Multinomial test

In statistics, the multinomial test is the test of the null hypothesis that the parameters of a multinomial distribution equal specified values. It is used for categorical data; see Read and Cressie.

We begin with a sample of ${\displaystyle N}$ items each of which has been observed to fall into one of ${\displaystyle k}$ categories. We can define ${\displaystyle \mathbf {x} =(x_{1},x_{2},\dots ,x_{k})}$ as the observed numbers of items in each cell. Hence ${\displaystyle \textstyle \sum _{i=1}^{k}x_{i}=N}$.

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