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Chapter 1: Exploring Data
Section 1.1
Analyzing Categorical Data


The values of a categorical variable are labels for the
different categories
The distribution of a categorical variable lists the count or
percent of individuals who fall into each category.
Example, page 8
Frequency Table
Format
Variable
Values
Relative Frequency Table
Count of Stations
Format
Percent of Stations
Adult Contemporary
1556
Adult Contemporary
Adult Standards
1196
Adult Standards
8.6
Contemporary Hit
4.1
Contemporary Hit
569
11.2
Country
2066
Country
14.9
News/Talk
2179
News/Talk
15.7
Oldies
1060
Oldies
Religious
2014
Religious
Rock
869
Spanish Language
750
Other Formats
Total
1579
13838
7.7
14.6
Rock
6.3
Count
Spanish Language
5.4
Other Formats
11.4
Total
99.9
Percent
Analyzing Categorical Data
Variables place individuals into one of
several groups or categories
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 Categorical
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categorical data
Frequency tables can be difficult to read. Sometimes
it is easier to analyze a distribution by displaying it
with a bar graph or pie chart.
Frequency Table
Format
Relative Frequency Table
Count of Stations
Format
Percent of Stations
Adult Contemporary
1556
Adult Contemporary
Adult Standards
1196
Adult Standards
8.6
Contemporary Hit
4.1
Contemporary Hit
569
11.2
Country
2066
Country
14.9
News/Talk
2179
News/Talk
15.7
Oldies
1060
Oldies
Religious
2014
Religious
7.7
14.6
Rock
869
Rock
6.3
Spanish Language
750
Spanish Language
5.4
Other Formats
Total
1579
13838
Other Formats
11.4
Total
99.9
Analyzing Categorical Data
 Displaying
Good and Bad
Our eyes react to the area of the bars as well as
height. Be sure to make your bars equally wide.
Analyzing Categorical Data
Bar graphs compare several quantities by comparing
the heights of bars that represent those quantities.
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 Graphs:
Good and Bad
Avoid the temptation to replace the bars with pictures
for greater appeal.
Analyzing Categorical Data
Bar graphs compare several quantities by comparing
the heights of bars that represent those quantities.
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 Graphs:
Good and Bad
Bar chart should always start at zero.
Analyzing Categorical Data
Bar graphs compare several quantities by comparing
the heights of bars that represent those quantities.
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 Graphs:
When a dataset involves two categorical variables, we begin by
examining the counts or percents in various categories for one
of the variables.
Definition:
Two-way Table – describes two categorical
variables, organizing counts according to a row
variable and a column variable.
What are the variables
described by this twoway table?
How many young adults
were surveyed?
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Tables and Marginal Distributions
Analyzing Categorical Data
 Two-Way
Definition:
The Marginal Distribution of one of the
categorical variables in a two-way table of
counts is the distribution of values of that
variable among all individuals described by the
table.
Note: Percents are often more informative than counts,
especially when comparing groups of different sizes.
To examine a marginal distribution,
1)Use the data in the table to calculate the marginal
distribution (in percents) of the row or column totals.
2)Make a graph to display the marginal distribution.
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Tables and Marginal Distributions
Analyzing Categorical Data
 Two-Way
Examine the marginal
distribution of chance
of getting rich.
Chance of being wealthy by age 30
Response
Percent
Almost no chance
194/4826 =
4.0%
Some chance
712/4826 =
14.8%
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Tables and Marginal Distributions
Analyzing Categorical Data
 Two-Way
35
30
A good chance
Almost certain
1416/4826 =
29.3%
1421/4826 =
29.4%
1083/4826 =
22.4%
Percent
25
A 50-50 chance
20
15
10
5
0
Almost none
Some chance
50-50 chance
Survey Response
Good chance
Almost certain
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Check Your Understanding page 14

Marginal distributions tell us nothing about the relationship
between two variables.
Response
Percent
Almost no chance
194/4826 =
4.0%
Some chance
712/4826 =
14.8%
A 50-50 chance
1416/4826 =
29.3%
A good chance
1421/4826 =
29.4%
Almost certain
1083/4826 =
22.4%
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Between Categorical Variables
Analyzing Categorical Data
 Relationships

Marginal distributions tell us nothing about the relationship
between two variables.
Definition:
A Conditional Distribution of a variable
describes the values of that variable among
individuals who have a specific value of
another variable.
To examine or compare conditional distributions,
1)Select the row(s) or column(s) of interest.
2)Use the data in the table to calculate the conditional
distribution (in percents) of the row(s) or column(s).
3)Make a graph to display the conditional distribution.
• Use a side-by-side bar graph or segmented bar
graph to compare distributions.
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Between Categorical Variables
Analyzing Categorical Data
 Relationships
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Tables and Conditional Distributions
Analyzing Categorical Data
 Two-Way
Calculate the conditional
distribution of opinion
among males.
Examine the relationship
between gender and
opinion.
Chance
by
age
Chanceofofbeing
being wealthy
wealthy
by
age
303030
Chance
being
wealthy
by
age
100%
Response
Male
Female
Almost no chance
98/2459 =
4.0%
96/2367 =
4.1%
286/2459 =
11.6%
426/2367 =35
18.0% 30
720/2459 =
29.3%
696/2367 =
20
29.4% 15
758/2459 =
30.8%
663/2367 =10
28.0% 5
A 50-50 chance
A good chance
Almost certain
597/2459 =
24.3%
80%
Percent
Percent
Percent
Some chance
90%
25
15
486/2367 =
20.5%
0
70%
60%
50%
40%
Almost no
chance
Some chance
30%
50-50 chance
20%
Almost no chance
Almost
chance
Male
Some chance
Some
chance
50-50 chance
50-50
chance
10%
0%
Males
Females
Good chance
Good
chance
Good chance
s
Males
Almost
certain
Femal
es
Almost certain
Almost
certain
Can we say there I san
association between gender
and opinion in the population
of young adults?
Making this determination
requires formal inference,
which will have to wait a few
chapters.
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Tables and Conditional Distributions
Analyzing Categorical Data
 Two-Way
No association mean the conditional distributions of opinion about becoming
rich would be the same for males and females.
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Check Your Understanding page 18
12, 19, 21
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Section 1.1 Homework, pages 20 - 24