Understand the hypothesis test
What an omnibus test can—and cannot—say
Cochran’s Q Test. An omnibus statistic asks whether all modeled groups, cells, conditions, or spreads follow one joint null statement.
1Partition or compare variation2Scale by null-model uncertainty3Use planned follow-up for location
Test statistic and reference model
Q=(k−1)[kΣCj²−T²]/[kT−ΣRi²], approximately χ²(k−1).
A significant omnibus result identifies some difference, not which condition pairs differ.
Responsible interpretation
A small p-value says that some modeled difference exists; it does not identify which comparisons differ. Follow-up work needs multiplicity control and effect estimates.
Required assumption: Rows are independent subjects, columns are related conditions, entries are zero or one, and follow-up comparisons need multiplicity control.
Quick guide
How to use this calculator
- Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
- Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
- Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.
Calculation method
How the cochran’s q test calculator works
Q=(k−1)[kΣCj²−T²]/[kT−ΣRi²], approximately χ²(k−1).
A significant omnibus result identifies some difference, not which condition pairs differ.
Worked example
Cochran’s Q Test example
Binary condition columns entered per subject test whether marginal success rates differ.
Q=(k−1)[kΣCj²−T²]/[kT−ΣRi²], approximately χ²(k−1).
Supported inputs
Precision and limits
Model and design
Rows are independent subjects, columns are related conditions, entries are zero or one, and follow-up comparisons need multiplicity control.
Input scope
Category lists accept up to 10,000 nonblank observations and render up to 200 distinct labels. Matching trims outer whitespace but remains case-sensitive; no numeric ordering or distance is inferred.
Interpretation
A significant omnibus result identifies some difference, not which condition pairs differ.
Decision boundary
The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.
Privacy
Entered values and calculated results stay in this browser and are not sent to an analytics service.
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