*The chi-square statistic for testing hypotheses concerning multinomial distributions derives its name from the asymptotic approximation to its distribution. Two important applications are the testing of independence in a two-way classification and the testing of goodness-of-fit. In the second application the multinomial distribution is created artificially by grouping the data, and the asymptotic chi-square approximation may be lost if the original data are used to estimate nuisance parameters*.

The *chi-square distribution* with *k* degrees of freedom is (by definition) the distribution of for i.i.d. *N*(0, 1)-distributed variables *Z*_{1},..., *Z*_{k}. The sum of squares is the squared norm ...

Start Free Trial

No credit card required