Chi-Square GOF Calculator
Calculate chi-square goodness-of-fit statistic from observed vs expected counts.
Chi-Square Goodness-of-Fit Calculator tests whether observed categorical counts match an expected distribution. Observed counts are the frequencies actually collected, while expected counts come from a theory, historical ratio, model, or stated probability distribution. The chi-square statistic sums the squared differences between observed and expected counts after scaling by expected counts, so larger discrepancies contribute more evidence against the model. Degrees of freedom depend on the number of categories and any estimated parameters. The p-value describes how unusual the observed mismatch would be if the expected distribution were correct. This test is useful for categorical model checks, but expected counts should generally be large enough and observations should be independent.