# Chi-square distribution

 related topics {math, number, function} {rate, high, increase} {household, population, female}

In probability theory and statistics, the chi-square distribution (also chi-squared or χ²-distribution) with k degrees of freedom is the distribution of a sum of the squares of k independent standard normal random variables. It is one of the most widely used probability distributions in inferential statistics, e.g. in hypothesis testing, or in construction of confidence intervals.[2][3][4][5] When there is a need to contrast it with the noncentral chi-square distribution, this distribution is sometimes called the central chi-square distribution.

The best-known situations in which the chi-square distribution is used are the common chi-square tests for goodness of fit of an observed distribution to a theoretical one, and of the independence of two criteria of classification of qualitative data, and a third well known use is the confidence interval estimation for a population standard deviation of a normal distribution from a sample standard deviation. Many other statistical tests also lead to a use of this distribution, like Friedman's analysis of variance by ranks.

The chi-square distribution is a special case of the gamma distribution.