Cochran’s Q test

When to consider it

• Compare marginal binary proportions over three or more repeated conditions.

Assumptions and scope

• Rows are subjects and columns repeated 0/1 conditions; subjects must be independent.
• Approximate chi-square inference; small samples need caution. Follow-up paired comparisons require multiplicity adjustment.

Required inputs

• Subjects × binary conditions — 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

Rows are independent subjects and columns are at least three repeated binary conditions (0/1). Tests equal marginal proportions using a chi-square approximation. Small samples need caution; pairwise follow-up requires multiplicity adjustment. Synthetic example: 60 simulated subjects in three conditions.

• statsmodels 0.14.4: statsmodels.stats.contingency_tables.cochrans_q

These are pinned library versions; saved results record the versions actually used at runtime.

Library references

• SciPy statistical methods
• statsmodels models and statistical tests
• scikit-learn clustering
• lifelines survival comparisons