Transcript Slide 1

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Statistics
Chapter 1: Exploring Data
Section 1.1
Analyzing Categorical Data
The Practice of Statistics, 4th edition - For AP*
STARNES, YATES, MOORE
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Chapter 1
Exploring Data
 Introduction:
Data Analysis: Making Sense of Data
 1.1
Analyzing Categorical Data
 1.2
Displaying Quantitative Data with Graphs
 1.3
Describing Quantitative Data with Numbers
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Section 1.1
Analyzing Categorical Data
Learning Objectives
After this section, you should be able to…

CONSTRUCT and INTERPRET bar graphs and pie charts
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RECOGNIZE “good” and “bad” graphs
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CONSTRUCT and INTERPRET two-way tables
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DESCRIBE relationships between two categorical variables
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ORGANIZE statistical problems
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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
14.6
Rock
869
Rock
Count
6.3
Spanish Language
750
Other Formats
Total
1579
13838
7.7
Spanish Language
Percent
5.4
Other Formats
11.4
Total
99.9
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
is is easier to analyze a distribution by displaying it
with a bar graph or pie chart.
Frequency Table
Format
Relative Frequency Table
Count of
Format
Count of Stations
Stations
Percent of
Percent ofStations
Stations
2500Adult Contemporary
1556
Adult Contemporary
2000Adult Standards
1196
Adult Standards
1500Contemporary Hit
Country
1000
569
2066
11%
11%
Contemporary
Hit
5%
6%
News/Talk
Oldies
1060
Oldies
Religious
2014
8%
Religious
Country
9%
Country
2179
0
8.6
Contemporary hit
News/Talk
500
Adult
11.2
Contemporary
Adult Standards
14.9
4%
News/Talk
Oldies
15%
15%
16%
4.1
15.7
Religious7.7
Rock
14.6
Rock
869
Rock
Spanish 6.3
Spanish Language
750
Spanish Language
Other
Other Formats
Total
1579
13838
5.4
Other Formats
11.4
Total
99.9
Analyzing Categorical Data
 Displaying
Statistics
Alternate Example
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What Personal Media Do You Own?
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Here are the percent of 15-18 year olds that own the following personal
media devices, according to the Kaiser Family Foundation:
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Device
Percent who Own
Cell Phone
85%
MP3 Player
83%
Handheld Video
Game Player
41%
Laptop
38%
Portable CD/
Tape Player
20%
Problem:
 (a) Make a well-labeled bar graph to display the data. Describe what you see.
 (b) Would it be appropriate to make a pie chart for these data? Why or why not?
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Practice
Good and Bad
Our eyes react to the area of the bars as well as
height. Be sure to make your bars equally wide.
Avoid the temptation to replace the bars with pictures
for greater appeal…this can be misleading!
Alternate Example
Statistics
This ad for DIRECTV
has multiple problems.
How many can you
point out?
Analyzing Categorical Data
Bar graphs compare several quantities by comparing
the heights of bars that represent those quantities.
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 Graphs:
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Section 1.1
Analyzing Categorical Data
Practice Problems
p. 22-24 #11, 13, 15, 17
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.
Example, p. 12
Young adults by gender and chance of getting rich
Female
Male
Total
Almost no chance
96
98
194
Some chance, but probably not
426
286
712
A 50-50 chance
696
720
1416
A good chance
663
758
1421
Almost certain
486
597
1083
Total
2367
2459
4826
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
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Tables and Marginal Distributions
Example, p. 13
Young adults by gender and chance of getting rich
Female
Male
Total
Almost no chance
96
98
194
Some chance, but probably not
426
286
712
A 50-50 chance
696
720
1416
A good chance
663
758
1421
Almost certain
486
597
1083
Total
2367
2459
4826
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%
i.e. Calculate the
percentage of each
response out of the Total
Chance of being wealthy by age 30
This is the
4%marginal
of respondents
35 answered
distribution
of survey
“Almost
30
25
response.
20 None”
Percent
Response
Examine the marginal
distribution of chance
of getting rich.
15
10
5
0
Make a graph to
display theAlmost
marginal
Some
distribution none chance
50-50
chance
Survey Response
Good
chance
Almost
certain
Analyzing Categorical Data
 Two-Way
