How to Use the Chi-Square Statistic Calculator
When you want to check how far your observed data deviates from an expected distribution, the chi-square (χ²) goodness-of-fit test is the tool for the job. This calculator takes the observed and expected values for each category and automatically computes the chi-square statistic and degrees of freedom.
The formula sums (observed - expected)² ÷ expected across every category. For example, if you roll a die 60 times and compare how often each number actually came up (observed) against the theoretical expectation (expected, 10 each), you can check whether the die is fair.
A larger chi-square value means a bigger gap between observed and expected values. Combined with degrees of freedom (categories minus 1), you can look up a chi-square distribution table to determine whether that gap is statistically significant.
Frequently Asked Questions
Sum (observed - expected)² ÷ expected across all categories. A larger value means a bigger gap between observed and expected values.
For a goodness-of-fit test, degrees of freedom equals the number of categories minus 1. It's used with a chi-square distribution table to assess statistical significance.
Since the formula divides by the expected value, the chi-square statistic can't be calculated when it's 0.