What is the Chi-Square Goodness of Fit Calculator?

The Chi-Square Goodness of Fit Calculator is a statistical tool used to determine how well observed categorical data matches expected frequencies. By entering observed and expected values, the calculator computes the Chi-Square statistic (χ²) using the formula χ² = Σ((O − E)² / E), where O is the observed frequency and E is the expected frequency. It also displays the degrees of freedom (df), which equals the number of categories minus one. A higher χ² value indicates a greater difference between the observed and expected data, helping assess whether deviations are due to random chance or a significant effect. The tool also provides a detailed table showing each step of the calculation for transparency.

How to Use:

1. Enter Observed Frequencies (O): Input the counts of each category as a comma-separated list, e.g., 25, 30, 20, 25.
2. Enter Expected Frequencies (E): Input the expected counts for the same categories, e.g., 25, 25, 25, 25.
3. Click “Calculate”: The calculator computes the Chi-Square statistic (χ²), degrees of freedom, and shows a step-by-step calculation table.
4. Review the Result: The output shows χ², df, and a table with each category’s observed value, expected value, difference, squared difference, and the contribution of each term to χ².