Lecture 16: Factorial Crossing
Chapter 6
Frog Dissection Experiment
Factorial Crossing.
We have actually seen this
in the experiment comparing
different methods of frog
dissection.
Experimental Units: Lab
sections of biology.
Response: Average score on
a test on the anatomy of the
frog.
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Frog Dissection Experiment
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Factors and Levels
Factor 1: Real Dissection
Treatments: Real, Virtual,
Both, None.
These treatments are really the
combination of two factors of
interest.
Levels: Yes, No
Factor 2: Virtual Dissection
Levels: Yes, No
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Treatments
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Treatments
With factorial crossing
treatments consist of all
possible combinations of
the levels of the factors.
Real Dissection?
Yes
Real Dissection?
No
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Virtual
Dissection?
Yes
Virtual
Dissection?
No
Both
Real
Virtual
None
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Lecture 16: Factorial Crossing
Why use factorial crossing?
Doing one experiment
using factorial crossing is
more efficient than doing
separate experiments, one
for each factor of interest.
Why use factorial crossing?
Doing one experiment
using factorial crossing
allows for the investigation
of possible interaction
between the factors.
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Efficiency
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Two Experiments
Experiment I: Compare Real
Dissection to No Real
Dissection.
Experiment II: Compare
Virtual Dissection to No
Virtual Dissection.
Alpha = 0.05
Beta = 0.10
1.4 standard deviation in
means.
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Sample Size
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One Experiment
Experiment I: 2 Groups, 12
per group, 24 lab sections.
Experiment II: 2 Groups, 12
per group, 24 lab sections.
Total of 48 lab sections.
Alpha = 0.05
Beta = 0.10
1.4 standard deviation in
means.
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Lecture 16: Factorial Crossing
One Experiment
Different Means
Experiment: 4 Groups, 16 per
group, 64 lab sections.
How is this more efficient?
There is a problem as the two
situations are referring to
different means.
Two experiments: difference
in factor level means.
One experiment: difference in
treatment means.
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Sample Size
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Real Dissection
Virtual
Virtual
Dissection? Dissection?
Yes
No
Real
Dissection?
Yes
Both
n=6
Real
n=6
12
Real
Dissection?
No
Virtual
n=6
None
n=6
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12
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Comparing real dissection to
no real dissection there are 12
lab sections per group.
Can detect a 1.4 standard
deviation difference in factor
level means, Alpha = 0.05,
Beta = 0.10.
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Virtual Dissection
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Greater Efficiency
Comparing virtual dissection
to no virtual dissection there
are 12 sections per group.
Can detect a 1.4 standard
deviation difference in factor
level means, Alpha = 0.05,
Beta = 0.10.
One experiment using 24 lab
sections can detect the same
size difference in factor level
means as 48 lab sections used
in two experiments.
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Lecture 16: Factorial Crossing
Important Distinction
Important Distinction
When there was only one
manipulated factor, the
factor levels were the
treatments.
Now that there are several
factors there is a difference
between factor levels and
treatments.
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Sample Size
Interaction
When using the sample size
tables be sure to note the
distinction between factor
level means and treatment
means.
In Stat 301 or 401, two
explanatory variables are said to
interact if the relationship
between the response variable
and one of the explanatory
variables changes for different
values of the second explanatory
variable.
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Interaction
Interaction
In Stat 402, two factors are
said to interact if the effect of
one factor on the response is
different for different levels of
the second factor.
The two definitions are
getting at the same idea just
with different terminology.
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Lecture 16: Factorial Crossing
Example
Yes:Virtual
Dissection
In the experiment with Real
Dissection; Yes, No and
Virtual Dissection; Yes, No as
the factors what would the
treatment means look like with
and without interaction?
Average Score
on test of
Frog Anatomy
No: Virtual
Dissection
No
Yes
Real Dissection
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No Interaction
In sections with no virtual
dissection the effect of real
dissection is the same as in
sections with virtual
dissection.
Average Score
on test of
Frog Anatomy
Yes:Virtual
Dissection
No: Virtual
Dissection
No
Yes
Real Dissection
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Interaction
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Interpretation
In sections with no virtual
dissection there is a positive
effect due to real dissection.
In sections with virtual
dissection there is no effect
due to real dissection.
The effect of real dissection on
the average score on the frog
anatomy test is different for
sections using, or not using,
virtual dissection.
Real dissection and Virtual
dissection factors interact.
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