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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
Example, p. 15
Young adults by gender and chance of getting rich
Female
Male
Total
Almost no chance
96
98
194
Some chance, but probably not
426
286
712
A 50-50 chance
696
720
1416
A good chance
663
758
1421
Almost certain
486
597
1083
Total
2367
2459
4826
Male
Female
Almost no chance
98/2459 =
4.0%
96/2367 =
4.1%
286/2459 =
11.6%
426/2367 =
18.0%
720/2459 =
29.3%
696/2367 =
29.4%
A good chance
758/2459 =
30.8%
663/2367 =
28.0%
Almost certain
597/2459 =
24.3%
486/2367 =
20.5%
Some chance
A 50-50 chance
This
Thisisisaasegmented
side-by-side
bar
(orgraph.
double) bar graph.
Chance
of
byage
age
30
Chance
ofofbeing
being
by
age
Chance
being wealthy
wealthy by
3030
This100%
is the conditional
90%
35
3580%
distribution
of survey
30
3070%
25
25
20
2060%
response
because
15
1550%
10
the105050distribution
of
40%
Almost
50-50
Good
30%
Almost
no Some
Some on
50-50
Good
opinion
is nobased
chance
chance
20%chance
chance chance
chance chance
chance
10%
the other
variable
0%
(gender). Males Opinion
Females
Percent
Percent
Percent
Response
Calculate the conditional
distribution of opinion
among males.
Examine the relationship
between gender and
opinion.
Opinion
Opinion
Almost certain
Good chance
Males
Males
50-50 chance
Females
Some chance
Almost
Almost
certain
Almost no chance
certain
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Tables and Conditional Distributions
Analyzing Categorical Data
 Two-Way
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Is there a relationship between gender and income outlook?
Definition:
We say that there is an association between
two variables if specific values of one variable
tend to occur in common with specific values of
the other.
Based on the sample
data, men seem more
optimistic about their
future income than
women.
Percent
Chance of being wealthy by age 30
35
30
25
20
15
10
5
0
Males
Females
Almost no Some
chance chance
50-50
chance
Good
chance
Opinion
Almost
certain
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Between Categorical Variables
Analyzing Categorical Data
 Relationships
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a Statistical Problem
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As you learn more about statistics, you will be asked to solve
more complex problems.
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Here is a four-step process you can follow.
How to Organize a Statistical Problem: A Four-Step Process
State: What’s the question that you’re trying to answer?
Plan: How will you go about answering the question? What
statistical techniques does this problem call for?
Remember:
Analyzing Categorical Data
 Organizing
Do: Make graphs and carry out needed calculations. Statistics Problems
Demand Consistency
Conclude: Give your practical conclusion in the setting of the
real-world problem.
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Section 1.1
Analyzing Categorical Data
Practice
p. 24-26
#19, 21, 23
Homework
Homework Expectations:
 Loose-Leaf Paper
 Heading
 Legible & Organized
HW: Read Ch.5 & 6 from “How to Lie with Statistics” p. 62-75,
Textbook: p. 23-26 #14, 16, 18, 20, 22, 27-32, 36
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Section 1.1
Analyzing Categorical Data
Summary
In this section, we learned that…

The distribution of a categorical variable lists the categories and gives
the count or percent of individuals that fall into each category.

Pie charts and bar graphs display the distribution of a categorical
variable.

A two-way table of counts organizes data about two categorical
variables.

The row-totals and column-totals in a two-way table give the marginal
distributions of the two individual variables.
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There are two sets of conditional distributions for a two-way table.
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Section 1.1
Analyzing Categorical Data
Summary, continued
In this section, we learned that…

We can use a side-by-side bar graph or a segmented bar graph
to display conditional distributions.
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To describe the association between the row and column variables,
compare an appropriate set of conditional distributions.

Even a strong association between two categorical variables can be
influenced by other variables lurking in the background.

You can organize many problems using the four steps state, plan,
do, and conclude.
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Looking Ahead…
In the next Section…
We’ll learn how to display quantitative data.
Dotplots
Stemplots
Histograms
We’ll also learn how to describe and compare
distributions of quantitative data.