Chi-Square Goodness of Fit Test
This test determines whether observed frequencies match expected frequencies based on a theoretical distribution (e.g., equal proportions, Mendelian ratios).
When to Use
- Testing if data follows a specific distribution
- Comparing observed to theoretically expected proportions
- One categorical variable with multiple levels
Examples
- Testing Mendelian inheritance ratios (3:1, 9:3:3:1)
- Checking if die is fair (equal 1/6 for each face)
- Testing equal preferences across categories
Null Hypothesis
H₀: Observed frequencies match expected frequencies
Assumptions and fitted parameters
Observations must be independent counts in mutually exclusive categories. Expected counts must be positive and sum to the observed total. Small counts can make the chi-square approximation unreliable.
With probabilities specified in advance, degrees of freedom are categories − 1. For regular models fitted by efficient maximum likelihood to these observations, subtract the number of fitted parameters. The calculator supports this adjustment, but other estimation methods and category selection can require a different null distribution. See the SciPy explanation of assumptions and degrees of freedom.
