For categorical variable testing, we have chi-square test. For example, we want to test if a dice is fair (assuming sample has
But from the previous post, the testing results are sensitive to the magnitudes of counts, say test statistic of
[600,600,600,600,600,600] is different from that of
[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?