Transcript Experimental Design

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4.2 Experiments, cont.
When a population consists of groups of individuals
that are “similar within but different between,” a
stratified random sample gives a better estimate
than a simple random sample. This same logic
applies in experiments.
A block is a group of experimental units that are known before the
experiment to be similar in some way that is expected to affect the
response to the treatments.
In a randomized block design, the random assignment of
experimental units to treatments is carried out separately within each
block.
A Smarter Design?
Suppose that a mobile phone company is considering two different keyboard designs
(A and B) for its new smart phone. The company decides to perform an experiment to
compare the two keyboards using a group of 10 volunteers. The response variable is
typing speed, measured in words per minute.
How should the company deal with the fact that four of the volunteers already use a
smart phone, whereas the remaining six volunteers do not? They could use a
completely randomized design and hope that the random assignment distributes the
smart-phone users and non-smart-phone users about evenly between the group using
keyboard A and the group using keyboard B. Even so, there might be a lot of variability
in typing speed in both groups because some members of each group are much more
familiar with smart phones than others. This additional variability might make it difficult
to detect a difference in the effectiveness of the two keyboards. What should the
researchers do?
A Smarter Design?
Because the company knows that experience with smart phones will affect typing
speed, they could start by separating the volunteers into two groups—one with
experienced smart-phone users and one with inexperienced smart-phone users. Each
of these groups of similar subjects is known as a block. Within each block, the
company could then randomly assign half of the subjects to use keyboard A and the
other half to use keyboard B. To control other variables, each subject should be given
the same passage to type while in a quiet room with no distractions. This randomized
block design helps account for the variation in typing speed that is due to experience
with smart phones.
A Smarter Design?
Men, Women, and Advertising
Women and men respond differently to advertising. Researchers would like to
design an experiment to compare the effectiveness of three advertisements for
the same product.
(a)
(b)
Explain why a randomized block design might be preferable to a completely
randomized design for this experiment.
Outline a randomized block design using 300 volunteers (180 men and 120
women) as subjects. Describe how you would carry out the random
assignment required by your design. Group 1
Ad 1
Women
n = 120
Random
Assignment
300
volunteer
subjects
Men
n = 180
Random
Assignment
n = 40
Group 2
n = 40
Ad 2
Group 3
n = 40
Ad 3
Group 1
n = 60
Ad 1
Group 2
n = 60
Ad 2
Group 3
n = 60
Ad 3
Compare
Reaction
Compare
Results
Compare
Reaction
A common type of randomized block design for comparing two treatments
is a matched pairs design. The idea is to create blocks by matching
pairs of similar experimental units.
A matched pairs design is a randomized blocked experiment in which
each block consists of a matching pair of similar experimental units.
Chance is used to determine which unit in each pair gets each
treatment.
Sometimes, a “pair” in a matched-pairs design consists of a single unit
that receives both treatments. Since the order of the treatments can
influence the response, chance is used to determine with treatment is
applied first for each unit.
Look, Ma, no hands! Does talking on a hands-free cell phone
distract drivers? Researchers recruit 40 student subjects for an
experiment to investigate this question. They have a driving
simulator equipped with a hands-free phone for use in the study.
Each subject will complete two sessions in the simulator: one while
talking on the hands-free phone and the other while just driving.
The order of the two sessions for each subject will be determined at
random. The route, driving conditions, and traffic flow will be the
same in both sessions.
Look, Ma, no hands! Does talking on a hands-free cell phone distract drivers? Researchers recruit
40 student subjects for an experiment to investigate this question. They have a driving simulator
equipped with a hands-free phone for use in the study. Each subject will complete two sessions in the
simulator: one while talking on the hands-free phone and the other while just driving. The order of
the two sessions for each subject will be determined at random. The route, driving conditions, and
traffic flow will be the same in both sessions.
(a) What type of design did the researchers use in their study?
Matched-Pairs Design
Look, Ma, no hands! Does talking on a hands-free cell phone distract drivers? Researchers recruit
40 student subjects for an experiment to investigate this question. They have a driving simulator
equipped with a hands-free phone for use in the study. Each subject will complete two sessions in the
simulator: one while talking on the hands-free phone and the other while just driving. The order of
the two sessions for each subject will be determined at random. The route, driving conditions, and
traffic flow will be the same in both sessions.
(b) Explain why the researchers chose this design instead of a completely
randomized design.
Differences between students could add variability to the response, making it
harder to detect if there is a difference caused by the treatments. Matched-pairs
design allows each student to be compared to their self.
Look, Ma, no hands! Does talking on a hands-free cell phone distract drivers? Researchers recruit
40 student subjects for an experiment to investigate this question. They have a driving simulator
equipped with a hands-free phone for use in the study. Each subject will complete two sessions in the
simulator: one while talking on the hands-free phone and the other while just driving. The order of
the two sessions for each subject will be determined at random. The route, driving conditions, and
traffic flow will be the same in both sessions.
(c) Why is it important to randomly assign the order of the treatments?
If all of the students use the hands-free phone first, we won’t know if they do better
the second time because they learned from mistakes or because they don’t have
the hands-free phone.
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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.
The Practice of Statistics, 5th Edition
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