Multinomial Test

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A Multinomial Test is a statistical testing of the null hypothesis that states the multinomial distribution parameters equal specified values.



References

2016

We begin with a sample of [math]\displaystyle{ N }[/math] items each of which has been observed to fall into one of [math]\displaystyle{ k }[/math] categories. We can define [math]\displaystyle{ \mathbf{x} = (x_1, x_2, \dots, x_k) }[/math] as the observed numbers of items in each cell. Hence [math]\displaystyle{ \textstyle \sum_{i=1}^k x_{i} = N }[/math]. Next, we define a vector of parameters [math]\displaystyle{ H_0: \mathbf{\pi} = (\pi_{1}, \pi_{2}, \dots, \pi_{k}) }[/math], where [math]\displaystyle{ \textstyle \sum_{i=1}^k \pi_{i} = 1 }[/math] These are the parameter values under the null hypothesis.