Describing and Visualizing Categorical Variables

Introduction

• At ZPD, Deputy Chief Okonkwo drops by again: “Numbers are great, but I also need to know who’s where. Break the recruits down by group for me.”

• In the last lecture, we described continuous variables: things measured on a number line, like a score or an income.

• Today we will describe categorical variables: things that sort recruits into groups rather than measuring them on a scale.

  • There is no “average” district the way there is an average exam score.

R Set Up

library(tidyverse)
library(ssstats)
zootopia <- read_csv("https://raw.githubusercontent.com/samanthaseals/SDSI/refs/heads/main/files/data/lectures/1-zootopia.csv")

Describing Categorical Data

• We have two main tools for describing a categorical variable:

  • Frequency
  • Relative frequency (proportion)

Frequency

• Frequencies answer the question: how many?

  • How many recruits are in Patrol?
  • How many recruits work in Sahara Square?

• Frequencies are useful, but interpreting them depends on the size of the dataset.

Relative Frequency

\text{proportion} = \frac{\text{count in category}}{\text{total number of observations}}

• Proportions answer the question: what share?

  • What share of recruits are in Patrol?
  • What share of recruits work in Sahara Square?

• Because proportions are standardized, they allow us to compare groups of very different sizes.

Describing the Data (R)

• We will use the n_pct() function from the ssstats package to describe the frequency and proportion of our categorical data.

1dataset_name |>
2  n_pct(variable)

• Just like mean_median(), we can use group_by() to get counts and percentages broken down by another categorical variable.

• Note: if you need help getting started in R, please see the R module on Canvas.

Describing the Data

• For illustrative purposes, we will describe the department variable in the zootopia dataset.

zootopia |>
  n_pct(department)

• This tells us that of the 30 recruits,

  • 18 (60.0%) are in Patrol,
  • 12 (40.0%) are on Desk duty.

Bar Graphs

Bar Graphs (R)

1dataset_name |>
2  ggplot(aes(x = category_name)) +
3  geom_bar()

• Sometimes we’d rather show the share of recruits in each category instead of the raw count.

1dataset_name |>
  ggplot(aes(x = category_name, 
2             y = after_stat(count) / sum(after_stat(count)))) +
3  geom_bar() +
4  scale_y_continuous(labels = scales::percent)

Contingency Tables

• So far we’ve described one categorical variable at a time.

• Just like a scatterplot let us compare two continuous variables, a contingency table lets us compare two categorical variables.

  • Is department evenly split across every district, or do some districts lean more Patrol or more Desk?

Contingency Tables (R)

• We can construct a contingency table using n_pct().

1dataset_name |>
2  n_pct(row_variable, column_variable)

• Note that n_pct() automatically returns the column percentage.

Example 1

• Let’s describe the characteristics of the recruits in the zootopia dataset.

  • Department

  • District

  • Academy status

Example 1

• Constructing the frequency distribution for department,

zootopia %>% n_pct(department)

Example 1

• Constructing the frequency distribution for district,

zootopia %>% n_pct(district)

Example 1

• Constructing the frequency distribution for academy status,

zootopia %>% n_pct(academy_status)

Example 1

• Constructing contingency tables,

zootopia %>% n_pct(district, department)

Example 1

• Constructing contingency tables,

zootopia %>% n_pct(district, academy_status)

Example 1

• Constructing contingency tables,

zootopia %>% n_pct(department, academy_status)

Example 1

• Looking at this graphically,

Wrap Up

• We have covered basics for describing and visualizing categorical variables.

  • Frequencies and proportions
    • Contingency tables
  • Bar graphs