Descriptive Statistics for Categorical Data in R: Contingency Tables

Summarise categorical data — frequency and contingency tables, proportions and margins — and visualize them with bar, pie and mosaic plots

Learn to summarise categorical data in R — build one-way frequency tables and two-way (and multi-way) contingency tables with table() and xtabs(), add proportions and margins with prop.table() and addmargins(), and visualize the counts with bar charts, pie/donut charts, balloon plots and mosaic plots. The first step before any categorical test.

TipKey takeaways

• Categorical data are summarised by counting — frequency tables (one variable) and contingency tables (two or more variables cross-tabulated).
• Build them with base R: table() or xtabs(); add proportions with prop.table() and row / column / grand totals with addmargins().
• Visualize counts with bar charts (incl. grouped / stacked), pie / donut charts, balloon plots and mosaic plots.
• This is the first step before any categorical test (chi-square, Fisher, …) — it shows you the shape of the table before you test it.

Introduction

Before testing categorical data, describe it: how many observations fall into each category, and how the categories of two variables cross-classify. The summaries are counts — a one-way frequency table for a single variable, and a two-way (or multi-way) contingency table for several. This lesson builds them with base R and visualizes them, using the built-in Titanic survival data (titanic.raw).

One categorical variable: frequency table

table() counts each category; wrap it in prop.table() for proportions:

data("titanic.raw", package = "datarium")

table(titanic.raw$Survived)                 # counts

  No  Yes 
1490  711 

round(prop.table(table(titanic.raw$Survived)), 2)   # proportions

  No  Yes 
0.68 0.32 

About 32% of the 2201 people survived.

Two variables: a contingency table

Cross-tabulate two variables with table() or xtabs() — here survival by passenger class:

data("titanic.raw", package = "datarium")

tab <- xtabs(~ Class + Survived, data = titanic.raw)
tab

      Survived
Class   No Yes
  1st  122 203
  2nd  167 118
  3rd  528 178
  Crew 673 212

Add margins (row / column / grand totals) and proportions:

data("titanic.raw", package = "datarium")
tab <- xtabs(~ Class + Survived, data = titanic.raw)

addmargins(tab)                       # totals

      Survived
Class    No  Yes  Sum
  1st   122  203  325
  2nd   167  118  285
  3rd   528  178  706
  Crew  673  212  885
  Sum  1490  711 2201

round(prop.table(tab, margin = 1), 2) # row proportions (survival rate within each class)

      Survived
Class    No  Yes
  1st  0.38 0.62
  2nd  0.59 0.41
  3rd  0.75 0.25
  Crew 0.76 0.24

The row proportions are the survival rate within each class — first class ≈ 62%, crew ≈ 24%.

Multi-way tables

xtabs() and ftable() (flat tables) handle three or more variables — survival by class and sex:

data("titanic.raw", package = "datarium")

ftable(xtabs(~ Class + Sex + Survived, data = titanic.raw))

             Survived  No Yes
Class Sex                    
1st   Male            118  62
      Female            4 141
2nd   Male            154  25
      Female           13  93
3rd   Male            422  88
      Female          106  90
Crew  Male            670 192
      Female            3  20

Visualize the table

A bar chart of the counts, grouped by survival:

library(ggpubr)

data("titanic.raw", package = "datarium")
df <- as.data.frame(xtabs(~ Class + Survived, data = titanic.raw))

ggbarplot(df, x = "Class", y = "Freq", fill = "Survived", palette = "jco",
          position = position_dodge(0.8), ylab = "Count")

A balloon plot shows the whole table at a glance — dot size = count:

library(ggpubr)

data("titanic.raw", package = "datarium")
df <- as.data.frame(xtabs(~ Class + Survived, data = titanic.raw))

ggballoonplot(df, x = "Survived", y = "Class", size = "Freq", fill = "Freq") +
  gradient_fill(c("white", "#3a86d4"))

A mosaic plot (base R) shows proportions as tile areas — the width of each class reflects its size, the split shows its survival rate:

data("titanic.raw", package = "datarium")
tab <- xtabs(~ Class + Survived, data = titanic.raw)

mosaicplot(tab, color = c("#cccccc", "#3a86d4"), main = "Survival by class")

A pie or donut chart suits a single variable’s shares:

library(ggpubr)

data("titanic.raw", package = "datarium")
df <- as.data.frame(table(titanic.raw$Survived))
names(df) <- c("Survived", "n")

ggdonutchart(df, "n", label = "Survived", fill = "Survived", palette = "jco")

Try it live

Tabulate and plot a different pair of variables — survival by sex. The sandbox boots on first Run.

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Common issues

You want proportions but got counts. Wrap the table in prop.table(). Use margin = 1 for row proportions, margin = 2 for column proportions, and no margin for the overall proportions.

Your variable is numeric but really categorical. Convert it to a factor first (mydata$x <- factor(mydata$x)) so table() treats each value as a category.

A multi-way table is hard to read. Use ftable() to flatten it into a readable layout, or a mosaicplot() to see the proportions visually.

Frequently asked questions

NoteHow do I make a contingency table in R?

Use table(var1, var2) or xtabs(~ var1 + var2, data = mydata) to cross-tabulate two categorical variables into a contingency table of counts. Add prop.table() for proportions and addmargins() for row/column/grand totals.

NoteHow do I compute proportions or percentages from a table?

Wrap the table in prop.table(): with no margin you get the overall proportions; margin = 1 gives row proportions (each row sums to 1), margin = 2 gives column proportions. Multiply by 100 for percentages.

NoteWhat plot is best for categorical data?

A bar chart for comparing category counts (grouped or stacked for two variables), a pie/donut chart for one variable’s shares, a balloon plot to show a whole contingency table at a glance, and a mosaic plot to show proportions as areas. Choose by how many variables you’re showing.

Test your understanding

ImportantPractice

1. Run it. In the live cell, build the sex-by-survival table and the survival rate within each sex. Fill the blank. Which sex had the higher survival rate?
2. Conceptual. You want the survival rate within each class, not raw counts. Which prop.table() margin do you use?

NoteHint

Fill the blank with 1 for row proportions (rate within each sex). For question 2, the class is the row variable, so you want the same margin.

NoteSolution

tab <- xtabs(~ Sex + Survived, data = titanic.raw)
round(prop.table(tab, margin = 1), 2)   #> females had a much higher survival rate.

For question 2: use margin = 1 (row proportions) — with class as the row variable, this gives the survival rate within each class, which is what you want. margin = 2 would instead give, within survivors and non-survivors, the share from each class.

TipWhat’s next?

Once you’ve described the table, test it:

• Are two categorical variables associated? → chi-square test of independence (or Fisher’s exact test for small counts).
• Does one variable fit expected proportions? → chi-square goodness-of-fit.
• Risk in a 2×2 table? → odds ratio & relative risk.

Conclusion

You can now describe categorical data in R: build frequency and contingency tables with table() / xtabs(), add proportions (prop.table()) and margins (addmargins()), flatten multi-way tables with ftable(), and visualize with bar, pie/donut, balloon and mosaic plots. It is the first, essential step — the picture of the table you then take to a chi-square or other categorical test.

Related lessons

• Chi-square test of independence in R — test whether the two variables in your table are associated. · Descriptive statistics in R — the equivalent for continuous variables. · Odds ratio & relative risk in R — effect sizes from a 2×2 table.
• Go further: Categorical data analysis · Biostatistics

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