# chi-squared distribution

**chi-squared distribution** An important probability distribution with many uses in statistical analysis. Denoted by the Greek symbol χ^{2}, it is the distribution of the sum of squares of *f* independent random variables, each being drawn from the normal distribution with zero mean and unit variance. The integer *f* is the number of degrees of freedom. Critical values of the probability distribution are widely available in tables, but exact calculations involve the incomplete gamma function. The most common applications are (a) testing for interactions between different classifications of data using contingency tables;(b) testing goodness-of-fit;(c) forming confidence intervals for estimates of variance.

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