Cross-tabulation

What it does

Builds a two-way table with row, column and total percentages, and an optional chi-square test.

Use it to compare how one category is distributed across another.

Data you need

• Two categorical variables

Supported data: Categorical. Level: Beginner.

Formula and method

E = (row total × column total) / n · χ² = Σ(O−E)² / E

Rows are counted into every combination of the two variables. Percentages are then taken along rows, columns and the whole table. Expected counts come from the margins and feed an optional Pearson chi-square test.

How to read the result

Compare row percentages across columns to see where groups differ.

Worked example

Illustrative run on Simulated study data (teaching data). These figures are the actual output of this model on that example, and they say nothing about your own data.

• 240 observations; chi-square = 4.8282, df = 2, p = 0.0894, Cramer's V = 0.1418.
• The association is not statistically significant at the 5% level.

Limitations

• Association does not establish causation

Numerical validation

Validated 16 of 16 automated checks passed, including numerical results, invalid input, missing values, small samples, constant variables, charts and the interpretation text.

Computed with python 3.13.2, numpy 2.2.5, scipy 1.14.1, pandas 2.3.3, statsmodels 0.14.4, scikit-learn 1.7.0, in your browser. A passing check confirms the listed comparison only. It does not make any result suitable for your data, and it is not a claim of equivalence with other statistical software.

Questions

Which percentage should I read?

Use row percentages when the row variable is the group being compared, and column percentages when the column variable is.