Counting Categorical Data

Categorical Data

We will be working with the survey data from the beginning of the semester.

Download the data and set it up in your coding environment.

library(tidyverse)

survey <- read_csv("data/student-data.csv")

Counting variables

We can use the count() function to count how many of each value (level) we have in a categorical variable.

survey |>
  count(eye_color)

Contingency Tables

When we count how many observations across two categorical variables, we are creating a cross-tab, cross-tabulation, or a contingency table.

• table that displays the frequency distribution of multiple variables
• shows how two or more categorical variables relate to each other
• commonly used in statistics for analyzing relationships between categorical data

Contingency Tables

survey |>
  count(personality, eye_color)

Contingency Tables

survey |>
  count(personality, eye_color) |>
  pivot_wider(names_from = personality, values_from = n)

Each cell shows the count (frequency) of individuals that fall into both categories.

Contingency Tables

From contingency tables, we can:

• Calculate proportions and percentages
• Perform statistical tests like chi-square tests to determine if there’s a significant relationship between variables
• Identify patterns or trends in categorical data
• Compute measures of association

Bar plot

A bar plot is a common way to display a single categorical variable.

survey |>
  ggplot(aes(x = eye_color)) +
  geom_bar()

Proportions

We can combine group_by(), summarize(), and mutate() to get proportions

survey |>
  group_by(eye_color) |>
  summarize(n = n()) |>
  mutate(total = sum(n),
         percent = n/total)

Relative Frequency Bar Plot

A bar plot where proportions instead of frequencies are shown is called a relative frequency bar plot.

survey |>
  group_by(eye_color) |>
  summarize(n = n()) |>
  mutate(total = sum(n),
         percent = n/total) |>
  ggplot(aes(x = eye_color, y = percent)) +
  geom_col()

How are bar plots different than histograms?

• Bar plots are used for displaying distributions of categorical variables, while histograms are used for numerical variables.
• The x-axis in a histogram is a number line, hence the order of the bars cannot be changed
• In a bar plot the categories can be listed in any order (though some orderings make more sense than others, especially for ordinal variables)

Ordering a bar plot

survey |>
  group_by(eye_color) |>
  summarize(n = n()) |>
  ggplot(aes(x = reorder(eye_color, -n), y = n)) +
  geom_col() +
  labs(x = "eye color")

Proportions in contingency tables

What is the personality split for each eye color?

survey |>
  group_by(eye_color, personality) |>
  summarize(n = n()) |>
  mutate(total = sum(n),
         percent = n/total)

Proportions in contingency tables

What’s the eye color proportion for each personality?

survey |>
  group_by(personality, eye_color) |>
  summarize(n = n()) |>
  mutate(total = sum(n),
         percent = n/total)

Bar plots with two variables

What’s the eye color proportion for each personality?

survey |>
  group_by(personality, eye_color) |>
  summarize(n = n()) |>
  mutate(total = sum(n),
         percent = n/total) |>
  ggplot(aes(x = personality, y = n, fill = eye_color)) +
  geom_col()

Bar plots with two variables

What’s the eye color proportion for each personality?

survey |>
  group_by(personality, eye_color) |>
  summarize(n = n()) |>
  mutate(total = sum(n),
         percent = n/total) |>
  ggplot(aes(x = personality, y = n, fill = eye_color)) +
  geom_col(position = "dodge")

Bar plots with two variables

What’s the eye color proportion for each personality?

survey |>
  group_by(personality, eye_color) |>
  summarize(n = n()) |>
  mutate(total = sum(n),
         percent = n/total) |>
  ggplot(aes(x = personality, y = n, fill = eye_color)) +
  geom_col(position = "fill")

Practice

What other questions can you answer with this data?

• Create contingency tables
• Create bar plots based on your tables

Gradescope activity

Go to gradescope and click on summarizing data and answer the questions about the survey data we have been working on