Chi-Square Calculator

This tool runs a Pearson chi-square test in two forms: goodness of fit against an expected distribution, and a test of independence on a contingency table of up to four rows. Enter the counts and it returns the chi-square statistic, the degrees of freedom, the p value, the 0.05 critical value and the expected values behind them. The statistic and the degrees of freedom are exact arithmetic, while the p value has no closed form and is computed numerically from the incomplete gamma function. Expected values below five are flagged, since the chi-square approximation weakens there.