Use the chi-square distribution in tests of statistical significance to:
Test how well a sample fits a theoretical distribution. For example, you can use a chi-square goodness-of-fit test to determine whether your sample data fit a Poisson distribution.
Test the independence between categorical variables. For example, a manufacturer wants to know if the occurrence of four types of defects (missing pin, broken clamp, loose fastener, and leaky seal) is related to shift (day, evening, overnight).
The chi-square distribution is a continuous distribution defined by the degrees of freedom and the noncentrality parameter. The distribution is positively skewed, but skewness decreases with more degrees of freedom.