Transcript AP Statistics Section 5.2 A Designing Experiments

AP Statistics Section 5.2 A
Designing Experiments
Recall the primary difference between an
observational study and an experiment.
In an experiment, we deliberately
do something to the individuals to
observe their responses.
The individuals on which an
experiment is conducted are called the
_________________.
experimental units When the units
are human beings, they are called
_________.
subjects
A specific experimental condition applied to the
units is called a _________.
treatment Any specific
treatment may have several different
components to it. These different components
are called _______
factors and will be the explanatory
variable(s) in our study. Many experiments study
the joint effects of several factors. In such an
experiment, each treatment is formed by
combining different amounts of each of the
factors. Each specific value of a factor is called a
_____.
level
Example: What are the effects of repeated
exposure to an advertising message? The
answer may depend both on the length of the
ad and how often it is repeated. An experiment
investigated this question using undergraduate
students. 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 1, 3 or 5 times
during the program.
How many different factors are present in the
experiment and what are they?
2 factors: length of commercial and the
number of repetitions
What are the different levels of each of the
factor?
Length: 30 secs. or 90 secs.
Repetitions: 1, 3 or 5
By combining the information above describe the
various treatments in this experiment. How many
treatments were present in the experiment?
30 sec .- 1 rep.
30 sec. - 3 rep.
30 sec. - 5 rep.
90 sec. - 1 rep.
90 sec. - 3 rep.
90 sec. - 5 rep.
After viewing the 40-minute
program, all of the subjects
answered questions about their
recall of the ad, their attitude
toward the camera and their
intention to purchase it. These are
the ________
response variables.
This example shows how
experiments allow us to study the
combined effects of several factors.
The inter-action of several factors
can produce effects that could not
be predicted from looking at the
effects of each factor alone.
Some experiments have a simple design
with only a single treatment which is
applied to all of the experimental units.
Such an experiment could be outlined in
the following way.
treatment  response
Experiments that are conducted in the
controlled environment of the laboratory
are protected from lurking variables.
When experiments are conducted in the
field or with living subjects, simple designs
can yield invalid data. That is, we cannot
tell whether the response was due to the
treatment or to lurking variables. This can
be particularly true in medical
experiments.
A placebo is a dummy treatment. The
response to the dummy treatment is
called the placebo effect. We can
defeat confounding by comparing two
groups of patients, one which receives
the treatment and the other which
receives the placebo.
The group of subjects who receives
the treatment is called the
treatment group while the group of
______________
subjects who receives the placebo is
called a ____________
control group because it
enables us to control the effects of
outside variables on the outcome.
There are 3 basic principles to
good experimental design:
Control is the first basic principle of
statistical design of experiments. Don’t
confuse control and control group.
Control refers to the overall effort to
minimize the variability in the way the
experimental units are obtained and
treated. Comparison of several
treatments in the same environment is
the simplest form of control.
Even with control, there will still be
natural variability among experimental
units. If each treatment is assigned to
only one unit, you won’t know
whether any systematic differences in
responses were due to the
treatments or to the natural variability
in the units.
We would like to see units within a
treatment group responding similarly
to one another but differently from
units in other treatment groups.
Then we can be sure that the treatment
groups really are responding differently
from each other.
replication: the use of enough
experimental units to reduce chance
variation. The purpose of replication is
not to eliminate chance variation but
to reduce its role and increase the
sensitivity of the experiment to
differences between treatments.
randomization: the rule used to
assign the experimental units to
the treatment groups must involve
randomization.
Comparison of the effects of several treatments
is valid only when all treatments are applied to
similar groups of experimental units.
Statisticians rely on chance to make an
assignment that does not depend on any
characteristic of the experimental units and that
does not rely on the judgment of the
experimenter in any way. Randomization allows
us to assert that treatment groups are
essentially similar, that there is no systematic
difference between them before treatments are
administered.
Example: Design an experiment to measure whether
listening to classical music while reading an unfamiliar
piece of literature aids retention. Assume there are 40
students in the experiment.
compare
retention
Label 01-40. Skip > 40 and
repeats. First 20 go in group
1 and next 20 in group 2
Example: Set up treatments to determine if regularly taking
aspirin and/or beta-carotene help protect people against
heart attacks and/or some forms of cancer. Assume there are
200 subjects in the experiment.