AP Statistics

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AP Statistics

• 5.2 Designing Experiments

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Essential Questions

• What are the principles of experimental design?
• How can the accuracy of an experimental design
  be improved?
• What is blocking as an experimental methodology?
• What cautions accompany the use of an
  experimental methodology?

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Designing Experiments

• An experiment is a study with a treatment imposed
  on all or a portion of the sample.

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Definitions

• Experimental Units the individuals on which the
  experiment is conducted. If the units are human
  beings, they are often referred to as subjects.
• Treatment a specific experimental condition
  applied to the units
• Factors the explanatory variable(s) in the
  experiment. Many studies include several
  explanatory variables or factors.
• Level the specific value or quantity of a factor

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Principles of Experimental Design

• Control by random assignment, the effects of
  lurking variables are accounted for
• Randomization the use of chance to select units
  for the sample and assign them to treatment
  groups
• Replication experiment is repeated on many
  subjects or on several occasions to reduce chance
  variation

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Comparative Experiments
Control

• Experiments where there are no lurking or
  confounding variables can have a very simple
  design where a treatment is provided to all
  experimental units and the response variable is
  then measured. The absence of lurking and
  confounding variables means that the observed
  response must have resulted directly from the
  treatment. No comparison is necessary.
• Example Testing the amount of weight a beam will
  support

Units
Treatment
Observe Response
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Comparative Experiments
Control

• In the presence of lurking variables, however,
  this simple design fails to provide internal
  validity.
• Example Treating ulcers (p. 270)

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Comparative Experiments
Randomization

• Comparison of the effects of several treatments
  is valid only when the treatments are applied to
  similar groups of experimental units.
• Chance or random assignment is the least bias and
  most accurate method of assuring that each
  treatment group contains similar lurking
  variables.
• The only difference between groups and thus the
  only reason that the observed response variable
  should vary is the treatment.

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Comparative Experiments
Randomization

• Randomized Comparative Design

Group 1
Treatment 1
Compare Response Variable
Random Assignment
Group 2
Treatment 2
Group 3
Treatment 3
If all experimental units are randomly allocated
among all treatment groups, the design is
completely randomized.
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Comparative Experiments
Replication

• By assigning each treatment to multiple
  experimental units, the effects of chance will
  average out.
• The fewer the number of experimental units in
  each group, the more likely that some lurking
  variables will be present in one and not the
  other.
• Use enough experimental units to reduce chance
  variation.

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Principles of Experimental Design

• Control
• Randomization
• Replication

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What are the principals of experimental
design(3)? Explain how each can be accomplished?

• Control design a comparative experiment and
  compare the response variable. (a control group
  could be used treatment is placebo)
• Randomization randomly assign units to the
  comparative groups and randomly assign units to
  each treatment
• Replication use many subjects/units to reduce
  the chance variation in the results

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Describe the units, factors, treatments and
response variable.

• The ability to grow in shade may help pines found
  in the dry forests of Arizona to resist drought.,
  How well do these pines grow in shade?
  Investigators planted pine seedlings in a
  greenhouse in either full light or light reduced
  to 5 of normal by shade cloth. At the end of
  the study, they dried the young trees and weighed
  them.

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• A large study used records from Canadas national
  health care system to compare the effectiveness
  of two ways to treat prostate disease. The two
  treatments are traditional surgery and a new
  method that does not require surgery. The
  records described many patients whose doctors had
  chosen each method. The study found that
  patients treated by the new method were
  significantly more likely to die within 8 years.
  
• What lurking variables might be present?
• Is this an observation study or an experiment?
• Describe the variables explanatory and
  response.
• If there are 300 prostate patients who are
  willing to serve as subjects, show, using a
  diagram, to demonstrate a completely randomized
  experiment. Include the amount of subjects in
  each group.

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Statistical Significance

• A result is statistically significant if it is so
  large that it is unlikely to have occurred by
  chance.

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Types of Experimental Design

• Blind the experimental units are not aware of
  which treatment group they are in (control
  placebo effect)
• Double-blind neither the subjects nor the people
  who have contact with them know which treatment
  group they are in (those who measure the response
  variable are unaware)

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Types of Experimental Design

• Block
• A block is a group of experimental units that are
  known prior to the experiment to be similar in
  some way that is expected to effect the response
  to the treatments (i.e. they share a potential
  lurking variable)
• In a block design, the random assignment of
  treatments to units is done within each block

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Block Design
Group 1
Treatment 1
Compare Response Variable
Random Assignment
Block 1
Group 2
Treatment 2
Group 3
Treatment 3
Subjects
Group 1
Treatment 1
Compare Response Variable
Random Assignment
Group 2
Treatment 2
Block 2
Group 3
Treatment 3
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Diagram a randomized block design.

• The progress of a type of cancer differs in women
  and men. A clinical experiment to compare three
  therapies for this cancer therefore treats gender
  as a blocking variable. Two separate
  randomizations are done, one assigning the female
  subjects to the treatments band the other
  assigning the male subjects.

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Types of Experimental Design

• Matched Pairs
• A matched pairs design is a type of block design
  where each block contains just two units
• Twin studies

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Caution

• The most serious potential weakness of an
  experiment is lack of realism. Often, the units,
  treatments, or setting of an experiment does not
  realistically duplicate or reflect the conditions
  under investigation.

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Essential Questions

• What are the principles of experimental design?
• How can the accuracy of an experimental design
  be improved?
• What is blocking as an experimental methodology?
• What cautions accompany the use of an
  experimental methodology?

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Assignment

• Identifying Components
• P. 268 5.26, - 5.28

Principles of Design P. 273 5.30 - 5.32
Experimental Design P. 277 5.35 5.37 P. 279
5.38 - 5.39 P. 282 5.40 5.41