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

Learn how to analyze and visualize categorical data using charts and tables, and understand the three rules of data analysis. Discover how to effectively use bar and pie charts to reveal important features in data.