Chapter 4: Displaying and Describing Categorical Data

Displaying and Describing Categorical Data

The Three Rules of Data Analysis

• Make a picture (visual representation) to reveal things not seen in tables of numbers
• Show important features and patterns in the data
• Provide an excellent means to report findings to others

Frequency Tables

• Organize data by recording counts and category names
• Categories are labeled in each row of the frequency table
• May lump values together in an "Other" category if there are too many

Relative Frequency Tables

• Display proportions or percentages of the total that lie in each category
• Examples: Table 4.2 shows percentages of Loblaw stores in eastern Canada

Charts

Bar Charts

• Display the distribution of a categorical variable, showing counts for each category
• Observe the area principle: the area occupied by a part of the graph corresponds to the magnitude of the value it represents
• May be drawn in vertical columns or horizontally
• Examples: Figure 4.4 shows the number of Loblaw stores by province in eastern Canada

Pie Charts

• Show the whole group as a circle ("pie") sliced into pieces
• The size of each piece is proportional to the fraction of the whole in each category
• Example: Figure 4.4 shows the number of Loblaw stores by province in eastern Canada

Before Making a Bar Chart or Pie Chart

• Ensure everything adds up to 100% (e.g., 100% of Loblaw stores in Canada)
• Check that categories don't overlap (e.g., no store is in both "Ontario" and "Other" categories)
• Consider what you want to communicate about the data and choose the proper method

Exploring Two Categorical Variables: Contingency Tables

What a Contingency Table Shows

• How the values of one variable are contingent on the value of another variable
• Example: Table 4.3 shows responses to using social networking sites in five countries

Marginal Distributions

• The marginal distribution of a variable is a frequency or relative frequency distribution of either the row or column variable
• Row and column totals of the contingency table provide the marginal distributions

Conditional Distributions

• Restrict variables in a distribution to show the distribution for just those cases that satisfy a specified condition
• Example: Table 4.6 shows the conditional distribution of Social Networking conditioned on two values of Country

Segmented (or Stacked) Bar Charts

• Treat each bar as the "whole" and divide it proportionally into segments corresponding to the percentage in each group
• Example: Figure 4.6 shows the distribution of responses to the question for men and women

Simpson's Paradox

• Results from inappropriately combining percentages of different groups
• Example: Table 4.7 shows the success rates of Peter and Katrina in selling different products

What Can Go Wrong?

• Violate the area principle in charts
• Keep it honest: avoid confusing percentages and ensure the scale of data is consistent
• Don't confuse percentages or forget to look at variables separately
• Use enough individuals or cases in gathering data and providing results
• Don't overstate your case or use unfair or inappropriate percentages
• Be aware of Simpson's Paradox when combining percentages of different groups