Tests for the parameters of a Multinomial distributionTests for the parameters of a multinomial distribution and their properties and assumptions.

Test	Purpose
Pearson X²	Tests if the proportions are equal to the hypothesized values. Uses the score statistic and computes an asymptotic p-value.
Likelihood ratio G²	Tests if the proportions are equal to the hypothesized values. Uses the likelihood ratio statistic and computes an asymptotic p-value. Pearson X² usually converges to the chi-squared distribution more quickly than G². The likelihood ratio test is commonly used in statistical modeling as the G² statistic is easier to compare between different models.

Test

Purpose

Pearson X²

Tests if the proportions are equal to the hypothesized values.

Uses the score statistic and computes an asymptotic p-value.

Likelihood ratio G²

Tests if the proportions are equal to the hypothesized values.

Uses the likelihood ratio statistic and computes an asymptotic p-value.

Pearson X² usually converges to the chi-squared distribution more quickly than G². The likelihood ratio test is commonly used in statistical modeling as the G² statistic is easier to compare between different models.

Related concepts

Multinomial distribution parameters hypothesis test

Testing normality and what to do

Choosing a statistical test

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