Statistics 101: Section L - Laboratory 9
This lab consists of two group activities. For the first activity, you will design an experiment to determine
the optimal cooking time for a new brand of microwave popcorn. For the second activity, you will design an
experiment to determine the effectiveness of the Atkins diet.
For all activities, keep in mind the three principles of good experiments: control of outside variables,
randomization and replication within the experiment.
Activity 1: Imagine you are employed in the test kitchen of Company Z. Company Z is rolling out a new
line of microwave popcorns. Your group must design an experiment to determine the optimal cooking time
for one of the new brands of microwave popcorn in this new line. The new popcorn will be sold in
individual packages, each with the same label weight. Your task is to design an experiment that will
produce data to help you make an informed decision as to the optimal cooking time for the new brand of
microwave popcorn.
a) First decide on a response. What aspect of the popcorn will help you decide on the optimal cooking
time? How will you measure your response? (Hint: Think about comparing the response between
the individual packages.) Be specific.
The number of popped kernels might be a good place to start. However, if popcorn is cooked
too long, the kernels will pop but then they will burn and not be edible. So, the number of
popped but unburned kernels would be better. Although the bags will all be the same weight,
approximately, they will not all contain the same number of kernels to begin with. Using the
percentage of popped but unburned kernels would be a better response.
b) What are the experimental units for this study? (In other words, what are you conducting the
experiment on?)
The experimental units are the bags of microwave popcorn.
c) What is the main factor for this experiment? How many levels of this factor will you include in
your experiment? What are these levels?
Cooking time is the main factor.
Have five different levels of cooking time: 3 min, 3 min 20 sec, 3 min 40 sec, 4 min, and 4 min
20 sec.
d) A secondary factor for this experiment is the wattage of the microwave. Explain how you will
incorporate two different wattage microwaves (700 watts and 1000 watts) into this experiment.
Use the five different levels of cooking time with each of the microwaves.
e) What are the treatment groups for your experiment?
There are 10 treatment groups. Each treatment group is a combination of cooking time and
wattage.
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f) Come up with a list of outside variables (variables other than the factors) that might affect your
response. How will you control for these variables in your study?
Each bag should be placed in the microwave in the same way.
Each microwave will have turntable and the turntable will be turned on during the popping.
The microwave should be allowed to cool down to room temperature before the next bag is
popped.
Any moisture in the microwave (from steam escaping from the bag) should be wiped up before
the next bag is popped.
g) How will you incorporate replication in your experiment?
To have replication you need several bags of popcorn for each treatment combination.
h) From a statistical point of view more replication is better, e.g. 100 experimental units in each
treatment group. From a practical point of view why might you have less replication, e.g. 10
experimental units in each treatment group?
For the experiment so far, there are 10 treatment combinations. 100 experimental units in
each treatment group means that you will pop 1000 bags of popcorn. It will be very time
consuming to pop 1000 bags of popcorn, the cooking time alone will be over 60 hours. Will 10
bags per treatment you could probably do the whole experiment in one day.
i)
How will you incorporate randomization in your experiment? Be specific about how you will
randomize. From your description, I should be able to perform the randomization.
Suppose we have 100 bags, 10 bags for each treatment combination. I would put chips in a
bag labeled with treatment combinations, 10 chips for each treatment combination. I would
mix the chips and draw a chip, without replacement, and grab a bag of microwave popcorn. I
would pop the bag according to the treatment combination on the chip and count the number
of popped but unburned kernels as well as the un-popped or burned kernels. I would continue
to mix the chips, draw one without replacement, pop the bag according to the chip’s treatment
combination and measure the response until all 100 bags were completed. Alternatively, I
would use JMP – Random – Col Shuffle to get a random order of the treatment combinations.
Draw a diagram of your experimental design.
100
bags
random assignment
j)
Group 1
10 bags
Group 2
10 bags
Group 3
10 bags
Group 4
10 bags
.
.
.
Group 10
10 bags
Treatment 1
700 W & 3 min
Treatment 2
700 W & 3 min 20 sec
Treatment 3
700 W & 3 min 40 sec
Treatment 4
700 W & 4 min
.
.
.
Treatment 10
100 W & 4 min 20 sec
Compare
% of
popped
and
unburned
kernels.
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Activity 2: There is considerable debate in the medical community about the benefits of the “Atkins Diet.”
This diet involves eating relatively large amounts of protein and fats and very few carbohydrates. We would
like to design an experiment to compare the weight loss achieved on the Atkins diet with the weight loss
achieved while on a diet based on the USDA food pyramid. There are 100 people available for this
experiment.
a) Who are the experimental units for this experiment? (In other words, who are we conducting the
experiment on?)
The experimental units are the 100 people available for the experiment.
b) What is the response variable for this experiment? How will you measure it? Be specific.
One response variable is the amount of weight lost (kg). You would have to weigh all people at
the beginning of the experiment and weigh them again after they had been on the diet (at the
end of the experiment). The difference in weight, (end – beginning), is the amount of weight
lost.
If you are concerned about heavier people having more weight to lose than less heavy people,
you could have the percentage weight loss, the weight loss relative to the beginning weight as
your response.
c) What is the factor for this experiment? How many levels does the factor have? What are they?
The factor in the experiment is the diet. There are two levels; Atkins Diet and Food Pyramid
Diet.
d) How will you incorporate control in this experiment? What are some variables that could influence
the response? How will you control for these variables?
Exercise can affect a person’s weight. All individuals in the experiment should follow the
same exercise plan.
The scale used to weigh people should be the same for all individuals in the experiment.
Calories in the diet can affect weight, so both diets should involve the same number of calories.
e) One important characteristic of our subjects that cannot be controlled for is gender. Suppose out of
the 100 people available for this experiment 60 are women and 40 are men. We wish to block on
gender. How will you incorporate replication in a block experiment?
Replication means having several experimental units in each treatment group for each block.
I would have 30 women assigned to each diet and 20 men assigned to each diet.
f) How will you incorporate randomization in this experiment?
Put the 60 women’s names in a hat. Mix the names, draw 30 without replacement and assign
those chosen to the Atkins Diet. The remaining 30 women are assigned to the Food Pyramid
Diet.
Put the 40 men’s names in a hat. Mix the names, draw 20 without replacement and assign
those to the Atkins Diet. The remaining 20 men are assigned to the Food Pyramid Diet.
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Block 2
40 men
random
assignment
60 women
40 men
Block
Block 1
60 women
random
assignment
g) Draw a diagram of your block experimental design.
Diet 1: Atkins
(30 women)
Diet 2: Food
Pyramid
(30 women)
Diet 1: Atkins
(20 men)
Diet 2: Food
Pyramid
(20 men)
Compare
Weight
Lost
Compare
Weight
Lost
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