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.
The experimental unit (or subject) is a person, object or
some other well-defined item upon which a treatment is
applied.
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.
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.
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.
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.
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.
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.
Steps in Conducting an Experiment
Step 3: Determine the number of experimental
units.
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.
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.
Steps in Conducting an Experiment
Step 6: Test the claim.
• This is the subject of inferential statistics.
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.
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
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.
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.
Completely Randomized Design
Random
assignment
of 12 cars
4 cars
87 octane
4 cars
89 octane
4 cars
92 octane
Compare
MPG
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.
Randomized Block Design
170 degrees
215 degrees
4 cars (87 octane)
185 degrees
200 degrees
215 degrees
Random
assignment
of 12 cars
200 degrees
4 cars (89 octane)
185 degrees
170 degrees
200 degrees
4 cars (92 octane)
215 degrees
185 degrees
170 degrees



Compare
MPG
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.)
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.