Multinomial Test

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

• See: Null Hypothesis, Likelihood Ratio Test, Statistical Test, Nonparametric Statistics, Categorical Data, Pearson's Chi-Squared Test, Binomial Test.

---

---

References

2016

• (Wikipedia, 2016) ⇒ http://en.wikipedia.org/wiki/Multinomial_test 2016-08-13
  • 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 [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.

---