Pearsons Chi-Squared Test

Pearson’s Test for Multinomial Data

Pearson’s chi-squared test is used for multinomial data. If has a multinomial distribution, then the MLE of is .

Let be some fixed vector and suppose we want to test

Definition

Pearson’s statistic is

where is the expected value of under .

Theorem

Under , . Hence the test: reject if has asymptotic level . The p-value is where is the observed value of the test statistic.

Sources

• Wasserman, L. (2010). All of Statistics: A concise Course in Statistical Inference. Chapter 10.4.