stb1e_ppt_ch03
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Describing Categorical Data
Chapter 3
3.1 Looking At Data
Which hosts send the most visitors to Amazon’s Web site?
Data set consists of 188,996 visits
Host is a categorical variable
To answer this question we must describe the variation in Host
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3.1 Looking At Data
Frequency and Relative Frequency Tables
The distribution of a categorical variable is a list of values with its associated count (frequency)
A frequency table summarizes the distribution of a categorical variable
A relative frequency table shows the proportion (or percentage) in each category
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3.1 Looking At Data
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3.2 Charts of Categorical Data
Bar Charts and Pie Charts
Unless you need to know exact counts, charts are better than tables for summarizing more than five categories
The two most common displays of a categorical variable are a bar chart and a pie chart
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3.2 Charts of Categorical Data
The Bar Chart
Uses horizontal or vertical bars to show the distribution of a categorical variable
Is called a Pareto chart when the categories are sorted by frequency (popular in quality control)
Becomes cluttered with too many categories
Is appropriate for ordinal categorical variables
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3.2 Charts of Categorical Data
Bar Chart (Horizontal) of Top 10 Hosts
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3.2 Charts of Categorical Data
Bar Chart (Vertical) of Top 10 Hosts
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3.2 Charts of Categorical Data
The Pie Chart
Uses wedges of a circle to show the distribution of a categorical variable
Commonly chosen to illustrate market shares or sources of revenue for a company
Less useful than bar charts if we want to compare actual counts (easier to compare bars than angles of wedges)
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3.2 Charts of Categorical Data
Pie Chart of Top 10 Hosts
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3.3 The Area Principle
The Fundamental Rule for Data Displays
The area occupied by a part of the graph/chart that displays data should be proportional to the amount of data it represents
Charts decorated to attract attention often violate the area principle
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3.3 The Area Principle
An Example Violating the Area Principle
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3.3 The Area Principle
The Same Example Respecting the Area Principle
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4M Example 3.1: ROLLING OVER
Motivation
Are certain types of vehicles more prone to roll-over accidents than others?
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4M Example 3.1: ROLLING OVER
Method
Data gathered from Fatality Analysis Reporting System (FARS) for roll-over accidents on interstate highways. Cases that make up the rows are accidents resulting in roll-overs in 2000. The column of interest is model of the car involved.
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4M Example 3.1: ROLLING OVER
Mechanics
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4M Example 3.1: ROLLING OVER
Mechanics
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4M Example 3.1: ROLLING OVER
Message
Ford Broncos were involved in more than twice as many roll-over accidents as the next-closest model.
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4M Example 3.2: CHIP SALES
Motivation
Infineon pled guilty to price fixing for DRAM’s in September 2004. Did Infineon gain a larger share of the market for chips during this period?
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4M Example 3.2: CHIP SALES
Method
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4M Example 3.2: CHIP SALES
Mechanics
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4M Example 3.2: CHIP SALES
Message
Infineon and Samsung increased their shares from 1999 to 2002. It appears to have been at the expense of smaller companies.
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3.4 Mode and Median
Mode
Category with the highest frequency
The longest bar in a bar chart
The widest slice in a pie chart
Two or more categories can tie with the highest frequency (bimodal or multimodal)
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3.4 Mode and Median
Median
Not appropriate for nominal data
Data must be ordinal
It is the category label of the middle observation in ordered data
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Best Practices
Use a bar chart to show the frequencies of a categorical variable.
Use a pie chart to show the proportions of a categorical variable.
Preserve the ordering of an ordinal variable.
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Best Practices (Continued)
Respect the area principle.
Show the best plots to answer the motivating question.
Label your chart to show the categories and indicate whether some have been combined or omitted.
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Pitfalls
Avoid elaborate plots that may be deceptive.
Do not show too many categories.
Do not put ordinal data in a pie chart.
Do not carelessly round data.
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