Chapter One Data Collection

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Chapter OneData Collection

• 1.5
• The Design of Experiments

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A designed experiment is a controlled study in
which one or more treatments are applied to
experimental units. The experimenter then
observes the effect of varying these treatments
on a response variable. Control, manipulation,
randomization and replication are the key
ingredients of a well-designed experiment.
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The experimental unit (or subject) is a person,
object or some other well-defined item upon which
a treatment is applied.
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The experimental unit (or subject) is a person,
object or some other well-defined item upon which
a treatment is applied. The treatment is a
condition applied to the experimental unit.
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The experimental unit (or subject) is a person,
object or some other well-defined item upon which
a treatment is applied. The treatment is a
condition applied to the experimental unit. A
response variable is a quantitative or
qualitative variable that represents our variable
of interest.
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The experimental unit (or subject) is a person,
object or some other well-defined item upon which
a treatment is applied. The treatment is a
condition applied to the experimental unit. A
response variable is a quantitative or
qualitative variable that represents our variable
of interest. An experiment is double-blind when
neither the experimental unit nor the
experimenter knows what treatment is being
administered to the experimental unit.
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The experimental unit (or subject) is a person,
object or some other well-defined item upon which
a treatment is applied. The treatment is a
condition applied to the experimental unit. A
response variable is a quantitative or
qualitative variable that represents our variable
of interest. An experiment is double-blind when
neither the experimental unit nor the
experimenter knows what treatment is being
administered to the experimental unit. A placebo
is an innocuous medication such as a sugar tablet
given to patients that serve in a control group.
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• Steps in Conducting an Experiment
• Step 1 Identify the problem to be solved.
• Should be explicit
• Should provide the researcher direction
• Should identify the response variable and the
  population to be studied.

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• Steps in Conducting an Experiment
• Step 2 Determine the factors that affect the
  response variable.
• These factors are called the predictor
  variables.
• Once the factors (predictor variables) are
  identified, it must be determined which factors
  are to be fixed at some predetermined level (the
  control), which factors will be manipulated and
  which factors will be uncontrolled.

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Steps in Conducting an Experiment Step 3
Determine the number of experimental units.
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• Steps in Conducting an Experiment
• Step 4 Determine the level of the predictor
  variables
• 3 LEVELS
• Control their levels so they remain fixed
  throughout the experiment. These are variables
  whose affect on the response variable is not of
  interest.
• Manipulate or set them at predetermined levels.
  These are the variables whose affect on the
  response variable interests us. These variables
  comprise the treatment in the experiment.
• Randomize so that the effects of variables whose
  level cannot be controlled is minimized. The
  idea is that randomization averages out the
  affect of uncontrolled predictor variables.

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• Steps in Conducting an Experiment
• Step 5 Collect and process the data
• This is the replication. Repeat the experiment
  on each experimental unit.
• Measure the value of the response variable.
• Organize the results.
• Any difference in the value of the response
  variable can be attributed to differences in the
  level of the treatment.

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• Steps in Conducting an Experiment
• Step 6 Test the claim.
• This is the subject of inferential statistics.

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EXAMPLE Designing an Experiment The octane of
fuel is a measure of its resistance to detonation
with a higher number indicating higher
resistance. An engineer wants to know whether
the level of octane in gasoline affects the gas
mileage of an automobile. Assist the engineer in
designing an experiment.
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EXAMPLE Designing an Experiment The octane of
fuel is a measure of its resistance to detonation
with a higher number indicating higher
resistance. An engineer wants to know whether
the level of octane in gasoline affects the gas
mileage of an automobile. Assist the engineer in
designing an experiment.
Step 1 The response variable in miles per
gallon. Step 2 Factors that affect miles per
gallon Engine size, outside temperature,
driving style, driving conditions,
characteristics of car
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• Step 3 We will use 12 cars all of the same model
  and year.
• Step 4 We list the variables and their level.
• Octane level - manipulated at 3 levels (87, 89,
  92)
• Engine size - fixed
• Temperature - uncontrolled, but will be the same
  for all 12 cars.
• Driving style/conditions - all 12 cars will be
  driven under the same conditions on a closed
  track - fixed.
• Other characteristics of car - all 12 cars will
  be the same model year, however, there is
  probably variation from car to car. To account
  for this, we randomly assign the cars to the
  octane level.

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Step 5 Randomly assign 4 cars to the 87 octane,
4 cars to the 89 octane, and 4 cars to the 92
octane. Give each car 3 gallons of gasoline.
Drive the cars until they run out of gas.
Compute the miles per gallon. Step 6 Determine
whether any differences exist in miles per gallon.
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EXAMPLE Designing an Experiment Suppose we
discovered that the cars were not running at the
same temperature. We would say that engine
temperature is confounded with octane rating
because we cannot tell whether differences in
miles per gallon are attributed to temperature or
octane. To resolve this, we might want to
control engine temperature at, say, 4 different
levels - 170, 185, and 200, and 215 degrees
Fahrenheit. We will randomly assign temperature
to the 4 cars at each octane level. This is an
example of a randomized block design.
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A matched pairs design is a randomized block
design in which the experimental units are
somehow related (i.e. the same person before and
after a treatment, twins, husband/wife, etc.)
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EXAMPLE A Matched Pairs Design A psychologist
wishes to know whether the IQs of twins differs.
She randomly selects 10 twins. She administers
IQ tests to all 20 participants, computes the IQ
score and computes the absolute difference in IQ
scores for each pair of twins for a total of ten
scores.