Ch 1.1 – Analyzing Categorical
Data
Categorical Data
• Good graphs to use:
– Pie charts
– Bar graphs
• Pie charts: you must have all categories
involved in the whole variable! (total)
• Bar graphs: don’t forget labels!!!!!
•
bars are evenly spaced and do
not touch
What makes a deceptive graph?
 Uneven widths of bars
 Pictures instead of bars
 Uneven scale
 Don’t have exact angle measure/percents
with pie charts – estimation is used too
much
So what is so deceptive about this
advertisement?
Marginal Distribution
• the totals of each categorical variable.
Usually given as a percent, but not always.
– Counts: a number total
– Percents: (counts of the variable) / (total
number of data)
Attitude toward recycled coffee filters: are recycled products
of better quality, the same quality, or worse quality than
normal products? The data below reflects the opinion of
people who use recycled products versus the opinion of
people who don’t use recycled products.
Higher Quality
Same Quality
Lower Quality
Buyers
20
7
9
Nonbuyers
29
25
43
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• 1. How many people does this table
describe? How many of these were buyers
of coffee filters made from recycled paper?
• 2. Give the marginal distribution of opinion
about the quality of recycled filters. What
percent think the quality of recycled filters
is the same or higher than the quality of
other filters?
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Conditional Distribution
• a particular variable is not compared to the total number
in the entire data set, but rather to a total of a particular
criteria.
• i.e. comparing the females who work more than 10 hours
a week in this class, to the total number of females in the
class - not the total number in the class.
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Recycled Filters Data
• If we want to know whether or not if someone is a buyer
influences their opinion about the quality of recycled
filters, what conditional distributions would we compare?
• Draw a conclusion from your findings.
Higher
Quality
Same Quality Lower Quality
Buyers
20
7
9
Nonbuyers
29
25
43
9
4 Step Process
•
Step 1: State
•
Step 2: Plan
• Step 3: Do
• Step 4: Conclude
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•
Yellowstone National Park surveyed a random sample of 1526 winter visitors
to the park. They asked each person whither they owned, rented, or had
never used a snowmobile. Respondents were also asked whether they
belonged to an environmental organization. The two-way table summarizes
the survey responses.
ENVIRONMENTAL CLUBS
•
No
Yes
Total
Never
445
212
657
Renter
497
77
574
Owner
279
16
295
Total
1221
305
1526
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• Do these data provide convincing evidence of an
association between environmental club membership and
snowmobile use for the population of visitors to
Yellowstone National Park?
• We will use the 4 Step
• process!
• State-Plan-Do-Conclude
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Step 1 - State
• What is the question we’re
trying to answer?
What is the relationship
between belonging to an
environmental organization
and using a snowmobile at
Yellowstone?
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Step 2 - Plan
• How will we answer our question?
• What statistical techniques will we need
to use?
I suspect belonging to an
environmental organization will
reduce the chances of using a
snowmobile.
I will compare the conditional
distributions of snowmobile use for
those who do and do not belong to
an environmental organization.
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Step 3 - Do
• Make graphs and do
calculations
Conditional Distributions:
Never/Belong - 69.5%
Rent/Belong - 25.2%
Own/Belong - 5.2%
Never/Don’t Belong - 36.4%
Rent/Don’t Belong - 40.7%
Own/Don’t Belong - 22.9%
Now construct a side-by-side bar
graph
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Step 4 - Conclude
• Give your conclusion IN THE
SETTING OF THE REALWORLD PROBLEM!!!!!!
People who are members of an environmental
organization are much more likely to have never
used a snowmobile, about 69.5% of this group will
have never used one, whereas only 36.4% of
non-members of an environmental group have
never used one. Those in an environmental
organization are less likely to have rented or
owned a snowmobile than those not in an
environmental group.
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