Calculator guide
Chi-square test calculator guide
The chi-square test calculator turns observed count data into a chi-square statistic, degrees of freedom, and p-value. It supports goodness-of-fit counts and contingency-table independence tests.
How to use this calculator
- Choose goodness-of-fit or independence test.
- For goodness-of-fit, enter observed and expected counts on each line.
- For independence, enter a contingency table with one row per category.
- Read the statistic, degrees of freedom, expected counts, and p-value.
How to interpret the result
Chi-square tests require count data, independent observations, and expected counts that are not too small. Combine sparse categories when needed before interpreting the result.
Before treating it as evidence
The chi-square test output is part of an inference workflow. That means the setup matters as much as the arithmetic. Identify the null value, confidence level, tail direction, degrees of freedom, or expected counts before entering anything. Then Choose goodness-of-fit or independence test. For goodness-of-fit, enter observed and expected counts on each line. If those choices are made after seeing the answer, the result can look more convincing than it really is.
The key calculation is χ2 = Σ(observed - expected)2 / expected. Keep the hypotheses or interval target beside the formula so the final number has a direction. A p-value answers a different question from a confidence interval, and a critical value answers a different question from an observed statistic. Mixing those roles is one of the fastest ways to misread the calculator output.
Chi-square tests require count data, independent observations, and expected counts that are not too small. Combine sparse categories when needed before interpreting the result. Report the result with the assumptions that support it, especially independence, sample size, expected-count rules, or the chosen alternative hypothesis. If the question changes from one sample to two samples, or from a test to an interval, use chi-square distribution, p-value from t and confidence interval rather than recycling the wrong setup. When do I use goodness-of-fit? Use it to compare observed counts across categories with expected counts from a theory or known distribution.