Chi-Square Distribution

A chi-square random variable is defined as the sum of squares of independently distributed standard normal random variables, which explains the additive property of independent chi-square random variables. Its probability distribution is described by a gamma probability density. The chi-square goodness-of-fit statistic, when sample size is large, is approximately a chi-square random variable. Tests of hypotheses relating to contingency tables are also based on a statistic with approximate chi-square distribution. Keywords: chi-square distribution; chi-square statistic; hypothesis testing; goodness-of-fit; contingency table