ClarityHow to use this tool
- Enter observed counts, expected counts, significance level.
- Select Calculate to view the result.
- Check the method and assumptions below before using the result.
The method, explained
χ² = sum[(observed−expected)²/expected]. Degrees of freedom = categories−1; no model parameters may be estimated from these observations.
Using observed counts = 18, 22, 25, 15, expected counts = 20, 20, 20, 20, significance level = 0.05, the result is 0.407301567 probability. Change these example inputs to match your task; use the method above to check each step.
What to keep in mind
Categories are mutually exclusive. Expected counts must be specified independently of the observed data. Sparse categories need a different test or a justified combination. A descriptive or probability calculation under the stated assumptions. Check the sample design and model before interpreting results.
Reference: NIST: statistical methods handbook
Common questions
Should I enter expected percentages or counts?
Enter expected counts that add to the observed total. For example, an expected share of 25% in a sample of 80 corresponds to an expected count of 20.
Can expected counts be fitted from these same observations?
This page assumes a fully specified model and uses categories minus one degrees of freedom. If you estimate model parameters from the observations, this degrees-of-freedom rule is not appropriate.
Methodology maintained by ClarityKit. How these tools are built and checked.