A chi-square test compares observed counts with counts expected under a categorical model. Goodness-of-fit and independence tests use different table structures, while adequate expected frequencies, independent observations, mutually exclusive categories, and appropriate degrees of freedom are central assumptions.
Chi-Square Test Calculator applies this concept to its defined inputs and workflow. It evaluates count data only after Calculate Chi-Square is clicked and warns about approximation assumptions.
The calculator evaluates observed counts and contingency table and returns chi-square statistic, p-value, and residuals using the stated method. Input structure, labels, missing values, and selected options must match the intended workflow. Users should interpret the output within the assumptions shown on the page and repeat the check with trusted reference values when the result affects engineering or research decisions. Small expected counts can make the approximation unreliable.