producing data: samples and experiments 01 - producing...they found 30 employees in texas that drive...
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Producing Data: Samples and
Experiments
Chapter 4
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Discussion example 1
One school board member noticed that students in band tended to be in the top 25% of their school. She compiled a list from each high school’s band director and took a random sample of 25 students from each school’s band. She then took a random sample of 25 students from each high school that wasn’t in band. She found a slightly higher average G.P.A. of student’s in band.
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Discussion example 1
Will this study give evidence that being in
band causes an increase in a students
G.P.A?
Will this study help her generalize that
student’s in band tend to have a slightly
higher G.P.A. than students not in band?
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Vocabulary from example 1
Observational study
a study based on data collected from individuals that
meet a determined criteria
Lurking variable (“extraneous variable”)
an outside factor that is not the explanatory (x-variable)
nor response (y-variable) variable
Variables we cannot control
In practice, we assume that all of these lurking
variables are randomly spread out equally enough to
not impact the response variable significantly
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Discussion example 2
Another school board member is surprised
the increase is so slight. First, he emails
each band director and asks for a list of 30
students. He then accesses each high
school’s roster takes the first 40 listed
striking any student’s name has already has.
He found the average G.P.A. of student’s in
band to be more significant than the first
study.
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Discussion example 2
Will this study give evidence that being in
band causes an increase in a students
G.P.A?
Will this study help her generalize that
student’s in band tend to have a slightly
higher G.P.A. than students not in band?
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Discussion example 3
Walmart is considering buying a gasoline additive that is suppose to improve gas mileage. They found 30 employees in Texas that drive the same car. Fifteen employees are randomly selected to receive the additive, the remaining fifteen are given a bottle with just gas. Each employee is given a set route around the city to drive. The gas mileage is recorded by an onboard computer which shows the additive gives the driver 12% better gas mileage.
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Discussion example 3
Will this study give evidence that using the additive will give a car better gas mileage?
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Vocabulary from example 3
Experiment
a planned study where deliberate conditions are
imposed to see how the response variable will change
Confounding variable
a variable associated (noncausal) with the explanatory
variable that affects the response variable in some
way
makes it difficult to tell if the treatment or the
confounding variable affected the response variable
significantly
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Lurking versus confounding
Observation study
x y
z
Lurking
Experiment
x y
z
Confounding
?
?
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Randomized comparative
experiments
Goal of an experiment: collect statistically
significant evidence for a cause-and-effect
relationship.
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Principles of Experimental Design
Control:
using comparison ensures that outside factors operate equally on all groups
comparison minimizes effects of confounding variables allowing effects of treatments to be better evaluated
control groups allow us to accurately assess the change in the response variable
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Principles of Experimental Design
Control:
Randomization:
use of impersonal chance in order equalize unanticipated factors so that groups that should be similar in all respects.
Creates homogenous groups to reduce variability allowing better assessment of treatments
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Principles of Experimental Design
Control:
Randomization:
Replication:
perform the experiment on as many subjects to reduce chance variation in the results
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Experimental Design Examples
Read each design example and write a
description on how each experiment should
be run.
Key terms: groups, treatments, comparison,
randomization
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Completely Randomized Design
Random
Allocation
Group 1
15 babies
Group 2
15 babies
Treatment 1
Her product
Treatment 2
Competitor’s
Compare
weight
gain
Babies will be numbered 01 to 30. Using a random number table, select
15 unique 2-digit numbers. The first 15 selected will be in Group 1
with the remaining placed in Group 2. Each babies’ weight will be
measured in pounds and compared.
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Block Design
Subjects
African
American men
White men
Random
assignment
Random
assignment
Group 1
Group 2
Group 3
Group 4
Treatment 1
Calcium
Treatment 1
Calcium
Treatment 2
Placebo
Treatment 2
Placebo
Compare
blood
pressure
All African American men will be assigned a random unique number. Half the
men who have the smallest numbers will be assigned group 1, the half
with the largest numbers will be assigned group 2. The process will repeat
for the white men. The reduction in blood pressure will be compared.
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Matched pair Design
Random
Allocation
Group 1
Group 2
Treatment 1
left hand
Treatment 2
right hand
Compare
difference
A coin will be flipped to decide which hand will be measured first by
each participant. Heads will squeeze the left hand first, tails will
squeeze the right hand first. The different in the pounds on the scale
will be compared.
Treatment 1
left hand
Treatment 2
right hand
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Calcium experiment revisted
What potential problems might we have
because we started with random assignment?
How should we (did we) alter our experiment?
Random
Assignment
Group 1
Group 2
Treatment 1
Calcium
Treatment 2
Placebo
Compare
blood
pressure
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Block Design
All participants
African
American men
White men
Completely randomized
experiment
Completely randomized
experiment
Big differences BETWEEN groups, but small
differences WITHIN groups
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Improving the Design
A block is a group of experimental units or
subjects that are known before the experiment to
be similar in some way that is expected to affect
the response to the treatments.
Block design has the same rationale as a stratified
random sample.
Blocks allow us to reduce the amount of variation
to improve the accuracy of our conclusions by
creating homogeneous groups.
single blind versus double blind
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Improving the Design
In a matched pair design, each subject in the experiment will receive two (and only two) treatments.
The order that each subject receives both treatments is randomly selected to preserve the important aspect of randomization.