# Are there statistical tests for testing multiple sample proportion?

For categorical variable testing, we have chi-square test. For example, we want to test if a dice is fair (assuming sample has [6,5,7,7,6,5] and [6,6,6,6,6,6]).

But from the previous post, the testing results are sensitive to the magnitudes of counts, say test statistic of [600,500,700,700,600,500] and [600,600,600,600,600,600] is different from that of [6,5,7,7,6,5] and [6,6,6,6,6,6]. Furthermore, if two independent samples have different sizes, chi-square test will be subtle too.

My question is whether there exists multiple categorical proportional testing, which is an extension of single proportion testing?

For example, we test [1/6, 5/36, 7/36, 7/36, 1/6, 5/36] and [1/6,1/6,1/6,1/6,1/6, 1/6]. In this case we don't worry about data magnitude and unequal sample size.

Can we just naively have individual proportion test 1/6 = 1/6, 5/36 = 1/6, 7/36=1/6, ...., and once all null hypotheses are right, the sample is from the population? Is it Chi-Square Test of Homogeneity?

• The extension is called the chi-squared test. – whuber Jan 11 '19 at 20:14
• It is typically approached by the chi-squared goodness-of-fit test. – Michael M Jan 11 '19 at 21:25