Statistics
Chi-Square Calculator
Assess how well observed counts agree with expected counts using the chi-square goodness-of-fit test.
chi-squaregoodness of fitcategorical
Chi-square Goodness of Fit
Enter observed counts and expected counts to test distribution fit.
Chi-square statistic
1.1111
Degrees of freedom
2
p-value
0.573753
Chi-square statistic
χ² = Σ (Oᵢ − Eᵢ)² / Eᵢ
The calculator also reports the degrees of freedom (categories − 1) and the corresponding right-tail p-value.
How to use
- Enter observed counts and matching expected counts.
- Ensure expected counts are positive and align with observed categories.
- Review χ², degrees of freedom, and the p-value.
Example
Input: Observed = 50,45,40; Expected = 45,45,45
Output: χ² ≈ 2.778, df = 2, p ≈ 0.249
FAQ & notes
Can I test contingency tables?
This calculator handles goodness-of-fit tests. For contingency tables, flatten the observed counts and compute expected frequencies first.
What if expected counts are zero?
Chi-square requires all expected counts to be positive. Combine categories or use Fisher’s exact test if counts are too small.