Chi-Square Goodness of Fit

Summary

Enter observed and expected category counts to compute the chi-square statistic, degrees of freedom, and p-value for a goodness-of-fit test.

How it works

1. Choose the number of categories (2 to 10).
2. Enter a label, the observed count, and the expected count or proportion for each category.
3. Select whether your expected values are counts or proportions; the tool normalizes proportions to the grand total automatically.
4. Click "Run Test" — the tool calculates the chi-square statistic as the sum of (observed - expected)^2 / expected across all categories.
5. Degrees of freedom equal the number of categories minus 1 (minus any estimated parameters if applicable).
6. The p-value is derived from the chi-square distribution; compare it to your chosen significance level.

Use cases

• Test whether a six-sided die is fair by comparing roll frequencies to a uniform distribution.
• Check whether customer complaint categories match historical proportions.
• Validate whether website traffic follows a predicted day-of-week pattern.
• Test whether genetic phenotype ratios fit a Mendelian 3:1 ratio.
• Evaluate whether survey response distributions match prior-year benchmarks.
• Determine if observed color preferences match a theorized distribution.

Frequently Asked Questions