Statistics Calculator

Chi-Square Test Calculator

Perform chi-square test of independence for categorical data with contingency tables.

Rows:2

Columns:2

	Col 1	Col 2
Row 1
Row 2

Learning Guide

What is Chi-Square Test?

The chi-square test determines whether there is a statistically significant association between two categorical variables. It compares observed frequencies to expected frequencies.

Chi-Square Formula

χ² = Σ [(O - E)² / E]

O = Observed frequency
E = Expected frequency

Expected Frequencies

E = (Row Total × Column Total) / Grand Total

Degrees of Freedom

df = (rows - 1) × (columns - 1)

Interpretation

Large χ²: Greater difference between observed and expected
p-value < 0.05: Reject null hypothesis (significant association)
p-value ≥ 0.05: Fail to reject null (no significant association)

Assumptions

Random sampling
Independent observations
Expected frequency ≥ 5 in each cell (ideally)
Categorical data only

Applications

Marketing: Product preference by demographic
Medicine: Treatment effectiveness by group
Quality control: Defect rates across machines
Social science: Survey response analysis