Chi-Square Goodness-of-Fit Test
Enter your observed counts and the expected counts under the null distribution. The test statistic χ² = Σ (O − E)²/E is compared against the chi-square distribution with df = k − 1, giving the p-value and the reject / fail-to-reject conclusion at your chosen α.
Frequently asked questions
What does the null hypothesis say?
That the observed counts are consistent with the expected distribution — i.e. the proposed model fits the data.
How small can the expected counts be?
A common rule of thumb is that every expected count should be at least 5; otherwise the chi-square approximation degrades and an exact test is preferred.
How are degrees of freedom set?
For a basic goodness-of-fit test, df = k − 1, where k is the number of categories. If you estimate parameters from the data, subtract one further degree of freedom per estimated parameter.