Exploring Categorical Data

Comic Characters

• 15,182 comic characters from DC and Marvel comics

• 11 variables, including

  • name
  • identity (id) gives information about personal identity (e.g., identity is kept secret)
  • alignment (align) gives information about whether character is good, bad, etc

CSV Data Files

• In J Lab 1 we learned how to import data from a CSV file into Jamovi
• The comics data set is also saved in a CSV file
• Let’s download the file and explore it using a text editor
• We can also open it with Jamovi

• First 10 rows of the comics data

Describing categorical data

• We can summarize a single categorical variable using a frequency table
• Counts the number of observations for each level of the variable

• We can also calculate proportions for each of the levels

Visualizing categorical data

• We can use a bar plot to visualize categorical data

Bar plot showing frequencies of levels of identity variable

Summarizing two categorical variables

• A contingency table is a table that can be used to summarize two categorical variables
• Each value is a count of the number of times a variable outcome combination occurs
• Usually includes row and column totals as well (marginal totals)

• It is also useful to create contingency tables with proportions
• The simplest version is obtained by dividing each count by the grand total
• In this case values in table sum to 1

• What does the value 0.0299 mean?

Conditional proportions

• We can also create tables of conditional proportions than can be helpful to explore associations between the variables
• We need to decide whether the proportions should be conditioned on rows (divide counts by row totals) or columns (divide counts by colum totals)
• If conditioned on rows, proportions sum to 1 along rows
• If conditioned on columns, proportions sum to 1 along columns

• These proportions are conditioned on rows (alignment)
• Allows us to compare proportions of identity types between different alignment groups
• For example, we can see that about 63% of bad characters have secret identities whereas only about 41% of good characters have secret identities.

• These proportions are conditioned on columns (identity)
• Allows us to compare proportions of alignment types between different identity groups
• For example, we can see that about 57% characters with secret identities are bad, whereas only about 32% of characters with secret identities are good.

Visualizing two categorical variables

• There are different ways to visualize two categorical variables using bar plots
• We can create stacked bar plot
• Colors show how composition varies within each group

Stacked bar plot showing alignment frequencies for different id levels

• We can also visualize the data using side-by-side (dodged) bar plots

Dodged bar plot showing alignment frequencies for different id levels

• Another alternative is to use faceted bar plots
• Facet according to one of the variables
• A facet (subplot) is created for each level of that variable

Faceted bar plot showing alignment frequencies for different id levels

• A fourth type of bar plot we can use to visualize two categorical variables is a standardized (filled) bar plot
• This shows conditional proportions (instead of counts) in a stacked format
• The following proportions are conditioned on id

Standardized bar plot showing alignment proportions for different id levels

• We can take a different perspective by exchanging the roles of the variables
• The following proportions are conditioned on align

Standardized bar plot showing id proportions for different alignment levels