Categorical data

Visualizations and contingency tables

2025-09-22

Housekeeping

  • Problem set 2 due tonight! Please be sure to submit both written and rendered parts by combining into a single PDF
  • Problem set 1 graded

Categorical data

  • Recall that a variable is either numerical or categorical

  • Categorical variables are variables that can take one of a limited (usually fixed) number of possible values, known as levels

    • Represent data that can be divided into groups

  • Two types:

    • Ordinal: the levels have a special ordering

    • Nominal: the levels don’t have an ordering

      • We almost exclusively treat categorical variables as nominal in this class

  • Example:

    • Blood type (A, B, AB, O)

    • Education level (high school, college, graduate degree, other)

Insurance data

Univariate EDA

If we are interested in understanding the distribution of a single categorical variable, it is common to:

Display a frequency table, which is a table of counts of each level

# A tibble: 2 × 2
  smoker     n
  <chr>  <int>
1 no       155
2 yes       45

Create a bar plot, where different levels are displayed on one axis and the counts are portrayed on the other

Bivariate EDA

  • Perhaps we are interested in examining the distribution of two categorical variables at the same time

  • Summarize the distribution using a two-way table known as a contingency table:

    • Each value in the table counts the number of times a particular combination of variable 1 and variable 2 levels occurred in data

      Contingency table
      smoker female male
      no 87 68
      yes 17 28

  • How can we use contingency table to obtain the distribution of just one of the variables?

Dodged bar plot

The dodged bar plot directly converts the contingency table to a visualization.

Contingency table
smoker female male
no 87 68
yes 17 28

Stacked bar plot

The stacked bar plot looks at the counts either row-wise or column-wise.

Contingency table
smoker female male
no 87 68
yes 17 28

Proportions

Can convert the contingency table to proportions row-wise or column-wise to obtain the fractional breakdown of one variable in another.

Contingency table
smoker female male
no 87 68
yes 17 28
Row-wise proportions
smoker female male
no 0.561 0.439
yes 0.378 0.622
  • What does the quantity 0.378 represent?
  • If we take the proportions row-wise, does each row need to sum to 1?
  • If we take the proportions row-wise, does each column need to sum to 1?

Proportions (cont.)

Set up how to find the column-wise proportions using our contingency table

Contingency table
smoker female male
no 87 68
yes 17 28

Standardized bar plot

The standardized bar plot visualizes these row-wise or column-wise proportions.

Choosing a bar plot

  • Using any of the plots, do you believe the smoker status and sex are associated?
  • When might you prefer to use the stacked, dodged, or standardized bar plot?

Live code

  • Bar plots
  • Aesthetics: fill, shape
  • Faceting
  • Plot background

Bar plot (univariate)

ggplot(data = insurance, mapping = aes(x = smoker)) +
  geom_bar()

Note: if your data are already in the form of frequency table, we should use geom_col() instead!

Bivariate bar plots

ggplot(insurance, aes(x = smoker, fill = sex)) +
  geom_bar(position = "dodge")  

ggplot(insurance, aes(x = smoker, fill = sex)) +
  geom_bar(position = "stack") # this is default

Bivariate bar plots (cont.)

ggplot(insurance, aes(x = smoker, fill = sex)) +
  geom_bar(position = "fill")

How might we make the bars horizontal instead of vertical?

Visualizing numerical and categorical

ggplot(data = insurance, mapping = aes(x = bmi, y = charges, col = smoker)) +
  geom_point()

What do you notice about the legend for color compared to the legend for color from last week?

Aesthetic: shape

ggplot(data = insurance, mapping = aes(x = bmi, y = charges, shape = smoker)) +
  geom_point()

facet_wrap()

Faceting is used when we want to split a particular visualization by the values of another (categorical) variable

ggplot(data = insurance, 
       mapping = aes(x = bmi)) +
  geom_histogram() +
  facet_wrap(~ smoker) 

ggplot(data = insurance, 
       mapping = aes(x = bmi)) +
  geom_histogram() +
  facet_wrap(~ smoker, scales = "free_y")

facet_grid()

ggplot(data = insurance, mapping = aes(x = bmi)) +
  geom_histogram() +
  facet_grid(sex ~ smoker)

Side-by-side box plots

ggplot(data = insurance, 
       mapping = aes(x = smoker, y = bmi)) +
  geom_boxplot()

Like faceting, but only for box plots. Really good for comparing a numerical variable across across a categorical!

Changing plot theme

Change the background of plots by adding on any one of the following:

  • theme_bw(), theme_minimal(), theme_gray(), theme_void() and a few more (see all options by checking the help file for any one of these)
ggplot(data = insurance, 
       mapping = aes(x = smoker, y = bmi)) +
  geom_boxplot() +
  theme_minimal()