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Project 03-03-04: Multivariate Frequency Tables & Mosaic Plots

What This Project Covers

This mini-project explores how to describe relationships between two or more qualitative (categorical) attributes using cross-tabulation and mosaic plots. It is part of Chapter 3 — Descriptive Multivariate Analysis.

Concepts Demonstrated

Concept Description
Joint frequency table 2D cross-tabulation: rows = values of attribute A, columns = values of attribute B, cells = co-occurrence counts
Joint relative frequency Each cell count divided by the grand total n; measures how common each combination is overall
Marginal frequencies Row totals and column totals; the 1D distribution of each attribute ignoring the other
Conditional frequencies P(B = v
3-way frequency table Extends cross-tabulation to three qualitative attributes: a nested dict / 3D array of counts
Mosaic plot Visual representation of a 2D (or 3D) cross-tabulation: column width proportional to the marginal frequency of the column variable; segment height within each column proportional to the conditional frequency of the row variable given that column value

Dataset

The Friends dataset (n = 14) records three qualitative attributes for each friend:

  • Gender — M or F
  • Company — Good or Bad
  • Food_pref — Meat, Mixed, or Vegetarian

All analyses use this dataset as a worked example.

Files

File Language Purpose
joint_frequency_mosaic.py Python 3 (stdlib only) Full analysis with ASCII tables and ASCII mosaic plot
joint_frequency_mosaic.R R (base only) Same analysis using table(), prop.table(), and mosaicplot()
project_README.md Markdown This file

How to Run

Python

python joint_frequency_mosaic.py

The script runs the demo automatically. To analyse your own CSV file:

python joint_frequency_mosaic.py your_data.csv

You will be prompted to select which columns to use as attribute A and B. A third column can optionally be chosen for a 3-way table.

Requirements: Python 3.x, standard library only (no pip installs needed).

R

Rscript joint_frequency_mosaic.R

Or open the file in RStudio and run it section by section.

Requirements: Base R (no additional packages needed). Graphical windows will open for each mosaic plot.

Expected Output

Python

Running python joint_frequency_mosaic.py prints to the terminal:

  1. Absolute joint frequency table for Gender x Company with row/column totals
  2. Relative joint frequency table (fractions summing to 1)
  3. Conditional frequency table P(Company | Gender) as percentages (each row sums to 100%)
  4. ASCII mosaic plot for Gender x Company — columns sized by Company marginal, segments by conditional Gender
  5. Absolute joint frequency table for Gender x Food_pref
  6. ASCII mosaic plot for Gender x Food_pref
  7. 3-way frequency table Gender x Company x Food_pref (one sub-table per Gender value)

Example snippet of the absolute Gender x Company table:

  [Absolute Joint Frequency Table]  Gender x Company
Gender x Company | Bad  | Good | Total
-----------------+------+------+------
F                | 5    | 1    | 6
M                | 2    | 6    | 8
-----------------+------+------+------
Total            | 7    | 7    | 14

Example snippet of the ASCII mosaic (Gender x Company):

  MOSAIC: Gender x Company
  ====================================================
  |##################################################|                    |
  |##################################################|                    |
  ...
  |##################################################|----------|  F (42.9%)
  |--------------------------------------------------|----------|
  ...
                     Bad              Good

R

Running the R script prints the same tables to the console and opens graphical mosaic plots:

  1. table() absolute counts for Gender x Company with addmargins()
  2. prop.table() relative and conditional frequencies
  3. Mosaic plot window: Gender x Company (base R mosaicplot())
  4. Tables for Gender x Food_pref
  5. Mosaic plot window: Gender x Food_pref
  6. ftable() for the 3-way Gender x Company x Food_pref table
  7. Mosaic plot window: 3-way mosaic

Key Takeaways

  • A joint frequency table is the foundation for all multivariate categorical analysis.
  • Marginal frequencies collapse the joint table to a single attribute, recovering the 1D distribution.
  • Conditional frequencies reveal whether and how the distribution of one attribute shifts across levels of another — this is the first step toward detecting association.
  • A mosaic plot makes the joint and conditional structure visible at a glance: if all column segments have the same relative heights, the two attributes are independent; unequal heights indicate association.
  • Extending to three attributes (3-way table / 3-way mosaic) allows detection of interaction effects — whether the relationship between two attributes changes depending on the value of a third.