Chi-Square Test Probability Formulas

Below you will find descriptions and details for the 3 formulas that are used to compute probabilities (p-values) for a chi-square test.

Cumulative distribution function (CDF) for the chi-square distribution:

Variable definitions:
γ(s, x) = lower incomplete gamma function
Γ(z) = gamma function

Gamma function:

Lower incomplete gamma function:

Variable definitions:
x = upper limit of integration
s = value of the shape parameter