Chi-Square Goodness-of-Fit Calculator
Calculate the chi-square (χ²) statistic and degrees of freedom for a goodness-of-fit test, comparing observed frequencies to expected frequencies.
About the Chi-Square Goodness-of-Fit Calculator
The chi-square goodness-of-fit test checks whether a set of observed category counts is consistent with a set of expected counts — such as testing whether a die is fair, or whether survey responses match an assumed distribution.
Formula: χ² = ∑ (O − E)² ÷ E, where O is each observed frequency and E is the corresponding expected frequency · Degrees of freedom = Number of Categories − 1
Enter matching lists of observed and expected counts to get the χ² statistic and its degrees of freedom. A larger χ² value means the observed data deviates more from what was expected; compare it against a chi-square critical value for the calculated degrees of freedom and your chosen significance level to decide whether the difference is statistically significant. This test assumes categories are independent and expected counts are reasonably large (typically at least 5) for the approximation to be reliable.