---
title: "Cross-tabulation (contingency table)"
method_id: SM.DSC.FRQ.BIV.CROSSTAB
family: Descriptive
version: 1.1.0
date_modified: 2026-06-18
canonical: https://clarus.ofrencber.com/library/crosstabulation.md
source: Clarus method library
---

# Cross-tabulation (contingency table)

> A classical statistical method in the Clarus library (Descriptive family).
> Clarus selects, assumption-checks and runs this method on your data with a
> deterministic rule engine and real numerical libraries (scipy / statsmodels);
> it never generates numbers, citations or results.

**Also known as:** contingency table; crosstab; two-way frequency table; r x c count table; joint frequency table.

## When to use it

Use this method when your goal is to:
- summarize joint distribution of two categoricals
- build contingency table
- describe counts and percentages across two factors
- pre step for chi square independence

## Data it expects

- **dependent:** not_applicable (purely descriptive — no outcome is modelled)
- **independent:** 2 nominal/ordinal variables (each observation falls into exactly one cell)
- **pairing:** independent (each observation contributes to exactly one cell)

## Assumptions

_not applicable._ Cross-tabulation makes no distributional or design assumptions — it only counts and re-expresses observations as percentages. There is no executable assumption gate (no normality, variance, independence-of-observations test) because no inference is performed. The expected-frequency and independence-of-observations assumptions belong to the chi-square sibling (SM.DIF.CAT.RXC.CHI2IND), not to the descriptive table.

## Honest limitations

- A cross-tabulation describes the sample; it does NOT test whether the two variables are related. For that, run the chi-square test of independence (SM.DIF.CAT.RXC.CHI2IND).
- The same table looks different depending on the percentage base — always state whether percentages are by row, by column, or of the grand total.
- Percentages computed over small cell counts are unstable; read the raw counts alongside them.
- An apparent pattern in the table is descriptive only and is never evidence of causation.
- Tables with many categories become unreadable; merging rare categories improves clarity but should be reported.
- Results describe only the sampled data and do not generalise to a wider population without an inferential test.

## Primary sources

- Pearson, K. (1900). On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philosophical Magazine, 50(302), 157-175. https://doi.org/10.1080/14786440009463897
- Yule, G. U. (1900). On the association of attributes in statistics. Philosophical Transactions of the Royal Society A, 194, 257-319. https://doi.org/10.1098/rsta.1900.0019
- Agresti, A. (2013). Categorical Data Analysis (3rd ed.). Wiley, Ch. 2-3 (contingency tables, marginal and conditional distributions).
- Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics (4th ed.), Ch. 18 (crosstabulating categorical data).
- pandas development team. pandas.crosstab — API reference (computing two-way frequency and percentage tables with margins and normalize).

## How to cite this

To cite this Clarus method page (the page itself — for the method's own primary sources, see above):

**Plain text**

Clarus, "Cross-tabulation (contingency table)", version 1.1.0, Clarus method library, 2026. https://clarus.ofrencber.com/library/crosstabulation.md

**APA**

Clarus. (2026). Cross-tabulation (contingency table) (Version 1.1.0) [Statistical method, Clarus method library]. Retrieved from https://clarus.ofrencber.com/library/crosstabulation.md

**BibTeX**

```bibtex
@misc{clarus-crosstabulation,
  author       = {Clarus},
  title        = {Cross-tabulation (contingency table)},
  howpublished = {Clarus method library},
  version      = {1.1.0},
  year         = {2026},
  url          = {https://clarus.ofrencber.com/library/crosstabulation.md}
}
```

_No DOI is minted for Clarus method pages yet; this citation uses the canonical URL, version and date. Cite the primary sources above for the method's scientific provenance._

---

METHOD SM.DSC.FRQ.BIV.CROSSTAB · VERSION 1.1.0 · UPDATED 2026-06-18 · SOURCE Clarus method library