Section 11 Analyzing Categorical Data The Practice of Statistics 4 th edition For AP STARNES YATES MOORE Chapter 1 Exploring Data Introduction Data Analysis Making Sense of Data ID: 650402
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Slide1
Chapter 1: Exploring Data
Section 1.1Analyzing Categorical Data
The Practice of Statistics, 4
th
edition - For AP*
STARNES, YATES, MOORESlide2
Chapter 1Exploring DataIntroduction: Data Analysis: Making Sense of Data1.1 Analyzing Categorical Data1.2 Displaying Quantitative Data with Graphs1.3
Describing Quantitative Data with NumbersSlide3
Section 1.1Analyzing Categorical DataAfter this section, you should be able to…CONSTRUCT and INTERPRET bar graphs and pie chartsRECOGNIZE “good” and “bad” graphsCONSTRUCT and INTERPRET two-way tablesDESCRIBE relationships between two categorical variables
ORGANIZE statistical problemsLearning ObjectivesSlide4
Analyzing Categorical DataCategorical Variables place individuals into one of several groups or categoriesThe values of a categorical variable are labels for the different categoriesThe distribution of a categorical variable lists the count or percent of individuals who fall into each category.
Frequency TableFormatCount of Stations
Adult Contemporary
1556
Adult Standards
1196
Contemporary Hit
569
Country
2066
News/Talk2179Oldies1060Religious2014Rock869Spanish Language750Other Formats1579Total13838
Relative Frequency TableFormatPercent of StationsAdult Contemporary11.2Adult Standards8.6Contemporary Hit4.1Country14.9News/Talk15.7Oldies7.7Religious14.6Rock6.3Spanish Language5.4Other Formats11.4Total99.9
Example, page 8
Count
Percent
Variable
ValuesSlide5
Analyzing Categorical DataDisplaying categorical dataFrequency 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 TableFormat
Count of Stations
Adult Contemporary
1556
Adult Standards
1196
Contemporary Hit
569
Country
2066News/Talk2179Oldies1060Religious2014Rock869Spanish Language750Other Formats1579Total
13838Relative Frequency TableFormatPercent of StationsAdult Contemporary11.2Adult Standards8.6Contemporary Hit4.1Country14.9News/Talk15.7Oldies7.7Religious14.6Rock6.3Spanish Language5.4Other Formats11.4Total
99.9Slide6
Ex: What personal media do you own? DevicePercent who OwnCell Phone85%MP3 Player
83%Handheld Video Game Player41%Laptop38%Portable CD/Tape Player20%
What Personal Media Do You Own?
Here are the percent of 15-18 year olds that own the following personal media devices, according to the Kaiser Family Foundation:
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?Slide7
Analyzing Categorical DataBar graphs compare several quantities by comparing the heights of bars that represent those quantities.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!
Graphs: Good and Bad
Alternate Example
This ad for DIRECTV has multiple problems. How many can you point out?Slide8
HomeworkLet’s stop for now. Homework:Textbook page 22Problems:10-18 (even)Slide9
Analyzing Categorical DataTwo-Way Tables and Marginal DistributionsWhen 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.
Young adults by gender and chance of getting rich
Female
Male
Total
Almost no chance
96
98
194
Some chance, but probably not426286712A 50-50 chance6967201416A good chance6637581421Almost certain486
5971083Total236724594826Example, p. 12What are the variables described by this two-way table?How many young adults were surveyed?Slide10
Ex: Superpowers FemaleMaleTotalInvisibility
171330Super Strength31720Telepathy39
5
44
Fly
36
18
54
Freeze Time
20
3252Total11585200Super PowersA sample of 200 children from the United Kingdom ages 9-17 was selected from the CensusAtSchool website (www.censusatschool.com). The gender of each student was recorded along with which super power they would most like to have: invisibility, super strength, telepathy (ability to read minds), ability to fly, or ability to freeze time. Here are the results:What is the row variable?What is the column variable?What two categorical variables are represented by this two-way table? Slide11
Analyzing Categorical DataTwo-Way Tables and Marginal Distributions
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,
Use the data in the table to calculate the marginal distribution (in percents) of the row or column totals.
