does eating dinner with their families improve students’ academic performance?
According to an ABC News article, “Teenagers who eat with their families at least
five times a week are more likely to get better grades in school. This finding was
based on a sample survey conducted by researchers at Columbia University.
Was this an observational study or experiment? Justify your
answer.
Observational Study because students were not
assigned to eat a particular number of meals with
their family per week.
8. Does eating dinner with their families improve students’ academic performance?
According to an ABC News article, “Teenagers who eat with their families at least
five times a week are more likely to get better grades in school. This finding was
based on a sample survey conducted by researchers at Columbia University.
What are the explanatory and response variables?
Explanatory: number of meals per week eaten with
family
Response: GPA
9. Does eating dinner with their families improve students’ academic performance?
According to an ABC News article, “Teenagers who eat with their families at least
five times a week are more likely to get better grades in school. This finding was
based on a sample survey conducted by researchers at Columbia University.
Explain clearly why such a study cannot establish a cause-and-
effect relationship. Suggest a variable that may be confounded
with whether families eat dinner together.
There are probably other variables that influence the
response variable. For example, students who have
part-time jobs may not be able to eat many meals
with their families and may not have much time to
study, leading to lower grades.
11. Here is the basic vocabulary of experiments:
A specific condition applied to the individuals in an experiment is
called a treatment. If an experiment has several explanatory
variables (factors), a treatment is a combination of levels of
these factors.
The experimental units are the smallest collection of individuals
to which treatments are applied. When the units are human
beings, they often are called subjects.
12. What are the effects of repeated exposure to an advertising
message? The answer may depend on both the length of the ad and
on how often it is repeated. An experiment investigated this
question using 120 undergraduate students who volunteered to
participate. All subjects viewed a 40-minute television program
that included ads for a digital camera. Some subjects saw a 30-
second commercial; others, a 90-second version. The same
commercial was shown either 1, 3, or 5 times during the program.
After viewing, all the subjects answered questions about their recall
of the ad, their attitude toward the camera, and their intention to
purchase it.
13. What are the effects of repeated exposure to an advertising message? The answer may depend on both
the length of the ad and on how often it is repeated. An experiment investigated this question using 120
undergraduate students who volunteered to participate. All subjects viewed a 40-minute television
program that included ads for a digital camera. Some subjects saw a 30-second commercial; others, a
90-second version. The same commercial was shown either 1, 3, or 5 times during the program. After
viewing, all the subjects answered questions about their recall of the ad, their attitude toward the
camera, and their intention to purchase it.
For the advertising study, identify the experimental units or
subjects, explanatory and response variables, the factors, and the
treatments.
Experimental Subjects: 120 undergraduate students
Response variables: recall of the ad, attitude about
the digital camera and whether they intend to
purchase it
14. What are the effects of repeated exposure to an advertising message? The answer may depend on both
the length of the ad and on how often it is repeated. An experiment investigated this question using 120
undergraduate students who volunteered to participate. All subjects viewed a 40-minute television
program that included ads for a digital camera. Some subjects saw a 30-second commercial; others, a
90-second version. The same commercial was shown either 1, 3, or 5 times during the program. After
viewing, all the subjects answered questions about their recall of the ad, their attitude toward the
camera, and their intention to purchase it.
For the advertising study, identify the experimental units or
subjects, explanatory and response variables, the factors, and the
treatments.
Factor B: Repetitions (Explanatory variable)
Factor A:
Length
(Explanatory
Variable)
1 time 3 times 5 times
30-sec
90-sec
Treatment 1 Treatment 2 Treatment 3
Treatment 4 Treatment 5 Treatment 6
15. For the advertising study, identify the experimental units or
subjects, explanatory and response variables, the factors, and the
treatments.
Factor B: Repetitions
Factor A:
Length
1 time 3 times 5 times
30-sec
90-sec
Treatment 1 Treatment 2 Treatment 3
Treatment 4 Treatment 5 Treatment 6
Treatment 5 = 90-sec
commercial 3 times
during the program.
3 levels
2 levels
16. For the advertising study, identify the experimental units or
subjects, explanatory and response variables, the factors, and the
treatments.
Factor B: Repetitions
Factor A:
Length
1 time 3 times 5 times
30-sec
90-sec
Treatment 1 Treatment 2 Treatment 3
Treatment 4 Treatment 5 Treatment 6
Hint: # of treatments = # levels
for Factor A x # of levels for
Factor B
EX: 2 x 3 = 6
In contrast to observational studies, experiments don’t just observe individuals or ask them questions. They actively impose some treatment in order to measure the response.
Skip explanatory for a minute.
Think about the # of factors and # of treatments. Watch until about 4:35. 2 factors: amount of money and how it is spent.
