Chi-Square Test

Analyze associations between categorical variables.

Definition

The Chi-square test (χ²) tests the independence between two categorical variables. It compares observed frequencies to theoretical frequencies expected under the independence hypothesis. StatsLab also offers Fisher's exact test for small samples.

When to use it

• Test the association between two nominal or ordinal variables
• Analyze a contingency table
• Compare proportions between independent groups

Requirements

• Categorical variables (nominal or ordinal)
• Expected frequency ≥ 5 in 80% of cells
• Fisher's test recommended if n < 20 or any cell < 5

What StatsLab computes

• χ² statistic and p-value
• Fisher's exact test (p-value)
• Cramér's V — effect size
• Contingency table with observed and expected frequencies
• Standardized residuals
• Grouped bar chart

Worked example

Context : Association between sex (M/F) and sport preference (Yes/No) in 120 people.

Result : χ²(1) = 6.8, p = 0.009, V = 0.24

Interpretation : Significant association (p < 0.05) between sex and sport practice. The moderate effect size (V = 0.24) indicates a real but non-deterministic association.

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