Make a graph to display the marginal distribution.Slide12
Young adults by gender and chance of getting rich
FemaleMale
Total
Almost no chance
96
98
194
Some chance, but probably not
426
286
712A 50-50 chance6967201416A good chance6637581421Almost certain4865971083Total2367
24594826Analyzing Categorical DataTwo-Way Tables and Marginal DistributionsResponsePercentAlmost no chance194/4826 = 4.0%Some chance712/4826 = 14.8%A 50-50 chance1416/4826 = 29.3%A good chance1421/4826 = 29.4%Almost certain1083/4826 = 22.4%Example, p. 13Examine the marginal distribution of chance of getting rich.Slide13
Ex. Superpowers FemaleMaleTotalInvisibility
171330Super Strength31720Telepathy39
5
44
Fly
36
18
54
Freeze Time
20
3252Total11585200Super PowersA sample of 200 children from the United Kingdom ages 9-17 was selected from theCensusAtSchool website (www.censusatschool.com). The gender of each student was recorded along with which super power they would most like to have: invisibility,super strength, telepathy (ability to read minds), ability to fly, or ability to freeze time. Here are the results:Use the data in the two-way table to calculate the marginal distribution (in percents) of superpower preferences. Make a graph to display the marginal distribution. Describe what you see. Slide14
Check your understanding1. Use the data in the two-way table on page 12 to calculate the marginal distribution (in percents) of gender.2. Make a graph to display the marginal distribution . Describe what you see. Slide15
Analyzing Categorical DataRelationships Between Categorical VariablesMarginal 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,
Select the row(s) or column(s) of interest.
Use the data in the table to calculate the conditional distribution (in percents) of the row(s) or column(s).
Make a graph to display the conditional distribution.
Use a
side-by-side bar graph
or
segmented bar graph
to compare distributions.Slide16
Young adults by gender and chance of getting rich
FemaleMale
Total
Almost no chance
96
98
194
Some chance, but probably not
426
286
712A 50-50 chance6967201416A good chance6637581421Almost certain4865971083Total2367
24594826Analyzing Categorical DataTwo-Way Tables and Conditional DistributionsResponseMaleAlmost no chance98/2459 = 4.0% Some chance286/2459 = 11.6%A 50-50 chance720/2459 = 29.3%A good chance758/2459 = 30.8%Almost certain597/2459 = 24.3%Example, p. 15Calculate the conditional distribution of opinion among males.Examine the relationship between gender and opinion.Female96/2367 = 4.1%426/2367 = 18.0%
696/2367 =
29.4%
663/2367 =
28.0%
486/2367 =
20.5%Slide17
Superpowers FemaleMaleTotalInvisibility
171330Super Strength31720Telepathy39
5
44
Fly
36
18
54
Freeze Time
20
3252Total11585200Super PowersA sample of 200 children from the United Kingdom ages 9-17 was selected from theCensusAtSchool website (www.censusatschool.com). The gender of each student was recorded along with which super power they would most like to have: invisibility, super strength, telepathy (ability to read minds), ability to fly, or ability to freeze time. Here are the results:Calculate the conditional distribution of responses for the males and females. Slide18
Check your understanding Find the conditional distributions of gender among each of the other four opinion categories (book did “almost certain” on pg 16). Use figure 1.5 or 1.6 to check that your answers are approximately correct. Slide19
Analyzing Categorical DataOrganizing a Statistical ProblemAs you learn more about statistics, you will be asked to solve more complex problems.Here is a four-step process you can follow.
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?Do: Make graphs and carry out needed calculations.Conclude: Give your practical conclusion in the setting of the real-world problem.
How to Organize a Statistical Problem: A Four-Step ProcessSlide20
Superpowers FemaleMaleTotalInvisibility
171330Super Strength31720Telepathy39
5
44
Fly
36
18
54
Freeze Time
20
3252Total11585200Super PowersA sample of 200 children from the United Kingdom ages 9-17 was selected from the CensusAtSchool website (www.censusatschool.com). The gender of each student was recorded along with which super power they would most like to have: invisibility, super strength, telepathy (ability to read minds), ability to fly, or ability to freeze time. Here are the results:Based on the survey data, can we conclude that boys and girls differ in their preference of superpower? Give appropriate evidence to support your answer. State:Plan:Do:Conclude:Slide21
Section 1.1Analyzing Categorical DataIn 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.There are two sets of conditional distributions for a two-way table.SummarySlide22
Section 1.1Analyzing Categorical DataIn this section, we learned that…We can use a side-by-side bar graph or a segmented bar graph to display conditional distributions.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.Summary, continuedSlide23
Looking Ahead…
We’ll learn how to display quantitative data.DotplotsStemplotsHistogramsWe’ll also learn how to describe and compare distributions of quantitative data.
In the next Section…Slide24
Homework
Problems:19, 21, 23, 25, 27-32
Textbook
pg
23