Calculator Input
Paste binary data with one subject per row. Use spaces, commas, tabs, or semicolons between values.
Example Data Table
This sample uses eight matched subjects measured across four related treatments.
| Subject | Method A | Method B | Method C | Method D |
|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 0 |
| 2 | 1 | 0 | 1 | 0 |
| 3 | 1 | 1 | 1 | 1 |
| 4 | 0 | 0 | 1 | 0 |
| 5 | 1 | 0 | 0 | 0 |
| 6 | 0 | 1 | 1 | 0 |
| 7 | 1 | 1 | 0 | 0 |
| 8 | 0 | 0 | 1 | 1 |
Formula Used
Cochran Q tests whether related treatments share the same success proportion when each matched subject produces only binary outcomes.
Q = (k - 1) × [k × Σ(Cj2) - T2] ÷ [k × T - Σ(Ri2)]
- k = number of related treatments.
- Cj = success total for treatment j.
- Ri = success total for subject i.
- T = overall number of successes in the full matrix.
- The p value is approximated from a chi-square distribution with k - 1 degrees of freedom.
How to Use This Calculator
- Enter a dataset name to keep exports identifiable.
- List treatment labels in the same order as your matrix columns.
- Paste one matched subject per row with only 0 and 1 values.
- Choose the significance level and preferred decimal places.
- Enable pairwise follow up when you want adjusted post hoc checks.
- Press the test button to show results below the header.
- Review the decision, treatment rates, and optional pairwise output.
- Use the CSV or PDF buttons to export the computed summary.
Frequently Asked Questions
1. What does Cochran Q test measure?
It tests whether three or more related treatments have the same success proportion when each subject contributes matched binary outcomes such as yes or no, pass or fail, or detected or not detected.
2. When should I use this calculator?
Use it for repeated measures or matched designs with binary responses, especially when the same participants, cases, or items are evaluated under several related conditions.
3. What input format does the matrix require?
Each row must represent one subject, each column one treatment, and every cell must contain only 0 or 1. Rows must all have the same column count.
4. Why does the calculator reject some datasets?
The test needs at least three treatments, matched subjects, binary values, and enough within-subject variation. Datasets with constant patterns or inconsistent row lengths cannot produce a valid statistic.
5. How is the p value computed?
The page calculates Cochran Q, then uses the chi-square approximation with degrees of freedom equal to the number of treatments minus one.
6. What are the optional pairwise results?
They run McNemar-style comparisons between treatment pairs, apply Bonferroni adjustment to alpha, and help identify where the overall difference may exist after a significant Q test.
7. Can I use this for nonbinary data?
No. Cochran Q is specifically designed for binary outcomes. Ordinal, count, continuous, or multicategory responses need different statistical procedures.
8. What should I report with my results?
Report the number of subjects, number of treatments, Q statistic, degrees of freedom, p value, alpha, and a clear statement about whether treatment proportions differ.