Transcript 3.1-3.2 First Steps and Design of Experiments

3.1-3.2
First Steps and
Design of
Experiments
Renee Smith
Josh Moline
First Steps
• Design for producing data
– Arrangements or patterns for producing data.
– How many and how to collect data.
– Avoid haphazard or incomplete data.
• Anecdotal Evidence
– This is based on haphazardly selected
individual cases, which often come to our
attention because they are striking in some
way. These cases need not be representative of
any larger group of cases.
First Steps
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• Available data
– Available data are data that were produced in
the past for some other purpose but that may
help answer a present question.
• Sampling
– Study a part to gain information about the
whole.
– Examples: Opinion polls, government reports,
quality of manufactured items.
First Steps
continued…
• Census
– Attempt to contact every individual in the
population.
– Often not reasonable
• Cost
• Time required
• Experiments
– Deliberately imposes some treatment on
experimental units or subjects.
First Steps
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• Experiments(continued)
– To see how nature responds to change, we must
actually impose the change.
• Confounding
– Skewed results because of certain type of
subject with special characteristics.
First Steps Examples
• When the discussion turns to the pros and cons of wearing
automobile seat belts, Herman always brings up the case of
a friend who survived an accident because he was not
wearing seat belts. The friend was thrown out of the car
and landed on a grassy bank, suffering only minor injuries,
while the car burst into flame and was destroyed. Explain
briefly why this anecdote does not provide good evidence
that it is safer not to wear seat belts.
• Because one experience cannot accurately represent the
population as a whole.
First Steps
Examples. . .
• A study of the effect of living in public housing on family
stability and other variables in poverty-level households
was carried out as follows. The researchers obtained a list
of all applicants for public housing during the previous
year. Some applicants had been accepted, and others had
been turned down by the housing authority. Both groups
were interviewed and compared. Was this study an
experiment? Why or why not? What are the explanatory
and response variable in the study?
• No. No treatment was imposed. The explanatory variable
was whether or not they live in public housing. The
response variable was family stability and other variables.
Design of
Experiments
• Experimental Units, Subjects, Treatment
– The objects on which the experiments is
performed are 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.
• Factor
– Explanatory variable in an experiment.
Design of
Experiments. . .
• Level
– A specific value in an experiment containing
several factors.
• Placebo Effect
– The effect of a patient thinking they have been
cured causing them to feel better.
• Control Group
– Group of patients who have been given a sham
treatment.
Design of
Experiments. . .
• Bias
– The design of a study is biased if it
systematically favors certain outcomes.
• Matching
– The pairing of subjects to have similar subjects
placed in opposite groups.
Design of
Experiments. . .
• Statistical significance
– A difference to large to attribute plausibly to chance.
• Principles of Experimental Design
– Control
– Of the effects of lurking variable on the response, most simply
by comparing several treatments.
– Randomization
– The use of chance to assign subjects to treatments to eliminate
bias due to systematic differences among the groups.
Design of
Experiments. . .
• Principles of experimental design (cont.)
– Replication
• Of the experiment on many subjects to reduce
chance variation in the results.
• Table of Random Digits
– A table of random digits is a long string of the
digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 with these two
properties:
Design of
Experiments. . .
– 1.) Each entry in the table is equally likely to be
any of the 10 digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
– 2.) The entries are independent of each other.
That is, knowledge of one part of the table
gives no information about any other part.
• Completely randomized design
– When all experimental units are allocated at
random among all treatments.
Design of
Experiments. . .
• Hidden Bias
– Great care must be taken to avoid this.
• Double-Blind Experiment
– An experiment in which neither the subject nor
the evaluator know which treatment the subject
received.
• Lack of Realism in Experiments
– The treatment supplied in the experiment does
not accurately portray the real problem.
Design of
Experiments. . .
• Matched Pairs Design
– Match up two subjects that are similar and give
them opposite treatments.
• Block Design
– A block is a group of experimental units or
subjects that are known before the experiment
to be similar in some way that is expected to
affect the response to the treatments. In a block
design, the random assignment of units to
treatments is carried out separately within each
block.
Design of
Experiments. . .
Randomized Block Design
Group 1
Men
Random
assignment
Group 2
Group 3
Therapy 1
Therapy 2
Compare
Survival
Therapy 3
Subjects
Group 1
Women
Random
assignment
Group 2
Group 3
Therapy 1
Therapy 2
Therapy 3
Compare
Survival
Design of
Experiment
Examples
• A manufacturer of food products uses package liners that
are sealed at the top by applying heated jaws after the
package is filled. The customer peels the sealed pieces
apart to open the package. What effect does the
temperature of the jaws have on the force required to peel
the liner? To answer this question, the engineers obtain 20
pairs of pieces of package liner. Five pairs are sealed at
each of 250 degrees F, 275 degrees F, 300 degrees F,and
325 degrees F. Then the peel strength of each seal is
measured.
Design of
Experiments
Examples
• Answer:
– Experimental units: pairs of pieces of package
liner. Explanatory variable: temperature of
jaws. Response variable: peel strength of the
seal.
Design of
Experiments
Examples
• Is the right hand generally stronger than the left in righthanded people? You can crudely measure hand strength by
placing a bathroom scales on a shelf with the end
protruding and then squeezing the scaled between the
thumb below and the four fingers above. The reading of
the scaled shows the force exerted. Describe the design of
a matched pairs experiment to compare the strength of the
right and left hands, using 10 right-handed people as
subjects. Use a coin to do the required randomization.
Design of
Experiments
Examples
• Answer
– For each person, flip the coin. If heads, measure
the right hand and then the left hand. If tails,
measure in reverse order.
Bibliography
Moore, David S. and George P. McCabe.
Introduction to the Practice of Statistics.
New York: W.H. Freeman and
Company, 1993.
“National Center For Education Statistics.”
HTTP://nces.edu.gov/, May 29, 2002.