Lecture 23: Forming Blocks
Blocking Design
How to make blocks?
Sorting.
Subdividing.
Reusing.
Make blocks so that the
experimental material within a
block is uniform.
Randomly assign treatments to
experimental units within each
block.
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Sorting
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Example
Response: Score on a
standardized 8th grade science
test.
Conditions: Textbook, Internet
Site.
Experimental Material: 8th grade
science students.
Sort experimental material
into blocks so that the
material within each block
is uniform.
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Conditions
Conditions
The material on a topic
covered in 8th grade science
will be found either in a text
book or on an interactive
internet site.
The textbook or internet site
will be assigned, at random,
to individual students in the
8th grade science class.
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Lecture 23: Forming Blocks
Experimental Material
Experimental Material
There will be a lot of variation
in the 8th grade science
students due to:
Sort students according to
their scores on the science
portion of the Iowa Test of
Basic Skills taken in 7th
grade.
Science knowledge
Ability to take standardized
tests.
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Blocks
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Blocks
Students with two highest
scores.
Students with the next two
highest scores.
Etc.
Students with the two lowest
scores.
Within each block the two
students will be similar in
terms of science knowledge
and test taking ability.
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Random Assignment
Sorting
Within each block, assign the
textbook to one student and
the internet site to the other
student.
This can be done with a flip of
a coin.
When using sorting to create
blocks you should sort on an
outside variable that is related
to the response in your
experiment.
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Lecture 23: Forming Blocks
Sorting
Subdividing
Sorting 8th grade students on
height would not be a good
way to form blocks.
Height of a student should not
affect how a student scores on
a standardized test on science.
Take large chunks of
uniform material and divide
it into smaller pieces.
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Example
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Experimental Material
Response: Surface roughness
for a hole.
Conditions: Speed of the drill.
Bars of carbon steel are made
by melting iron ore in a
furnace, adding carbon to
strengthen the steel and
pouring the molten steel into
molds.
500 rpm, 1000 rpm, 1500 rpm
Experimental material: Bars of
carbon steel.
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Experimental Material
Experimental Material
Several bars can be made from
each heat of steel.
Different heats can produce
bars with quite different
characteristics, e.g. hardness.
A single bar will be quite
similar from one part to the
next.
Different bars can be quite
different.
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Lecture 23: Forming Blocks
Subdivide the bars
Conditions
Randomly assign the three
speeds to pieces of each bar.
Each bar is drilled with all
three speeds.
1000 rpm 500 rpm 1500 rpm
1500 rpm 500 rpm 1000 rpm
500 rpm 1500 rpm 1000 rpm
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Subdividing
Reusing
We could actually divide
each bar into separate
pieces.
1000 rpm
500 rpm
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Reuse the experimental
material so that each piece of
experimental material
experiences all the treatments
in a random order.
1500 rpm
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Example
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Reusing Material
Each person will sit in a chair
and rise to a standing position.
Each person will do this three
times, once with each foot
position.
The order of the three foot
positions will be randomized for
each person.
Response: torque on knee
Conditions: placement of feet
Feet back, feet neutral, feet
staggered
Experimental Material: men who
have had knee replacement.
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Lecture 23: Forming Blocks
Comment
Another Example
When you can reuse material
you have the most uniformity
within a block (the individual)
because all outside variables
(height, weight, strength, age,
etc.) are exactly the same
within a block (the individual).
Response: number and size of
skin cancer tumors.
Conditions: skin cream, skin
cream with caffeine.
Experimental Material:
hairless mice.
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Conditions
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Response
A mouse’s skin is coated with
the cream or the cream
containing caffeine.
The mouse is then exposed to
large doses of ultraviolet
radiation (tanning bed).
After exposure to the
ultraviolet radiation, the
number and size of skin
cancers are noted and
measured.
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Reusing?
Forming Blocks
Once a mouse is exposed to
the ultraviolet radiation, it
has skin cancer and so
cannot be reused with the
other treatment.
Could sort mice into pairs
according to genetics, size,
gender, etc.
Could subdivide mice, put
cream on half and cream with
caffeine on the other half.
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