Chi-square (χ2) distribution

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.
Chi-square distribution with 20 degrees of freedom
Chi-square distribution with 40 degrees of freedom

When the degrees of freedom are 30 or more, the distribution can be approximated by a normal distribution.

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