Chi-square test of independence
Hypothesis tests · Method and input reference
Nonnegative integer counts. Fisher and McNemar require 2×2. McNemar uses the exact binomial test for paired binary outcomes. Synthetic example: Three treatment groups by response category (complete, partial, none); cells contain counts, not participant rows.
Open calculator · Compare methods in the decision matrix
When to consider it
- Test association between categorical variables using an independent-samples contingency table.
Assumptions and scope
- Observations must be independent between subjects; repeated rows from one subject are not independent samples.
- Review expected cell counts; Fisher’s exact is available for sparse 2×2 tables. Sparse larger tables need methods outside this calculator.
Required inputs
- Observed count matrix — Numeric observations; preserve the row and column structure described above.
Review missing values and data coding before running. Sample inputs are synthetic teaching examples.
Implementation
Lifescio validates inputs and formats results; listed functions are the principal calculation routines, not an exhaustive transitive dependency list.
- scipy 1.15.3: scipy.stats.chi2_contingency
These are pinned library versions; saved results record the versions actually used at runtime.