Examples
Examples
Try the starting example
- Observed counts
- 10,20
- Expected counts
- 15,15
- Chi-square statistic
- 3.333333
- Degrees of freedom
- 1
- Upper-tail p-value
- 0.067889
Try another scenario
- Observed counts
- 8,22
- Expected counts
- 15,15
- Chi-square statistic
- 6.533333
- Degrees of freedom
- 1
- Upper-tail p-value
- 0.010587
Calculation method
Calculation method
Chi-square statistic
Sum (observed−expected)²/expected across categories; expected totals must equal observed totals.
Degrees of freedom
Number of categories minus one, assuming no parameters were fitted to these observations.
Upper-tail p-value
Upper-tail chi-square probability Q(df/2, statistic/2).
Symbols and units
- a
- Observed counts
- b
- Expected counts
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- Reports the chi-square statistic, degrees of freedom and an upper-tail p-value. Expected counts must have the same total; fitted-parameter adjustments are not included. Lists support up to 1,000 finite values. The p-value uses an asymptotic chi-square model with fixed expected proportions and no fitted parameters; sparse expected counts can make the approximation unreliable.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
Background reading; this does not imply endorsement or independent review of SumFizz.