Lecture 12: Popcorn Experiment
Chapter 5
Popcorn Experiment
Chapter 5 revisits some of
the ideas presented in
Chapter 3 and extends
them.
Response?
Conditions?
Experimental Material?
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Response?
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Conditions?
Percentage of popped and
unburned popcorn.
Percentage of un-popped or
burned popcorn.
Volume of popped and
unburned popcorn.
Manipulate the cooking time
to form treatments.
1.25 minutes
1.75 minutes
2.25 minutes
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Experimental Material
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Control of Outside Variables
Size of bag – snack size, 1.5
oz or 42.5 g.
Microwave – use only one.
Power – use only one power
setting.
Small bags of microwave
popcorn.
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Lecture 12: Popcorn Experiment
Control of Outside Variables
Control Group?
Brand/type – Pop Secret
Home style.
Procedure – Allow microwave
to cool down. Wipe out
moisture after every popping.
If we think of the control
group as bags of popcorn
exposed to none of the
manipulated variable (no time)
a control group doesn’t make
sense in this context.
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Comparison Group?
Replication?
Bags of popcorn exposed to
the recommended time
given in the package
directions would be a
comparison group.
Replication within the
experiment requires that
several bags be popped at each
of the times.
How many bags are needed?
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Sample Size
Sample Size
Alpha: the probability of a Type
I error, the chance of declaring
an observed difference in sample
means statistically significant
when the true difference in
population means is zero (there
is no difference).
Beta: the probability of a
Type II error, the chance of
missing a difference in
population means when one
actually exists (when there is a
difference).
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Lecture 12: Popcorn Experiment
Sample Size
Problem
Δ
: the size of the
detectable difference in
population means.
σ : the standard deviation of
the response.
Most experimenters can come
up with a size of a detectable
difference in population means
but cannot come up with the
standard deviation.
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Problem
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Solution
In order to have an idea of
what the standard deviation
is you need data but you are
trying to figure out how
much data to collect.
Report the size of the
detectable difference in
population means in terms of
the number of standard
deviations: .
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Sample Size Tables
Resources?
 Number of groups: 3
 Alpha = 0.05
 Beta = 0.05
 A one standard deviation difference in
population means: = 1.
 n = 32 for each group or a total of 3*32
= 96 bags of microwave popcorn.
Often the number arrived at
using the sample size tables
is too large for the available
resources; time, money,
experimental material.
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Lecture 12: Popcorn Experiment
Compromise
Compromise
Increase the chance of making
an error.
Alpha = 0.05, Beta = 0.10, a
one standard deviation in
population means: =1; n =
27, or 81 total.
Increase the size of the
difference in population means,
Δ.
Alpha = 0.05, Beta = 0.05, a two
standard deviation difference in
population means, = 2; n = 9 or
27 total.
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Compromise
Random Assignment
Do both.
Alpha = 0.05, Beta = 0.10, a
two and one half standard
deviation difference in
population means, = 2.5; n = 6
or 18 total.
Random assignment of
treatments (times) to
experimental units (bags of
popcorn).
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Random Assignment
Random Assignment
Remember that time of day is
often a uncontrolled outside
variable. We would also like
to randomize the order in
which the bags are popped.
Put the 18 bags of microwave
popcorn in a bowl. Mix
thoroughly.
Put 18 poker chips; 6 red, 6
white and 6 blue, in another
bowl mix thoroughly.
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Lecture 12: Popcorn Experiment
Treatments
Random Assignment
Blue = 1.25 minutes
Red = 1.75 minutes
White = 2.25 minutes
Draw a bag from the bowl,
without replacement.
Draw a chip from the other
bowl without replacement.
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Random Assignment
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Random Assignment
Not only are treatments
(times) assigned at random to
experimental units (bags) but
the order of popping and
measuring are also
randomized over time.
Pop that bag at the time
indicated by the color of the
chip.
Measure the volume of
popped but unburnt kernels.
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Random Selection?
Repeating?
Because microwave popcorn is
packaged using a continuously
running production line when we
buy packages of popcorn we are
probably not getting a random
selection from the population.
We could always repeat the
entire experiment using
different bags, maybe even
a different brand or type.
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